Research ArticleVibration Signal Forecasting on Rotating Machinery by means ofSignal Decomposition and Neurofuzzy Modeling

Daniel Zurita-Millaacuten1 Miguel Delgado-Prieto1 Juan Joseacute Saucedo-Dorantes2

Jesus Adolfo Carintildeo-Corrales1 Roque A Osornio-Rios2

Juan Antonio Ortega-Redondo1 and Rene de J Romero-Troncoso3

1MCIA Research Center Department of Electronic Engineering Technical University of Catalonia (UPC)Rambla San Nebridi No 22 Gaia Research Building 08222 Terrassa Spain2CA Mecatronica Facultad de Ingenieria Universidad Autonoma de Queretaro Campus San Juan del RioRio Moctezuma 249 Colonia San Cayetano 76807 San Juan del Rio QRO Mexico3CA Telematica DICIS Universidad de Guanajuato Carretera Salamanca-Valle km 35+18 Palo Blanco36885 Salamanca GTO Mexico

Correspondence should be addressed to Daniel Zurita-Millan danielzuritamciaupcedu

Received 6 May 2016 Revised 18 July 2016 Accepted 18 July 2016

Academic Editor Mario Terzo

Copyright copy 2016 Daniel Zurita-Millan et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Vibration monitoring plays a key role in the industrial machinery reliability since it allows enhancing the performance of themachinery under supervision through the detection of failure modes Thus vibration monitoring schemes that give informationregarding future condition that is prognosis approaches are of growing interest for the scientific and industrial communitiesThis work proposes a vibration signal prognosis methodology applied to a rotating electromechanical system and its associatedkinematic chainThemethod combines the adaptability of neurofuzzy modeling with a signal decomposition strategy to model thepatterns of the vibrations signal under different fault scenarios The model tuning is performed by means of Genetic Algorithmsalongwith a correlation based interval selection procedureTheperformance and effectiveness of the proposedmethod are validatedexperimentally with an electromechanical test bench containing a kinematic chain The results of the study indicate the suitabilityof the method for vibration forecasting in complex electromechanical systems and their associated kinematic chains

1 Introduction

Rotatingmachinery like compressors steam turbines indus-trial fans and so forth is widely used in many indus-trial fields Its reliability is an extensively investigated fieldaimed at prolonging their life span and minimizing theirmaintenance cost Maintenance programs try to avoid fatalbreakdowns of machines and prevent production loss andhuman casualties The early fault diagnosis is a challengingproblem and has received more and more attention in recentyears [1] In order to reduce maintenance costs and maintainmachine uptime at the highest possible level maintenanceshould be carried out in a proactive way That means atransformation of maintenance strategy from the traditionalfail-and-fix practices (diagnostics) to a predict-and-prevent

methodology (prognostics) [2]The current and future healthstatus of a machine component or system have to be knownin order to predict and prevent an eventual occurrence of afailure enabling the achievement of near-zero downtime per-formance

Vibration measurement is an effective nonintrusivemethod to monitor machine condition during start-upsshutdowns and normal operation [3] Vibration analysis isused on rotating equipment to determine the operating andoperation condition of the equipment A major advantageis that vibration analysis can identify developing problemsbefore they become too serious and cause unscheduleddowntime A majority of the mechanical faults such asdefective bearings mechanical looseness worn or brokengears misalignment and unbalance could be detected by

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 2683269 13 pageshttpdxdoiorg10115520162683269

2 Shock and Vibration

vibration analysis Vibration signals collected from thisequipment during operation contain valuable informationabout the equipment condition Great research effort hasbeen carried out for the development of several algorithmsfor faults detection anddiagnosis in rotatingmachinery basedon vibration monitoring [4] The most popular methods ofrotating machine condition monitoring utilize the steadystate spectral components of the vibration signals Thesespectral components of the vibration are used to diagnosefaults of rotating machinery and the energy of vibrationsignals in the frequency domain being the most commonlyused method to evaluate the severity of a fault

Nevertheless the vibration signal is often a complexsignal which contains stationary nonstationary and noisycomponents Therefore the appropriate signal processingtechniques have to be applied in order to compute numer-ical fault indicators or features [5] Features are parame-ters derived from the measured data that robustly indicatethe presence of faults in rotating machinery The majorfeature-calculation methods are time domain methods fre-quency domain methods and time-frequency methodsTime domain methods such as peak amplitude Root-Mean-Square amplitude crest factor kurtosis and shock pulsecounting have been successfully applied [6 7] Frequencydomain methods include Fourier spectra time waveformcepstrum analysis and the spectral envelope technique[8 9] A comparative study of various feature-calculationmethods in frequency domain such as the Fast FourierTransform (FFT) and spectral envelope and in the time-frequency domain such as the Short Time Fourier Transform(STFT) Wigner Ville and wavelet analysis is presented in[10 11]

Clearly the opportunity of conducting forecasting basedon vibrations presentsmultiple benefits (i) correct deviationsbefore they affect the correct behavior of the system (ii)anticipate the response towards failures and (iii) assist thediagnosis algorithm in order to assess the future condition ofthe system [12 13] Unfortunately little work has been donein the area with vibration forecasting and there is a lack ofmethodology to perform such approaches [14]Themodelingof the vibration as a physical magnitude is a complexprocess furthermore vibration in electromechanical systemsis affected by several factors such as multiple emissionsources mechanical properties operation condition How-ever the modeling of numerical features that characterizethe vibration is a more affordable problem since raw datapresents redundant or nonimportant information from theelectromechanical components degradation point of viewThis is the case when time domain features such as the Root-Mean-Square (RMS) value or kurtosis offer a more reliableview of the machine condition [15] As a result the temporalmodeling of features extracted from the vibration signal is amatter of interest for many researchers Therefore the utilityof a vibrationrsquos feature forecasting model relies on the earlydetection of deviations from the correct behavior as earlyas the model output is extended in the future The optimalscenario of such approaches is themodeling of the RMS valueof the vibrations during the start-up operation of themachinetill it reaches the thermal stability in order to indicate

the abnormal behaviors as soon as possible to minimize thedamage of operating under failure conditions

Consequently the forecasting of such vibration featuresignals can be approached from the time series modelingpoint of view Current modeling and forecasting techniquescan be categorized into three classes namely model-baseddata-driven and hybrid prognostics approaches [16] Model-based techniques describe the future evolution of the sys-tem based on the mathematical equations that describeits physical properties [17] Data-driven techniques takeadvantage of the past records to learn the system behaviorand conduct the predictions Hybrid techniques are a com-bination of model-based and data-driven techniques [18] Inthis regard Adaptive Neurofuzzy Inference System (ANFIS)represents a hybrid data-driven forecastingmethod that fusesthe parametric adaptability of ANN and the generalizationcapabilities of the fuzzy logic ANFIS offers a reliable androbust condition predictor since it can capture the systemdynamic behavior quickly and accurately [19]

When facing vibration forecasting the problem is howto decide for a given application the optimal forecastinghorizon and the configuration of the models In this regardvibration signals usually present faster or at least equaldynamics in comparison with other magnitudes inherent toan electromechanical system such as voltage electric currentand temperature Due to this fact the modeling problemshould be approached as a time series forecasting [20] Itis necessary to emphasize that the result of a forecastingmethod is critically associated with the forecasting horizonused to train and validate the models In many applica-tions the forecasting horizon is usually fixed by applicationrequirements ormodeling limitations [21] Yet the procedureto select the best horizon for a given application is notwell established in the literature For this reason this paperproposes performing a study relating the selected forecastinghorizon and the prediction error once the application isdefined In this regard three open issues can be found inliterature (i) the decision of the optimal prediction horizon(ii) the configuration of the models in terms of numberof inputs and past values to be considered and (iii) thedecomposition of the signal in different details in order toincrease accuracy

In this paper the authors propose a study in order tooptimize these three open issues to obtain a methodologyfor modeling the RMS of the vibrations from an electrome-chanical system and its associated kinematic chainThereforethe contributions of this work include a novel vibrationforecasting method that utilizes the theory behind vibrationsignature under electromechanical failures to decomposethe vibration signal in three frequency bands related to thevibration signature to enhance the forecasting accuracy andadaptability towards different dynamic contents Then thecore of the methodology consists of the generation of threecollaborative ANFIS models that are in charge of forecastingthe evolution of specific spectral content of the vibrationsignal The configuration of the model is optimized onestep beyond the literature by analyzing cross-correlationsbetween the signal and past instants which are selected byusing Genetic Algorithm (GA) optimization to find the best

Shock and Vibration 3

input configuration Complementarily the paper includesa systematic study of the forecasting horizon affectation ofthe model configuration step in order to establish a validmethod for selecting the best forecasting horizon with regardto a proposed application Finally the proposed method isvalidated experimentally bymeans of vibration data extractedfrom a complex kinematic chain working under differentfailure conditions

The paper is structured as follows Section 2 introducesthe theoretical aspects of the vibration in rotating machineryand the theory behind ANFIS for time series forecasting InSection 3 the basis of the proposed method is explainedSection 4 presents the verification of the method capabilitieswith experimental results of vibration data extracted from akinematic chain Conclusions are presented in Section 5

2 Theoretical Background

21 Vibration Analysis in Rotating Machinery The classi-cal vibration condition monitoring schemes focused onmechanical and electrical defects are based on the consid-eration of specific vibrational frequency components [22]The spectral analysis of the vibration signature either inthe motor case in an external bearing house or in anyspecific component allows the evaluation of characteristicsfault frequencies related to cyclic single-point defects Forinstance in bearing failures the fault frequencies presentedin the vibration spectrum are related to the bearing designgeometry and follow the well-known equations showed in[23] Vibration analysis is also applied to diagnose thedegradation of rotor bars in induction motors The failurehere is presented in a form of a partial or complete crackin the section of the bar Such bars may break becauseof manufacturing defects frequent starts at rated voltagethermal stresses andor mechanical stress caused by bearingfaults and metal fatigue Furthermore the diagnosis of thebroken rotor bar is performed by calculating specific spectralindexes [24]

Nevertheless these characteristic frequencies of thevibration modes apart from possible electrical and mechan-ical noise during the acquisition are affected by the specificstructure of the considered system (ie the kinematic chain)and the component deterioration stage Indeed the intensityof the impact produced between raceways and rolling ele-ments under a bearing defect is attenuated throughout thepropagation from the generation point to the transducer loca-tionTherefore the vibrationmeasurement is done generallyas close as possible to the mechanical element under test Yetthough favoring the measurement of bearing faults vibrationeffects the resulting spectrum contains additional vibrationmodes produced by the rest of the mechanical interactionsThese additional vibration frequencies mask or complicatethe comprehension of the signal

The detection of one of the characteristic fault frequenciesin the resulting spectrum should be interpreted as an exis-tence of the corresponding fault in the component Howeverthe absence of clear characteristic fault frequencies shouldnot be interpreted as a completely healthy condition In this

Am

plitu

de

Frequency (Hz)

Sidebands

Characteristic frequencies

Z1 Z4Z2 Z3

1timesfr

2timesfr

3timesfr

Figure 1 Main frequency zones in mechanical degradation

regard a more general approach to the monitoring of theelectromechanical components can be found in the literatureas a four-stage process [25] These four stages are related tothe apparition of failure effects in some of the four zones inwhich the vibration spectrum is divided for electromechan-ical failure detection A graphical example of the frequencyspectrum of the vibration signal versus the different spectralzones in which electromechanical failures occur is presentedin Figure 1 The frequency band 119885

1is related to electrome-

chanical failures eventually in an advanced degradation stageor presenting high severity which affects or is related tothe rotational speed of the machine This kind of failuresappears in 119885

1as sidebands of the fundamental frequency 119885

2

is related to the regular degradation such as gears or bearingsIndeed 119885

2is the frequency band in which the characteristic

bearing faulty frequencies are located 1198853corresponds to a

high frequency band in which early or incipient degradationoccurs The failure detection in this area is generally doneby means of feature bases characterization since the failurepattern is not as specific as the characteristic ones in the lowfrequency bands 119885

4covers the very-high frequency part of

the spectrum This area is related to the premature degrada-tion of any electric or mechanical component Neverthelessit is also very close to the electrical noise inherent in everyelectromechanical system Due to this fact the patterns inthis area are very chaotic and are rarely considered for regulardiagnosis purposes

In conclusion the first three spectral zones are of majorinterest from the diagnosis and the vibration monitoringpoint of view The forecasting method is intended to takeadvantage from this spectral decomposition in order to iso-late each frequency band and gain forecasting performanceby modeling each band from 119885

1to 1198853 with a dedicated

ANFIS model It should be noticed that 1198854is discarded for

forecasting purposes since the noisy and random patternsmake the model very complex with regard to the vibrationinformation provided by this frequency region

22 Adaptive Neurofuzzy Inference System There are differ-ent techniques to design forecasting models Yet the pri-marily used schemes are frequently based on the concept ofhybrid forecasting which means that the method integratesdifferent techniques in order to take advantage of each oneinvolved In this topic one of the most important hybridsystems is ANFIS [26] This method fuses the parametricadaptability of artificial neural-networks and the generaliza-tion capabilities of the fuzzy logic ANFIS based prognostic

4 Shock and Vibration

x

x

y

y

x y

z

Input

Output

Input

L1

L2

N

N

L3L4

L5

A1

A2

B1

B2

w1

w2

w1

w2

z1w1

z2w2

sum

prod

prod

Figure 2 Adaptive network-based Fuzzy Inference System schemewith two inputs four membership functions two rules and onesingle output

system offers a reliable and robust condition predictor sinceit can capture the system dynamic behavior quickly andaccurately [27]

The neural-fuzzy architecture can be divided into fivedifferent layers as shown in Figure 2 For the specificarchitecture shown in this figure the method aims to find arelationship between the output signal 119911 and a set of differentinput signals 119909 and 119910 by means of the activation of differentpolynomials regarding the fuzzification of the input signalsby means of the membership functions 119860

1 1198602 1198611 and 119861

2

Theoutput is computed regarding the pertinence of the inputsand the two if -then rules as defined in (1)

The input layer 1198711 is in charge of addressing the input

signals to a node Each node 119892 of each layer 119895 is anadaptive node with an output function 119874119895

119892 defined in (2)

where 120583119860119892

and 120583119861119892minus2

represent the membership degree of therespective input with regard to the membership functionsIn the fuzzification layer 119871

2 the weight of each rule is

computed bymeans of a fuzzy ANDoperation thatmultipliesthe input signals The outputs of this layer 119882

119892 represent

the activation variables of a fuzzy rule (3) The fuzzy rulesdefinition layer 119871

3 provides the antecedent consequence

statements of fuzzy logic Each node calculates the reasonbetween the 119892th activation variable and the sum of all theactivation variables (4) The outputs of this layer are callednormalized activation variables 119882

119892 In the defuzzification

layer 1198714 each node computes the contribution of the 119892th

fuzzy rule over all the outputs (5) It should be noticed that119901119892 119902119892 and 119903

119892are the polynomial coefficients that would be

estimated during the learning phase of the algorithm Theoutputs of each node are named consequents The nodes ofthe output layer 119871

5 calculate the output signal 119911 as the

summation of all the input signals (6) Consider

Rule 1 if 119909 isin 1198601cup 119910 isin 119861

1997888rarr 1199111= 1199011119909 + 1199021119910 + 1199031

Rule 2 if 119909 isin 1198602cup 119910 isin 119861

2997888rarr 1199112= 1199012119909 + 1199022119910 + 1199032

(1)

1198741

119892= 120583119860119892(119909) 119892 = 1 2

1198741

119892= 120583119861119892minus2

(119910) 119892 = 3 4

(2)

1198742

119892= 119882119892= 120583119860119892(119909) sdot 120583

119861119892+2(119910) 119892 = 1 2 (3)

1198743

119892= 119882119892=

119908119892

1199081+ 1199082

119892 = 1 2 (4)

1198744

119892= 119882119892sdot 119911119892= 119882119892sdot (119901119892119909 + 119902119892119910 + 119903119892) 119892 = 1 2 (5)

1198745

119892= 119911 = sum

119892

119882119892sdot 119911119892=

sum119892119882119892sdot 119911119892

sum119892119882119892

(6)

The ANFIS structure allows the consideration of a data-driven modeling approach with adaptive rule changing capa-bility and fast convergence rate and does not require extensiveexperience about the process to include such patterns in thefuzzy rules

3 Methodology

Theobjective of the proposedmethod is tomodel and forecastthe evolution curve of the vibrationrsquos RMS signal during thestart-up and the thermal stabilization of an electromechanicalactuator The main point is to obtain a forecasting modelof the RMS capable of giving the future value with enoughresolution taking into consideration the dynamics of differentfailures occurring to the system After the output of themethod the presence of the failure can be anticipated byknowing the future value of the RMS and a simply statisticalcharacterization as a diagnosis method

Therefore the challenge is to develop a vibration modelwith enough performance in terms of forecasted signal errorand forecasting horizon that considers the dynamics modesgenerated by different faulty scenarios of different elementsof the electromechanical actuatorThe general block diagramof the method is shown in Figure 3 including the trainingprocedure and the online operation The main limitation inthe modeling of complex signals is that a unique forecastingmodel is not able to capture all the particular dynamicsthat different fault scenarios may cause In this regard themethod uses a decomposition of the vibration signal in thethree frequency bands in order to provide resolution andgeneralization towards multiple failure scenarios by improv-ing the response towards their specific spectral componentsdynamics Then the previous prefiltering stage and the RMScalculation are the authorrsquos contribution in order to increasethemodel resolution by limiting the amount of dynamics thateach ANFIS model should face

31 Training Procedure The training procedure correspondsto the off-line learning process in order to do the following (i)tuning of the structure of the forecasting models (ii) analysisof the optimum inputs delays and (iii) identification of thelongest forecasting horizon

The first step Step 1 aims to decompose the vibrationsignal 119910(119905) with a length 119871 in three different details that aremodeled with a specific ANFIS This decomposition is madewith Finite Impulse Response (FIR) digital filters the cuttingfrequencies follow theoretical considerations of mechanicalfault appearance explained in Section 21 Then the outputsignal of a certain filter 119885

119894is considered to be 119910

119911119894(119905) Three

FIR filters are defined

Shock and Vibration 5

Frequency

Signal detailsRaw signalForecasting

outcomeTarget signalT(t)

Delay selection

Delay selection

Delay selection

ANFIS

ANFIS

ANFIS

Windowed RMS Model optimization

Interval finding

Interval finding

Interval finding

Detail of training

Online behavior

Signal recombination

Training procedure

3x RMScalculation

3x RMScalculation

3x optimalGANFIS modeling

Signal recombination

Forecasting outcome

Step 1 Step 2 Step 3 Step 4

Raw signal filtering

Raw signal filtering

Step 5

Correlation based interval finding

Step 6

Step 1 Step 2 Step 3 Step 4 Step 5

3x ANFISprojection

Forecastingoutcome

Z1 Z2 Z3

RMS in Z1

RMS in Z2

RMS in Z3

sum+

Figure 3 Block diagram of the proposed method

(i) First filter band 1198851 is defined as a low pass filter and

covers the low frequency band of the spectrum Thisfilter isolates those frequencies related to the rotatingmechanical frequencies and first harmonics

(ii) Second filter band 1198852 is defined as a bandpass filter

covering the middle frequency band This band isrelated to different mechanical degradations such asbearing defects This filter isolates those componentsin order to gain forecasting resolution in these kindsof failures

(iii) Third filter band 1198853 is a bandpass that covers the

rest of the frequencies till the Nyquist frequencyIt is designed to model high frequency modes thatappear in the vibration signal under incipient failurescenarios

The next step Step 2 deals with the calculation of theenergy as a windowed Root-Mean-Square (RMS) value foreach of the three resulting filtered signals As the method isintended to be used online this calculation is made as shownin (7) that is by means of a sliding window ℎ(119905) with adefinedwidth119908

ℎ and an overlapping factor ovRMS Note that

overlapping is defined to smooth the response of the filterversus new signals Therefore the signals to be modeled toforecast the vibration of the system are the obtained RMSof each filter 119864

119885119894 Note that the temporal duration of 119908

ℎis

configured to be short in comparison with the high dynamicsof the signal For this reason the obtained RMS should beconsidered as a signal giving information of the instantaneousvariation of the vibration RMS instead of a static feature Dueto this fact the resulting RMS presents characteristic andquantifiable dynamics that can be analyzed

119864119885119894(119905) = radic

1

119908ℎ

sdot

119871

sum

119905=1

(119910119911119894(119905) sdot ℎ (119905))

2

(7)

Prior to the model generation the identification of thebest past intervals to enhance the forecasting performanceis proposed as Step 3 The optimization process gets simpleas the search space is being bounded The interval selectionis made by calculating the correlation of the objective signal119864119885119894(119905+119901) with successive delays of the same signal119864

119885119894(119905minus119899)

where 119899 isin [0 10119901]The resulting correlation coefficient is obtained by (8) and

represents a measure of statistical similitude between 119910(119905)and its successive delays represented by 119899 The evolution ofthis coefficient as 119899 increases shows signal oscillation modesand periodicities in which the target signal and its delaysare significantly correlated Then the interval is selectedby setting a correlation threshold 119862th and selecting thoseintervals with the highest accumulated correlation

119862coef (119899) =cov (119864

119911119894(119905 minus 119899) 119864

119911119894(119905 + 119901))

120590 (119864119911119894(119905 minus 119899)) sdot 120590 (119864

119911119894(119905 + 119901))

for 119899 = 0 10119901

(8)

It is common to find modeling situations especially withvibration signals inwhich it is necessary to deal with differenttraining sets or operating conditions In these situations thesearch for the optimal intervals turns into an iterative processthat tries to localize those intervals with a consistent correla-tion and once identified select themaximum common rangethat accumulates the highest correlation

The following step Step 4 consists in the generation andthe training of the ANFIS based models to predict the energyof each filter output being respectively119872

11988511198721198852 and119872

1198853

The structure of themodels is fixed and corresponds to (i) thecurrent value of the energy in the 119894th filter 119864

119885119894(119905) (ii) a past

value of the energy in the 119894th filter delayed 1198991samples 119864

119885119894(119905minus

1198991) and (iii) another past value of the RMS in the 119894th filter

delayed 1198992samples 119864

119885119894(119905 minus 119899

2) The three inputs combined

6 Shock and Vibration

with the ANFIS model give the predicted vibration energy119864(119905 + 119901) as shown in

119864 (119905 + 119901)

=

3

sum

119894=1

ANFIS119885119894(119864119885119894(119905) 119864119885119894(119905 minus 119899

1) 119864119885119894(119905 minus 119899

2))

(9)

Although each model presents the same quantity ofinputs the delayed samples 119899

1and 119899

2could be different for

each filter depending on the optimization results The identi-fied correlation intervals are here introduced as boundariesfor the Genetic Algorithm (GA) The cost function of theoptimization procedure is defined as the Root-Mean-SquareError (RMSE) of the forecasting model that can be seen in(10) The three models are trained independently with allthe available information regarding the different operatingconditions and failure scenariosUltimately in Step 5 the finalforecasting outcome of the vibration is obtained by means ofthe direct combination of three filters models outputs

In order to evaluate the performance of the modelsclassical statistical metrics have been used which are RMSEdefined in (10)MeanAbsolute Error (MAE) in (11) andMeanAbsolute Percentage Error (MAPE) in (12) These metricshave been widely used and accepted from the researchcommunity as indicated in [28] or [29] RMSE is one ofthe most used performance metrics for the development offorecasting models it is a measure of the standard deviationof the differences between predicted values and observedvalues It is useful in order to analyze the global behavior ofthe model but it is very sensitive to the amplitude In thisregard the MAE is used to evaluate the forecast since it is lesssensitive to outliers Finally theMAPEhelps to determine themean deviation of each sample normalized by the amplitudeso it helps to unify the scale and can be used to compare theerrors of signals with different levels of amplitudes

RMSE = radicsum119871

119905=1(119864 (119905) minus (119905))

2

119871

(10)

MAE = radicsum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905))

10038161003816100381610038161003816

119871

(11)

MAPE =sum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905)) 119864 (119905)

10038161003816100381610038161003816

119871sdot 100 (12)

32 Online Behavior One of the primary characteristics ofthe proposed method is that it is prepared to work contin-uously online that is receiving new data from the machineas shown in Figure 3 Therefore after the training procedureof the method vibration signal is acquired periodically fromthe machine under study Then the signal is filtered with thedefined three digital filters and the correspondingRMSvaluesare calculated As the structure of the models and the bestpast inputs are already defined the trained models are usedto project the three energies among the specified 119901 Finallythe output of the three models is combined giving with it thenew forecasted value of the vibration energy

Gearbox

Load

VFD

DAS

Inductionmotor

AccelerometerEncoder

PC

Figure 4 Electromechanical test bench used for experimentalvalidation of the method

4 Experimental Results

The test bench used to obtain experimental vibrations isshown in Figure 4 This test bench consists of a kinematicchain composed of a three-phase 1492 119882 induction motorWEG 00236ET3E145T-W22 whose speed is controlled bya variable frequency drive (VFD) and WEG CFW08 theoperating speed being fixed to 60Hz for all experiments A4 1 ratio gearbox BALDOR GCF4X01AA is used to couplethe drive motor to a DC generator BALDOR CDP3604 TheDC motor is used as a noncontrolled mechanical load thatcomprises around 20 of the nominal torque of the drivingmotor The DAS is a proprietary low-cost design based onfield programable gate array technology The output rota-tional speed is obtained by using a digital encoder the motorstart-up is controlled by a relay in order to automatize thetest run A 12-bit 4-channel serial-output sampling analog-to-digital converter ADS7841 is used in the onboard dataacquisition system (DAS)

Vibration signal from the perpendicular plane of themotor axis is acquired using a triaxial accelerometerLIS3L02AS4 mounted on a board with the signal condition-ing and antialiasing filtering Sampling frequency is set to3 kHz for vibration acquisitionThe data retrieved by theDASis stored in a regular computer (PC)

Four scenarios have been considered that is the healthycondition HC a bearing failure (BF) condition a half-broken rotor bar (HBRB) condition and full-broken rotor bar(FBRB) The detail of the failures is shown in Figure 5 Thefailure in a 6205-2ZNR bearing has been induced by meansof a hole of 1191mm in the outer race the hole has beenproduced by a tungsten drill bit HBRB failure is artificiallyproduced by drilling a 6mm holewith a depth of 3mm thatcorresponds mostly to the 22 of the section of the rotor barFinally FBRB is produced by a through-hole with a diameterof 6mm and a depth of 14mm which corresponds to thecomplete section of the rotor bar

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

2 Shock and Vibration

vibration analysis Vibration signals collected from thisequipment during operation contain valuable informationabout the equipment condition Great research effort hasbeen carried out for the development of several algorithmsfor faults detection anddiagnosis in rotatingmachinery basedon vibration monitoring [4] The most popular methods ofrotating machine condition monitoring utilize the steadystate spectral components of the vibration signals Thesespectral components of the vibration are used to diagnosefaults of rotating machinery and the energy of vibrationsignals in the frequency domain being the most commonlyused method to evaluate the severity of a fault

Nevertheless the vibration signal is often a complexsignal which contains stationary nonstationary and noisycomponents Therefore the appropriate signal processingtechniques have to be applied in order to compute numer-ical fault indicators or features [5] Features are parame-ters derived from the measured data that robustly indicatethe presence of faults in rotating machinery The majorfeature-calculation methods are time domain methods fre-quency domain methods and time-frequency methodsTime domain methods such as peak amplitude Root-Mean-Square amplitude crest factor kurtosis and shock pulsecounting have been successfully applied [6 7] Frequencydomain methods include Fourier spectra time waveformcepstrum analysis and the spectral envelope technique[8 9] A comparative study of various feature-calculationmethods in frequency domain such as the Fast FourierTransform (FFT) and spectral envelope and in the time-frequency domain such as the Short Time Fourier Transform(STFT) Wigner Ville and wavelet analysis is presented in[10 11]

Clearly the opportunity of conducting forecasting basedon vibrations presentsmultiple benefits (i) correct deviationsbefore they affect the correct behavior of the system (ii)anticipate the response towards failures and (iii) assist thediagnosis algorithm in order to assess the future condition ofthe system [12 13] Unfortunately little work has been donein the area with vibration forecasting and there is a lack ofmethodology to perform such approaches [14]Themodelingof the vibration as a physical magnitude is a complexprocess furthermore vibration in electromechanical systemsis affected by several factors such as multiple emissionsources mechanical properties operation condition How-ever the modeling of numerical features that characterizethe vibration is a more affordable problem since raw datapresents redundant or nonimportant information from theelectromechanical components degradation point of viewThis is the case when time domain features such as the Root-Mean-Square (RMS) value or kurtosis offer a more reliableview of the machine condition [15] As a result the temporalmodeling of features extracted from the vibration signal is amatter of interest for many researchers Therefore the utilityof a vibrationrsquos feature forecasting model relies on the earlydetection of deviations from the correct behavior as earlyas the model output is extended in the future The optimalscenario of such approaches is themodeling of the RMS valueof the vibrations during the start-up operation of themachinetill it reaches the thermal stability in order to indicate

the abnormal behaviors as soon as possible to minimize thedamage of operating under failure conditions

Consequently the forecasting of such vibration featuresignals can be approached from the time series modelingpoint of view Current modeling and forecasting techniquescan be categorized into three classes namely model-baseddata-driven and hybrid prognostics approaches [16] Model-based techniques describe the future evolution of the sys-tem based on the mathematical equations that describeits physical properties [17] Data-driven techniques takeadvantage of the past records to learn the system behaviorand conduct the predictions Hybrid techniques are a com-bination of model-based and data-driven techniques [18] Inthis regard Adaptive Neurofuzzy Inference System (ANFIS)represents a hybrid data-driven forecastingmethod that fusesthe parametric adaptability of ANN and the generalizationcapabilities of the fuzzy logic ANFIS offers a reliable androbust condition predictor since it can capture the systemdynamic behavior quickly and accurately [19]

When facing vibration forecasting the problem is howto decide for a given application the optimal forecastinghorizon and the configuration of the models In this regardvibration signals usually present faster or at least equaldynamics in comparison with other magnitudes inherent toan electromechanical system such as voltage electric currentand temperature Due to this fact the modeling problemshould be approached as a time series forecasting [20] Itis necessary to emphasize that the result of a forecastingmethod is critically associated with the forecasting horizonused to train and validate the models In many applica-tions the forecasting horizon is usually fixed by applicationrequirements ormodeling limitations [21] Yet the procedureto select the best horizon for a given application is notwell established in the literature For this reason this paperproposes performing a study relating the selected forecastinghorizon and the prediction error once the application isdefined In this regard three open issues can be found inliterature (i) the decision of the optimal prediction horizon(ii) the configuration of the models in terms of numberof inputs and past values to be considered and (iii) thedecomposition of the signal in different details in order toincrease accuracy

In this paper the authors propose a study in order tooptimize these three open issues to obtain a methodologyfor modeling the RMS of the vibrations from an electrome-chanical system and its associated kinematic chainThereforethe contributions of this work include a novel vibrationforecasting method that utilizes the theory behind vibrationsignature under electromechanical failures to decomposethe vibration signal in three frequency bands related to thevibration signature to enhance the forecasting accuracy andadaptability towards different dynamic contents Then thecore of the methodology consists of the generation of threecollaborative ANFIS models that are in charge of forecastingthe evolution of specific spectral content of the vibrationsignal The configuration of the model is optimized onestep beyond the literature by analyzing cross-correlationsbetween the signal and past instants which are selected byusing Genetic Algorithm (GA) optimization to find the best

Shock and Vibration 3

input configuration Complementarily the paper includesa systematic study of the forecasting horizon affectation ofthe model configuration step in order to establish a validmethod for selecting the best forecasting horizon with regardto a proposed application Finally the proposed method isvalidated experimentally bymeans of vibration data extractedfrom a complex kinematic chain working under differentfailure conditions

The paper is structured as follows Section 2 introducesthe theoretical aspects of the vibration in rotating machineryand the theory behind ANFIS for time series forecasting InSection 3 the basis of the proposed method is explainedSection 4 presents the verification of the method capabilitieswith experimental results of vibration data extracted from akinematic chain Conclusions are presented in Section 5

2 Theoretical Background

21 Vibration Analysis in Rotating Machinery The classi-cal vibration condition monitoring schemes focused onmechanical and electrical defects are based on the consid-eration of specific vibrational frequency components [22]The spectral analysis of the vibration signature either inthe motor case in an external bearing house or in anyspecific component allows the evaluation of characteristicsfault frequencies related to cyclic single-point defects Forinstance in bearing failures the fault frequencies presentedin the vibration spectrum are related to the bearing designgeometry and follow the well-known equations showed in[23] Vibration analysis is also applied to diagnose thedegradation of rotor bars in induction motors The failurehere is presented in a form of a partial or complete crackin the section of the bar Such bars may break becauseof manufacturing defects frequent starts at rated voltagethermal stresses andor mechanical stress caused by bearingfaults and metal fatigue Furthermore the diagnosis of thebroken rotor bar is performed by calculating specific spectralindexes [24]

Nevertheless these characteristic frequencies of thevibration modes apart from possible electrical and mechan-ical noise during the acquisition are affected by the specificstructure of the considered system (ie the kinematic chain)and the component deterioration stage Indeed the intensityof the impact produced between raceways and rolling ele-ments under a bearing defect is attenuated throughout thepropagation from the generation point to the transducer loca-tionTherefore the vibrationmeasurement is done generallyas close as possible to the mechanical element under test Yetthough favoring the measurement of bearing faults vibrationeffects the resulting spectrum contains additional vibrationmodes produced by the rest of the mechanical interactionsThese additional vibration frequencies mask or complicatethe comprehension of the signal

The detection of one of the characteristic fault frequenciesin the resulting spectrum should be interpreted as an exis-tence of the corresponding fault in the component Howeverthe absence of clear characteristic fault frequencies shouldnot be interpreted as a completely healthy condition In this

Am

plitu

de

Frequency (Hz)

Sidebands

Characteristic frequencies

Z1 Z4Z2 Z3

1timesfr

2timesfr

3timesfr

Figure 1 Main frequency zones in mechanical degradation

regard a more general approach to the monitoring of theelectromechanical components can be found in the literatureas a four-stage process [25] These four stages are related tothe apparition of failure effects in some of the four zones inwhich the vibration spectrum is divided for electromechan-ical failure detection A graphical example of the frequencyspectrum of the vibration signal versus the different spectralzones in which electromechanical failures occur is presentedin Figure 1 The frequency band 119885

1is related to electrome-

chanical failures eventually in an advanced degradation stageor presenting high severity which affects or is related tothe rotational speed of the machine This kind of failuresappears in 119885

1as sidebands of the fundamental frequency 119885

2

is related to the regular degradation such as gears or bearingsIndeed 119885

2is the frequency band in which the characteristic

bearing faulty frequencies are located 1198853corresponds to a

high frequency band in which early or incipient degradationoccurs The failure detection in this area is generally doneby means of feature bases characterization since the failurepattern is not as specific as the characteristic ones in the lowfrequency bands 119885

4covers the very-high frequency part of

the spectrum This area is related to the premature degrada-tion of any electric or mechanical component Neverthelessit is also very close to the electrical noise inherent in everyelectromechanical system Due to this fact the patterns inthis area are very chaotic and are rarely considered for regulardiagnosis purposes

In conclusion the first three spectral zones are of majorinterest from the diagnosis and the vibration monitoringpoint of view The forecasting method is intended to takeadvantage from this spectral decomposition in order to iso-late each frequency band and gain forecasting performanceby modeling each band from 119885

1to 1198853 with a dedicated

ANFIS model It should be noticed that 1198854is discarded for

forecasting purposes since the noisy and random patternsmake the model very complex with regard to the vibrationinformation provided by this frequency region

22 Adaptive Neurofuzzy Inference System There are differ-ent techniques to design forecasting models Yet the pri-marily used schemes are frequently based on the concept ofhybrid forecasting which means that the method integratesdifferent techniques in order to take advantage of each oneinvolved In this topic one of the most important hybridsystems is ANFIS [26] This method fuses the parametricadaptability of artificial neural-networks and the generaliza-tion capabilities of the fuzzy logic ANFIS based prognostic

4 Shock and Vibration

x

x

y

y

x y

z

Input

Output

Input

L1

L2

N

N

L3L4

L5

A1

A2

B1

B2

w1

w2

w1

w2

z1w1

z2w2

sum

prod

prod

Figure 2 Adaptive network-based Fuzzy Inference System schemewith two inputs four membership functions two rules and onesingle output

system offers a reliable and robust condition predictor sinceit can capture the system dynamic behavior quickly andaccurately [27]

The neural-fuzzy architecture can be divided into fivedifferent layers as shown in Figure 2 For the specificarchitecture shown in this figure the method aims to find arelationship between the output signal 119911 and a set of differentinput signals 119909 and 119910 by means of the activation of differentpolynomials regarding the fuzzification of the input signalsby means of the membership functions 119860

1 1198602 1198611 and 119861

2

Theoutput is computed regarding the pertinence of the inputsand the two if -then rules as defined in (1)

The input layer 1198711 is in charge of addressing the input

signals to a node Each node 119892 of each layer 119895 is anadaptive node with an output function 119874119895

119892 defined in (2)

where 120583119860119892

and 120583119861119892minus2

represent the membership degree of therespective input with regard to the membership functionsIn the fuzzification layer 119871

2 the weight of each rule is

computed bymeans of a fuzzy ANDoperation thatmultipliesthe input signals The outputs of this layer 119882

119892 represent

the activation variables of a fuzzy rule (3) The fuzzy rulesdefinition layer 119871

3 provides the antecedent consequence

statements of fuzzy logic Each node calculates the reasonbetween the 119892th activation variable and the sum of all theactivation variables (4) The outputs of this layer are callednormalized activation variables 119882

119892 In the defuzzification

layer 1198714 each node computes the contribution of the 119892th

fuzzy rule over all the outputs (5) It should be noticed that119901119892 119902119892 and 119903

119892are the polynomial coefficients that would be

estimated during the learning phase of the algorithm Theoutputs of each node are named consequents The nodes ofthe output layer 119871

5 calculate the output signal 119911 as the

summation of all the input signals (6) Consider

Rule 1 if 119909 isin 1198601cup 119910 isin 119861

1997888rarr 1199111= 1199011119909 + 1199021119910 + 1199031

Rule 2 if 119909 isin 1198602cup 119910 isin 119861

2997888rarr 1199112= 1199012119909 + 1199022119910 + 1199032

(1)

1198741

119892= 120583119860119892(119909) 119892 = 1 2

1198741

119892= 120583119861119892minus2

(119910) 119892 = 3 4

(2)

1198742

119892= 119882119892= 120583119860119892(119909) sdot 120583

119861119892+2(119910) 119892 = 1 2 (3)

1198743

119892= 119882119892=

119908119892

1199081+ 1199082

119892 = 1 2 (4)

1198744

119892= 119882119892sdot 119911119892= 119882119892sdot (119901119892119909 + 119902119892119910 + 119903119892) 119892 = 1 2 (5)

1198745

119892= 119911 = sum

119892

119882119892sdot 119911119892=

sum119892119882119892sdot 119911119892

sum119892119882119892

(6)

The ANFIS structure allows the consideration of a data-driven modeling approach with adaptive rule changing capa-bility and fast convergence rate and does not require extensiveexperience about the process to include such patterns in thefuzzy rules

3 Methodology

Theobjective of the proposedmethod is tomodel and forecastthe evolution curve of the vibrationrsquos RMS signal during thestart-up and the thermal stabilization of an electromechanicalactuator The main point is to obtain a forecasting modelof the RMS capable of giving the future value with enoughresolution taking into consideration the dynamics of differentfailures occurring to the system After the output of themethod the presence of the failure can be anticipated byknowing the future value of the RMS and a simply statisticalcharacterization as a diagnosis method

Therefore the challenge is to develop a vibration modelwith enough performance in terms of forecasted signal errorand forecasting horizon that considers the dynamics modesgenerated by different faulty scenarios of different elementsof the electromechanical actuatorThe general block diagramof the method is shown in Figure 3 including the trainingprocedure and the online operation The main limitation inthe modeling of complex signals is that a unique forecastingmodel is not able to capture all the particular dynamicsthat different fault scenarios may cause In this regard themethod uses a decomposition of the vibration signal in thethree frequency bands in order to provide resolution andgeneralization towards multiple failure scenarios by improv-ing the response towards their specific spectral componentsdynamics Then the previous prefiltering stage and the RMScalculation are the authorrsquos contribution in order to increasethemodel resolution by limiting the amount of dynamics thateach ANFIS model should face

31 Training Procedure The training procedure correspondsto the off-line learning process in order to do the following (i)tuning of the structure of the forecasting models (ii) analysisof the optimum inputs delays and (iii) identification of thelongest forecasting horizon

The first step Step 1 aims to decompose the vibrationsignal 119910(119905) with a length 119871 in three different details that aremodeled with a specific ANFIS This decomposition is madewith Finite Impulse Response (FIR) digital filters the cuttingfrequencies follow theoretical considerations of mechanicalfault appearance explained in Section 21 Then the outputsignal of a certain filter 119885

119894is considered to be 119910

119911119894(119905) Three

FIR filters are defined

Shock and Vibration 5

Frequency

Signal detailsRaw signalForecasting

outcomeTarget signalT(t)

Delay selection

Delay selection

Delay selection

ANFIS

ANFIS

ANFIS

Windowed RMS Model optimization

Interval finding

Interval finding

Interval finding

Detail of training

Online behavior

Signal recombination

Training procedure

3x RMScalculation

3x RMScalculation

3x optimalGANFIS modeling

Signal recombination

Forecasting outcome

Step 1 Step 2 Step 3 Step 4

Raw signal filtering

Raw signal filtering

Step 5

Correlation based interval finding

Step 6

Step 1 Step 2 Step 3 Step 4 Step 5

3x ANFISprojection

Forecastingoutcome

Z1 Z2 Z3

RMS in Z1

RMS in Z2

RMS in Z3

sum+

Figure 3 Block diagram of the proposed method

(i) First filter band 1198851 is defined as a low pass filter and

covers the low frequency band of the spectrum Thisfilter isolates those frequencies related to the rotatingmechanical frequencies and first harmonics

(ii) Second filter band 1198852 is defined as a bandpass filter

covering the middle frequency band This band isrelated to different mechanical degradations such asbearing defects This filter isolates those componentsin order to gain forecasting resolution in these kindsof failures

(iii) Third filter band 1198853 is a bandpass that covers the

rest of the frequencies till the Nyquist frequencyIt is designed to model high frequency modes thatappear in the vibration signal under incipient failurescenarios

The next step Step 2 deals with the calculation of theenergy as a windowed Root-Mean-Square (RMS) value foreach of the three resulting filtered signals As the method isintended to be used online this calculation is made as shownin (7) that is by means of a sliding window ℎ(119905) with adefinedwidth119908

ℎ and an overlapping factor ovRMS Note that

overlapping is defined to smooth the response of the filterversus new signals Therefore the signals to be modeled toforecast the vibration of the system are the obtained RMSof each filter 119864

119885119894 Note that the temporal duration of 119908

ℎis

configured to be short in comparison with the high dynamicsof the signal For this reason the obtained RMS should beconsidered as a signal giving information of the instantaneousvariation of the vibration RMS instead of a static feature Dueto this fact the resulting RMS presents characteristic andquantifiable dynamics that can be analyzed

119864119885119894(119905) = radic

1

119908ℎ

sdot

119871

sum

119905=1

(119910119911119894(119905) sdot ℎ (119905))

2

(7)

Prior to the model generation the identification of thebest past intervals to enhance the forecasting performanceis proposed as Step 3 The optimization process gets simpleas the search space is being bounded The interval selectionis made by calculating the correlation of the objective signal119864119885119894(119905+119901) with successive delays of the same signal119864

119885119894(119905minus119899)

where 119899 isin [0 10119901]The resulting correlation coefficient is obtained by (8) and

represents a measure of statistical similitude between 119910(119905)and its successive delays represented by 119899 The evolution ofthis coefficient as 119899 increases shows signal oscillation modesand periodicities in which the target signal and its delaysare significantly correlated Then the interval is selectedby setting a correlation threshold 119862th and selecting thoseintervals with the highest accumulated correlation

119862coef (119899) =cov (119864

119911119894(119905 minus 119899) 119864

119911119894(119905 + 119901))

120590 (119864119911119894(119905 minus 119899)) sdot 120590 (119864

119911119894(119905 + 119901))

for 119899 = 0 10119901

(8)

It is common to find modeling situations especially withvibration signals inwhich it is necessary to deal with differenttraining sets or operating conditions In these situations thesearch for the optimal intervals turns into an iterative processthat tries to localize those intervals with a consistent correla-tion and once identified select themaximum common rangethat accumulates the highest correlation

The following step Step 4 consists in the generation andthe training of the ANFIS based models to predict the energyof each filter output being respectively119872

11988511198721198852 and119872

1198853

The structure of themodels is fixed and corresponds to (i) thecurrent value of the energy in the 119894th filter 119864

119885119894(119905) (ii) a past

value of the energy in the 119894th filter delayed 1198991samples 119864

119885119894(119905minus

1198991) and (iii) another past value of the RMS in the 119894th filter

delayed 1198992samples 119864

119885119894(119905 minus 119899

2) The three inputs combined

6 Shock and Vibration

with the ANFIS model give the predicted vibration energy119864(119905 + 119901) as shown in

119864 (119905 + 119901)

=

3

sum

119894=1

ANFIS119885119894(119864119885119894(119905) 119864119885119894(119905 minus 119899

1) 119864119885119894(119905 minus 119899

2))

(9)

Although each model presents the same quantity ofinputs the delayed samples 119899

1and 119899

2could be different for

each filter depending on the optimization results The identi-fied correlation intervals are here introduced as boundariesfor the Genetic Algorithm (GA) The cost function of theoptimization procedure is defined as the Root-Mean-SquareError (RMSE) of the forecasting model that can be seen in(10) The three models are trained independently with allthe available information regarding the different operatingconditions and failure scenariosUltimately in Step 5 the finalforecasting outcome of the vibration is obtained by means ofthe direct combination of three filters models outputs

In order to evaluate the performance of the modelsclassical statistical metrics have been used which are RMSEdefined in (10)MeanAbsolute Error (MAE) in (11) andMeanAbsolute Percentage Error (MAPE) in (12) These metricshave been widely used and accepted from the researchcommunity as indicated in [28] or [29] RMSE is one ofthe most used performance metrics for the development offorecasting models it is a measure of the standard deviationof the differences between predicted values and observedvalues It is useful in order to analyze the global behavior ofthe model but it is very sensitive to the amplitude In thisregard the MAE is used to evaluate the forecast since it is lesssensitive to outliers Finally theMAPEhelps to determine themean deviation of each sample normalized by the amplitudeso it helps to unify the scale and can be used to compare theerrors of signals with different levels of amplitudes

RMSE = radicsum119871

119905=1(119864 (119905) minus (119905))

2

119871

(10)

MAE = radicsum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905))

10038161003816100381610038161003816

119871

(11)

MAPE =sum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905)) 119864 (119905)

10038161003816100381610038161003816

119871sdot 100 (12)

32 Online Behavior One of the primary characteristics ofthe proposed method is that it is prepared to work contin-uously online that is receiving new data from the machineas shown in Figure 3 Therefore after the training procedureof the method vibration signal is acquired periodically fromthe machine under study Then the signal is filtered with thedefined three digital filters and the correspondingRMSvaluesare calculated As the structure of the models and the bestpast inputs are already defined the trained models are usedto project the three energies among the specified 119901 Finallythe output of the three models is combined giving with it thenew forecasted value of the vibration energy

Gearbox

Load

VFD

DAS

Inductionmotor

AccelerometerEncoder

PC

Figure 4 Electromechanical test bench used for experimentalvalidation of the method

4 Experimental Results

The test bench used to obtain experimental vibrations isshown in Figure 4 This test bench consists of a kinematicchain composed of a three-phase 1492 119882 induction motorWEG 00236ET3E145T-W22 whose speed is controlled bya variable frequency drive (VFD) and WEG CFW08 theoperating speed being fixed to 60Hz for all experiments A4 1 ratio gearbox BALDOR GCF4X01AA is used to couplethe drive motor to a DC generator BALDOR CDP3604 TheDC motor is used as a noncontrolled mechanical load thatcomprises around 20 of the nominal torque of the drivingmotor The DAS is a proprietary low-cost design based onfield programable gate array technology The output rota-tional speed is obtained by using a digital encoder the motorstart-up is controlled by a relay in order to automatize thetest run A 12-bit 4-channel serial-output sampling analog-to-digital converter ADS7841 is used in the onboard dataacquisition system (DAS)

Vibration signal from the perpendicular plane of themotor axis is acquired using a triaxial accelerometerLIS3L02AS4 mounted on a board with the signal condition-ing and antialiasing filtering Sampling frequency is set to3 kHz for vibration acquisitionThe data retrieved by theDASis stored in a regular computer (PC)

Four scenarios have been considered that is the healthycondition HC a bearing failure (BF) condition a half-broken rotor bar (HBRB) condition and full-broken rotor bar(FBRB) The detail of the failures is shown in Figure 5 Thefailure in a 6205-2ZNR bearing has been induced by meansof a hole of 1191mm in the outer race the hole has beenproduced by a tungsten drill bit HBRB failure is artificiallyproduced by drilling a 6mm holewith a depth of 3mm thatcorresponds mostly to the 22 of the section of the rotor barFinally FBRB is produced by a through-hole with a diameterof 6mm and a depth of 14mm which corresponds to thecomplete section of the rotor bar

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

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AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 3

input configuration Complementarily the paper includesa systematic study of the forecasting horizon affectation ofthe model configuration step in order to establish a validmethod for selecting the best forecasting horizon with regardto a proposed application Finally the proposed method isvalidated experimentally bymeans of vibration data extractedfrom a complex kinematic chain working under differentfailure conditions

The paper is structured as follows Section 2 introducesthe theoretical aspects of the vibration in rotating machineryand the theory behind ANFIS for time series forecasting InSection 3 the basis of the proposed method is explainedSection 4 presents the verification of the method capabilitieswith experimental results of vibration data extracted from akinematic chain Conclusions are presented in Section 5

2 Theoretical Background

21 Vibration Analysis in Rotating Machinery The classi-cal vibration condition monitoring schemes focused onmechanical and electrical defects are based on the consid-eration of specific vibrational frequency components [22]The spectral analysis of the vibration signature either inthe motor case in an external bearing house or in anyspecific component allows the evaluation of characteristicsfault frequencies related to cyclic single-point defects Forinstance in bearing failures the fault frequencies presentedin the vibration spectrum are related to the bearing designgeometry and follow the well-known equations showed in[23] Vibration analysis is also applied to diagnose thedegradation of rotor bars in induction motors The failurehere is presented in a form of a partial or complete crackin the section of the bar Such bars may break becauseof manufacturing defects frequent starts at rated voltagethermal stresses andor mechanical stress caused by bearingfaults and metal fatigue Furthermore the diagnosis of thebroken rotor bar is performed by calculating specific spectralindexes [24]

Nevertheless these characteristic frequencies of thevibration modes apart from possible electrical and mechan-ical noise during the acquisition are affected by the specificstructure of the considered system (ie the kinematic chain)and the component deterioration stage Indeed the intensityof the impact produced between raceways and rolling ele-ments under a bearing defect is attenuated throughout thepropagation from the generation point to the transducer loca-tionTherefore the vibrationmeasurement is done generallyas close as possible to the mechanical element under test Yetthough favoring the measurement of bearing faults vibrationeffects the resulting spectrum contains additional vibrationmodes produced by the rest of the mechanical interactionsThese additional vibration frequencies mask or complicatethe comprehension of the signal

The detection of one of the characteristic fault frequenciesin the resulting spectrum should be interpreted as an exis-tence of the corresponding fault in the component Howeverthe absence of clear characteristic fault frequencies shouldnot be interpreted as a completely healthy condition In this

Am

plitu

de

Frequency (Hz)

Sidebands

Characteristic frequencies

Z1 Z4Z2 Z3

1timesfr

2timesfr

3timesfr

Figure 1 Main frequency zones in mechanical degradation

regard a more general approach to the monitoring of theelectromechanical components can be found in the literatureas a four-stage process [25] These four stages are related tothe apparition of failure effects in some of the four zones inwhich the vibration spectrum is divided for electromechan-ical failure detection A graphical example of the frequencyspectrum of the vibration signal versus the different spectralzones in which electromechanical failures occur is presentedin Figure 1 The frequency band 119885

1is related to electrome-

chanical failures eventually in an advanced degradation stageor presenting high severity which affects or is related tothe rotational speed of the machine This kind of failuresappears in 119885

1as sidebands of the fundamental frequency 119885

2

is related to the regular degradation such as gears or bearingsIndeed 119885

2is the frequency band in which the characteristic

bearing faulty frequencies are located 1198853corresponds to a

high frequency band in which early or incipient degradationoccurs The failure detection in this area is generally doneby means of feature bases characterization since the failurepattern is not as specific as the characteristic ones in the lowfrequency bands 119885

4covers the very-high frequency part of

the spectrum This area is related to the premature degrada-tion of any electric or mechanical component Neverthelessit is also very close to the electrical noise inherent in everyelectromechanical system Due to this fact the patterns inthis area are very chaotic and are rarely considered for regulardiagnosis purposes

In conclusion the first three spectral zones are of majorinterest from the diagnosis and the vibration monitoringpoint of view The forecasting method is intended to takeadvantage from this spectral decomposition in order to iso-late each frequency band and gain forecasting performanceby modeling each band from 119885

1to 1198853 with a dedicated

ANFIS model It should be noticed that 1198854is discarded for

forecasting purposes since the noisy and random patternsmake the model very complex with regard to the vibrationinformation provided by this frequency region

22 Adaptive Neurofuzzy Inference System There are differ-ent techniques to design forecasting models Yet the pri-marily used schemes are frequently based on the concept ofhybrid forecasting which means that the method integratesdifferent techniques in order to take advantage of each oneinvolved In this topic one of the most important hybridsystems is ANFIS [26] This method fuses the parametricadaptability of artificial neural-networks and the generaliza-tion capabilities of the fuzzy logic ANFIS based prognostic

4 Shock and Vibration

x

x

y

y

x y

z

Input

Output

Input

L1

L2

N

N

L3L4

L5

A1

A2

B1

B2

w1

w2

w1

w2

z1w1

z2w2

sum

prod

prod

Figure 2 Adaptive network-based Fuzzy Inference System schemewith two inputs four membership functions two rules and onesingle output

system offers a reliable and robust condition predictor sinceit can capture the system dynamic behavior quickly andaccurately [27]

The neural-fuzzy architecture can be divided into fivedifferent layers as shown in Figure 2 For the specificarchitecture shown in this figure the method aims to find arelationship between the output signal 119911 and a set of differentinput signals 119909 and 119910 by means of the activation of differentpolynomials regarding the fuzzification of the input signalsby means of the membership functions 119860

1 1198602 1198611 and 119861

2

Theoutput is computed regarding the pertinence of the inputsand the two if -then rules as defined in (1)

The input layer 1198711 is in charge of addressing the input

signals to a node Each node 119892 of each layer 119895 is anadaptive node with an output function 119874119895

119892 defined in (2)

where 120583119860119892

and 120583119861119892minus2

represent the membership degree of therespective input with regard to the membership functionsIn the fuzzification layer 119871

2 the weight of each rule is

computed bymeans of a fuzzy ANDoperation thatmultipliesthe input signals The outputs of this layer 119882

119892 represent

the activation variables of a fuzzy rule (3) The fuzzy rulesdefinition layer 119871

3 provides the antecedent consequence

statements of fuzzy logic Each node calculates the reasonbetween the 119892th activation variable and the sum of all theactivation variables (4) The outputs of this layer are callednormalized activation variables 119882

119892 In the defuzzification

layer 1198714 each node computes the contribution of the 119892th

fuzzy rule over all the outputs (5) It should be noticed that119901119892 119902119892 and 119903

119892are the polynomial coefficients that would be

estimated during the learning phase of the algorithm Theoutputs of each node are named consequents The nodes ofthe output layer 119871

5 calculate the output signal 119911 as the

summation of all the input signals (6) Consider

Rule 1 if 119909 isin 1198601cup 119910 isin 119861

1997888rarr 1199111= 1199011119909 + 1199021119910 + 1199031

Rule 2 if 119909 isin 1198602cup 119910 isin 119861

2997888rarr 1199112= 1199012119909 + 1199022119910 + 1199032

(1)

1198741

119892= 120583119860119892(119909) 119892 = 1 2

1198741

119892= 120583119861119892minus2

(119910) 119892 = 3 4

(2)

1198742

119892= 119882119892= 120583119860119892(119909) sdot 120583

119861119892+2(119910) 119892 = 1 2 (3)

1198743

119892= 119882119892=

119908119892

1199081+ 1199082

119892 = 1 2 (4)

1198744

119892= 119882119892sdot 119911119892= 119882119892sdot (119901119892119909 + 119902119892119910 + 119903119892) 119892 = 1 2 (5)

1198745

119892= 119911 = sum

119892

119882119892sdot 119911119892=

sum119892119882119892sdot 119911119892

sum119892119882119892

(6)

The ANFIS structure allows the consideration of a data-driven modeling approach with adaptive rule changing capa-bility and fast convergence rate and does not require extensiveexperience about the process to include such patterns in thefuzzy rules

3 Methodology

Theobjective of the proposedmethod is tomodel and forecastthe evolution curve of the vibrationrsquos RMS signal during thestart-up and the thermal stabilization of an electromechanicalactuator The main point is to obtain a forecasting modelof the RMS capable of giving the future value with enoughresolution taking into consideration the dynamics of differentfailures occurring to the system After the output of themethod the presence of the failure can be anticipated byknowing the future value of the RMS and a simply statisticalcharacterization as a diagnosis method

Therefore the challenge is to develop a vibration modelwith enough performance in terms of forecasted signal errorand forecasting horizon that considers the dynamics modesgenerated by different faulty scenarios of different elementsof the electromechanical actuatorThe general block diagramof the method is shown in Figure 3 including the trainingprocedure and the online operation The main limitation inthe modeling of complex signals is that a unique forecastingmodel is not able to capture all the particular dynamicsthat different fault scenarios may cause In this regard themethod uses a decomposition of the vibration signal in thethree frequency bands in order to provide resolution andgeneralization towards multiple failure scenarios by improv-ing the response towards their specific spectral componentsdynamics Then the previous prefiltering stage and the RMScalculation are the authorrsquos contribution in order to increasethemodel resolution by limiting the amount of dynamics thateach ANFIS model should face

31 Training Procedure The training procedure correspondsto the off-line learning process in order to do the following (i)tuning of the structure of the forecasting models (ii) analysisof the optimum inputs delays and (iii) identification of thelongest forecasting horizon

The first step Step 1 aims to decompose the vibrationsignal 119910(119905) with a length 119871 in three different details that aremodeled with a specific ANFIS This decomposition is madewith Finite Impulse Response (FIR) digital filters the cuttingfrequencies follow theoretical considerations of mechanicalfault appearance explained in Section 21 Then the outputsignal of a certain filter 119885

119894is considered to be 119910

119911119894(119905) Three

FIR filters are defined

Shock and Vibration 5

Frequency

Signal detailsRaw signalForecasting

outcomeTarget signalT(t)

Delay selection

Delay selection

Delay selection

ANFIS

ANFIS

ANFIS

Windowed RMS Model optimization

Interval finding

Interval finding

Interval finding

Detail of training

Online behavior

Signal recombination

Training procedure

3x RMScalculation

3x RMScalculation

3x optimalGANFIS modeling

Signal recombination

Forecasting outcome

Step 1 Step 2 Step 3 Step 4

Raw signal filtering

Raw signal filtering

Step 5

Correlation based interval finding

Step 6

Step 1 Step 2 Step 3 Step 4 Step 5

3x ANFISprojection

Forecastingoutcome

Z1 Z2 Z3

RMS in Z1

RMS in Z2

RMS in Z3

sum+

Figure 3 Block diagram of the proposed method

(i) First filter band 1198851 is defined as a low pass filter and

covers the low frequency band of the spectrum Thisfilter isolates those frequencies related to the rotatingmechanical frequencies and first harmonics

(ii) Second filter band 1198852 is defined as a bandpass filter

covering the middle frequency band This band isrelated to different mechanical degradations such asbearing defects This filter isolates those componentsin order to gain forecasting resolution in these kindsof failures

(iii) Third filter band 1198853 is a bandpass that covers the

rest of the frequencies till the Nyquist frequencyIt is designed to model high frequency modes thatappear in the vibration signal under incipient failurescenarios

The next step Step 2 deals with the calculation of theenergy as a windowed Root-Mean-Square (RMS) value foreach of the three resulting filtered signals As the method isintended to be used online this calculation is made as shownin (7) that is by means of a sliding window ℎ(119905) with adefinedwidth119908

ℎ and an overlapping factor ovRMS Note that

overlapping is defined to smooth the response of the filterversus new signals Therefore the signals to be modeled toforecast the vibration of the system are the obtained RMSof each filter 119864

119885119894 Note that the temporal duration of 119908

ℎis

configured to be short in comparison with the high dynamicsof the signal For this reason the obtained RMS should beconsidered as a signal giving information of the instantaneousvariation of the vibration RMS instead of a static feature Dueto this fact the resulting RMS presents characteristic andquantifiable dynamics that can be analyzed

119864119885119894(119905) = radic

1

119908ℎ

sdot

119871

sum

119905=1

(119910119911119894(119905) sdot ℎ (119905))

2

(7)

Prior to the model generation the identification of thebest past intervals to enhance the forecasting performanceis proposed as Step 3 The optimization process gets simpleas the search space is being bounded The interval selectionis made by calculating the correlation of the objective signal119864119885119894(119905+119901) with successive delays of the same signal119864

119885119894(119905minus119899)

where 119899 isin [0 10119901]The resulting correlation coefficient is obtained by (8) and

represents a measure of statistical similitude between 119910(119905)and its successive delays represented by 119899 The evolution ofthis coefficient as 119899 increases shows signal oscillation modesand periodicities in which the target signal and its delaysare significantly correlated Then the interval is selectedby setting a correlation threshold 119862th and selecting thoseintervals with the highest accumulated correlation

119862coef (119899) =cov (119864

119911119894(119905 minus 119899) 119864

119911119894(119905 + 119901))

120590 (119864119911119894(119905 minus 119899)) sdot 120590 (119864

119911119894(119905 + 119901))

for 119899 = 0 10119901

(8)

It is common to find modeling situations especially withvibration signals inwhich it is necessary to deal with differenttraining sets or operating conditions In these situations thesearch for the optimal intervals turns into an iterative processthat tries to localize those intervals with a consistent correla-tion and once identified select themaximum common rangethat accumulates the highest correlation

The following step Step 4 consists in the generation andthe training of the ANFIS based models to predict the energyof each filter output being respectively119872

11988511198721198852 and119872

1198853

The structure of themodels is fixed and corresponds to (i) thecurrent value of the energy in the 119894th filter 119864

119885119894(119905) (ii) a past

value of the energy in the 119894th filter delayed 1198991samples 119864

119885119894(119905minus

1198991) and (iii) another past value of the RMS in the 119894th filter

delayed 1198992samples 119864

119885119894(119905 minus 119899

2) The three inputs combined

6 Shock and Vibration

with the ANFIS model give the predicted vibration energy119864(119905 + 119901) as shown in

119864 (119905 + 119901)

=

3

sum

119894=1

ANFIS119885119894(119864119885119894(119905) 119864119885119894(119905 minus 119899

1) 119864119885119894(119905 minus 119899

2))

(9)

Although each model presents the same quantity ofinputs the delayed samples 119899

1and 119899

2could be different for

each filter depending on the optimization results The identi-fied correlation intervals are here introduced as boundariesfor the Genetic Algorithm (GA) The cost function of theoptimization procedure is defined as the Root-Mean-SquareError (RMSE) of the forecasting model that can be seen in(10) The three models are trained independently with allthe available information regarding the different operatingconditions and failure scenariosUltimately in Step 5 the finalforecasting outcome of the vibration is obtained by means ofthe direct combination of three filters models outputs

In order to evaluate the performance of the modelsclassical statistical metrics have been used which are RMSEdefined in (10)MeanAbsolute Error (MAE) in (11) andMeanAbsolute Percentage Error (MAPE) in (12) These metricshave been widely used and accepted from the researchcommunity as indicated in [28] or [29] RMSE is one ofthe most used performance metrics for the development offorecasting models it is a measure of the standard deviationof the differences between predicted values and observedvalues It is useful in order to analyze the global behavior ofthe model but it is very sensitive to the amplitude In thisregard the MAE is used to evaluate the forecast since it is lesssensitive to outliers Finally theMAPEhelps to determine themean deviation of each sample normalized by the amplitudeso it helps to unify the scale and can be used to compare theerrors of signals with different levels of amplitudes

RMSE = radicsum119871

119905=1(119864 (119905) minus (119905))

2

119871

(10)

MAE = radicsum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905))

10038161003816100381610038161003816

119871

(11)

MAPE =sum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905)) 119864 (119905)

10038161003816100381610038161003816

119871sdot 100 (12)

32 Online Behavior One of the primary characteristics ofthe proposed method is that it is prepared to work contin-uously online that is receiving new data from the machineas shown in Figure 3 Therefore after the training procedureof the method vibration signal is acquired periodically fromthe machine under study Then the signal is filtered with thedefined three digital filters and the correspondingRMSvaluesare calculated As the structure of the models and the bestpast inputs are already defined the trained models are usedto project the three energies among the specified 119901 Finallythe output of the three models is combined giving with it thenew forecasted value of the vibration energy

Gearbox

Load

VFD

DAS

Inductionmotor

AccelerometerEncoder

PC

Figure 4 Electromechanical test bench used for experimentalvalidation of the method

4 Experimental Results

The test bench used to obtain experimental vibrations isshown in Figure 4 This test bench consists of a kinematicchain composed of a three-phase 1492 119882 induction motorWEG 00236ET3E145T-W22 whose speed is controlled bya variable frequency drive (VFD) and WEG CFW08 theoperating speed being fixed to 60Hz for all experiments A4 1 ratio gearbox BALDOR GCF4X01AA is used to couplethe drive motor to a DC generator BALDOR CDP3604 TheDC motor is used as a noncontrolled mechanical load thatcomprises around 20 of the nominal torque of the drivingmotor The DAS is a proprietary low-cost design based onfield programable gate array technology The output rota-tional speed is obtained by using a digital encoder the motorstart-up is controlled by a relay in order to automatize thetest run A 12-bit 4-channel serial-output sampling analog-to-digital converter ADS7841 is used in the onboard dataacquisition system (DAS)

Vibration signal from the perpendicular plane of themotor axis is acquired using a triaxial accelerometerLIS3L02AS4 mounted on a board with the signal condition-ing and antialiasing filtering Sampling frequency is set to3 kHz for vibration acquisitionThe data retrieved by theDASis stored in a regular computer (PC)

Four scenarios have been considered that is the healthycondition HC a bearing failure (BF) condition a half-broken rotor bar (HBRB) condition and full-broken rotor bar(FBRB) The detail of the failures is shown in Figure 5 Thefailure in a 6205-2ZNR bearing has been induced by meansof a hole of 1191mm in the outer race the hole has beenproduced by a tungsten drill bit HBRB failure is artificiallyproduced by drilling a 6mm holewith a depth of 3mm thatcorresponds mostly to the 22 of the section of the rotor barFinally FBRB is produced by a through-hole with a diameterof 6mm and a depth of 14mm which corresponds to thecomplete section of the rotor bar

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

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DistributedSensor Networks

International Journal of

4 Shock and Vibration

x

x

y

y

x y

z

Input

Output

Input

L1

L2

N

N

L3L4

L5

A1

A2

B1

B2

w1

w2

w1

w2

z1w1

z2w2

sum

prod

prod

Figure 2 Adaptive network-based Fuzzy Inference System schemewith two inputs four membership functions two rules and onesingle output

system offers a reliable and robust condition predictor sinceit can capture the system dynamic behavior quickly andaccurately [27]

The neural-fuzzy architecture can be divided into fivedifferent layers as shown in Figure 2 For the specificarchitecture shown in this figure the method aims to find arelationship between the output signal 119911 and a set of differentinput signals 119909 and 119910 by means of the activation of differentpolynomials regarding the fuzzification of the input signalsby means of the membership functions 119860

1 1198602 1198611 and 119861

2

Theoutput is computed regarding the pertinence of the inputsand the two if -then rules as defined in (1)

The input layer 1198711 is in charge of addressing the input

signals to a node Each node 119892 of each layer 119895 is anadaptive node with an output function 119874119895

119892 defined in (2)

where 120583119860119892

and 120583119861119892minus2

represent the membership degree of therespective input with regard to the membership functionsIn the fuzzification layer 119871

2 the weight of each rule is

computed bymeans of a fuzzy ANDoperation thatmultipliesthe input signals The outputs of this layer 119882

119892 represent

the activation variables of a fuzzy rule (3) The fuzzy rulesdefinition layer 119871

3 provides the antecedent consequence

statements of fuzzy logic Each node calculates the reasonbetween the 119892th activation variable and the sum of all theactivation variables (4) The outputs of this layer are callednormalized activation variables 119882

119892 In the defuzzification

layer 1198714 each node computes the contribution of the 119892th

fuzzy rule over all the outputs (5) It should be noticed that119901119892 119902119892 and 119903

119892are the polynomial coefficients that would be

estimated during the learning phase of the algorithm Theoutputs of each node are named consequents The nodes ofthe output layer 119871

5 calculate the output signal 119911 as the

summation of all the input signals (6) Consider

Rule 1 if 119909 isin 1198601cup 119910 isin 119861

1997888rarr 1199111= 1199011119909 + 1199021119910 + 1199031

Rule 2 if 119909 isin 1198602cup 119910 isin 119861

2997888rarr 1199112= 1199012119909 + 1199022119910 + 1199032

(1)

1198741

119892= 120583119860119892(119909) 119892 = 1 2

1198741

119892= 120583119861119892minus2

(119910) 119892 = 3 4

(2)

1198742

119892= 119882119892= 120583119860119892(119909) sdot 120583

119861119892+2(119910) 119892 = 1 2 (3)

1198743

119892= 119882119892=

119908119892

1199081+ 1199082

119892 = 1 2 (4)

1198744

119892= 119882119892sdot 119911119892= 119882119892sdot (119901119892119909 + 119902119892119910 + 119903119892) 119892 = 1 2 (5)

1198745

119892= 119911 = sum

119892

119882119892sdot 119911119892=

sum119892119882119892sdot 119911119892

sum119892119882119892

(6)

The ANFIS structure allows the consideration of a data-driven modeling approach with adaptive rule changing capa-bility and fast convergence rate and does not require extensiveexperience about the process to include such patterns in thefuzzy rules

3 Methodology

Theobjective of the proposedmethod is tomodel and forecastthe evolution curve of the vibrationrsquos RMS signal during thestart-up and the thermal stabilization of an electromechanicalactuator The main point is to obtain a forecasting modelof the RMS capable of giving the future value with enoughresolution taking into consideration the dynamics of differentfailures occurring to the system After the output of themethod the presence of the failure can be anticipated byknowing the future value of the RMS and a simply statisticalcharacterization as a diagnosis method

Therefore the challenge is to develop a vibration modelwith enough performance in terms of forecasted signal errorand forecasting horizon that considers the dynamics modesgenerated by different faulty scenarios of different elementsof the electromechanical actuatorThe general block diagramof the method is shown in Figure 3 including the trainingprocedure and the online operation The main limitation inthe modeling of complex signals is that a unique forecastingmodel is not able to capture all the particular dynamicsthat different fault scenarios may cause In this regard themethod uses a decomposition of the vibration signal in thethree frequency bands in order to provide resolution andgeneralization towards multiple failure scenarios by improv-ing the response towards their specific spectral componentsdynamics Then the previous prefiltering stage and the RMScalculation are the authorrsquos contribution in order to increasethemodel resolution by limiting the amount of dynamics thateach ANFIS model should face

31 Training Procedure The training procedure correspondsto the off-line learning process in order to do the following (i)tuning of the structure of the forecasting models (ii) analysisof the optimum inputs delays and (iii) identification of thelongest forecasting horizon

The first step Step 1 aims to decompose the vibrationsignal 119910(119905) with a length 119871 in three different details that aremodeled with a specific ANFIS This decomposition is madewith Finite Impulse Response (FIR) digital filters the cuttingfrequencies follow theoretical considerations of mechanicalfault appearance explained in Section 21 Then the outputsignal of a certain filter 119885

119894is considered to be 119910

119911119894(119905) Three

FIR filters are defined

Shock and Vibration 5

Frequency

Signal detailsRaw signalForecasting

outcomeTarget signalT(t)

Delay selection

Delay selection

Delay selection

ANFIS

ANFIS

ANFIS

Windowed RMS Model optimization

Interval finding

Interval finding

Interval finding

Detail of training

Online behavior

Signal recombination

Training procedure

3x RMScalculation

3x RMScalculation

3x optimalGANFIS modeling

Signal recombination

Forecasting outcome

Step 1 Step 2 Step 3 Step 4

Raw signal filtering

Raw signal filtering

Step 5

Correlation based interval finding

Step 6

Step 1 Step 2 Step 3 Step 4 Step 5

3x ANFISprojection

Forecastingoutcome

Z1 Z2 Z3

RMS in Z1

RMS in Z2

RMS in Z3

sum+

Figure 3 Block diagram of the proposed method

(i) First filter band 1198851 is defined as a low pass filter and

covers the low frequency band of the spectrum Thisfilter isolates those frequencies related to the rotatingmechanical frequencies and first harmonics

(ii) Second filter band 1198852 is defined as a bandpass filter

covering the middle frequency band This band isrelated to different mechanical degradations such asbearing defects This filter isolates those componentsin order to gain forecasting resolution in these kindsof failures

(iii) Third filter band 1198853 is a bandpass that covers the

rest of the frequencies till the Nyquist frequencyIt is designed to model high frequency modes thatappear in the vibration signal under incipient failurescenarios

The next step Step 2 deals with the calculation of theenergy as a windowed Root-Mean-Square (RMS) value foreach of the three resulting filtered signals As the method isintended to be used online this calculation is made as shownin (7) that is by means of a sliding window ℎ(119905) with adefinedwidth119908

ℎ and an overlapping factor ovRMS Note that

overlapping is defined to smooth the response of the filterversus new signals Therefore the signals to be modeled toforecast the vibration of the system are the obtained RMSof each filter 119864

119885119894 Note that the temporal duration of 119908

ℎis

configured to be short in comparison with the high dynamicsof the signal For this reason the obtained RMS should beconsidered as a signal giving information of the instantaneousvariation of the vibration RMS instead of a static feature Dueto this fact the resulting RMS presents characteristic andquantifiable dynamics that can be analyzed

119864119885119894(119905) = radic

1

119908ℎ

sdot

119871

sum

119905=1

(119910119911119894(119905) sdot ℎ (119905))

2

(7)

Prior to the model generation the identification of thebest past intervals to enhance the forecasting performanceis proposed as Step 3 The optimization process gets simpleas the search space is being bounded The interval selectionis made by calculating the correlation of the objective signal119864119885119894(119905+119901) with successive delays of the same signal119864

119885119894(119905minus119899)

where 119899 isin [0 10119901]The resulting correlation coefficient is obtained by (8) and

represents a measure of statistical similitude between 119910(119905)and its successive delays represented by 119899 The evolution ofthis coefficient as 119899 increases shows signal oscillation modesand periodicities in which the target signal and its delaysare significantly correlated Then the interval is selectedby setting a correlation threshold 119862th and selecting thoseintervals with the highest accumulated correlation

119862coef (119899) =cov (119864

119911119894(119905 minus 119899) 119864

119911119894(119905 + 119901))

120590 (119864119911119894(119905 minus 119899)) sdot 120590 (119864

119911119894(119905 + 119901))

for 119899 = 0 10119901

(8)

It is common to find modeling situations especially withvibration signals inwhich it is necessary to deal with differenttraining sets or operating conditions In these situations thesearch for the optimal intervals turns into an iterative processthat tries to localize those intervals with a consistent correla-tion and once identified select themaximum common rangethat accumulates the highest correlation

The following step Step 4 consists in the generation andthe training of the ANFIS based models to predict the energyof each filter output being respectively119872

11988511198721198852 and119872

1198853

The structure of themodels is fixed and corresponds to (i) thecurrent value of the energy in the 119894th filter 119864

119885119894(119905) (ii) a past

value of the energy in the 119894th filter delayed 1198991samples 119864

119885119894(119905minus

1198991) and (iii) another past value of the RMS in the 119894th filter

delayed 1198992samples 119864

119885119894(119905 minus 119899

2) The three inputs combined

6 Shock and Vibration

with the ANFIS model give the predicted vibration energy119864(119905 + 119901) as shown in

119864 (119905 + 119901)

=

3

sum

119894=1

ANFIS119885119894(119864119885119894(119905) 119864119885119894(119905 minus 119899

1) 119864119885119894(119905 minus 119899

2))

(9)

Although each model presents the same quantity ofinputs the delayed samples 119899

1and 119899

2could be different for

each filter depending on the optimization results The identi-fied correlation intervals are here introduced as boundariesfor the Genetic Algorithm (GA) The cost function of theoptimization procedure is defined as the Root-Mean-SquareError (RMSE) of the forecasting model that can be seen in(10) The three models are trained independently with allthe available information regarding the different operatingconditions and failure scenariosUltimately in Step 5 the finalforecasting outcome of the vibration is obtained by means ofthe direct combination of three filters models outputs

In order to evaluate the performance of the modelsclassical statistical metrics have been used which are RMSEdefined in (10)MeanAbsolute Error (MAE) in (11) andMeanAbsolute Percentage Error (MAPE) in (12) These metricshave been widely used and accepted from the researchcommunity as indicated in [28] or [29] RMSE is one ofthe most used performance metrics for the development offorecasting models it is a measure of the standard deviationof the differences between predicted values and observedvalues It is useful in order to analyze the global behavior ofthe model but it is very sensitive to the amplitude In thisregard the MAE is used to evaluate the forecast since it is lesssensitive to outliers Finally theMAPEhelps to determine themean deviation of each sample normalized by the amplitudeso it helps to unify the scale and can be used to compare theerrors of signals with different levels of amplitudes

RMSE = radicsum119871

119905=1(119864 (119905) minus (119905))

2

119871

(10)

MAE = radicsum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905))

10038161003816100381610038161003816

119871

(11)

MAPE =sum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905)) 119864 (119905)

10038161003816100381610038161003816

119871sdot 100 (12)

32 Online Behavior One of the primary characteristics ofthe proposed method is that it is prepared to work contin-uously online that is receiving new data from the machineas shown in Figure 3 Therefore after the training procedureof the method vibration signal is acquired periodically fromthe machine under study Then the signal is filtered with thedefined three digital filters and the correspondingRMSvaluesare calculated As the structure of the models and the bestpast inputs are already defined the trained models are usedto project the three energies among the specified 119901 Finallythe output of the three models is combined giving with it thenew forecasted value of the vibration energy

Gearbox

Load

VFD

DAS

Inductionmotor

AccelerometerEncoder

PC

Figure 4 Electromechanical test bench used for experimentalvalidation of the method

4 Experimental Results

The test bench used to obtain experimental vibrations isshown in Figure 4 This test bench consists of a kinematicchain composed of a three-phase 1492 119882 induction motorWEG 00236ET3E145T-W22 whose speed is controlled bya variable frequency drive (VFD) and WEG CFW08 theoperating speed being fixed to 60Hz for all experiments A4 1 ratio gearbox BALDOR GCF4X01AA is used to couplethe drive motor to a DC generator BALDOR CDP3604 TheDC motor is used as a noncontrolled mechanical load thatcomprises around 20 of the nominal torque of the drivingmotor The DAS is a proprietary low-cost design based onfield programable gate array technology The output rota-tional speed is obtained by using a digital encoder the motorstart-up is controlled by a relay in order to automatize thetest run A 12-bit 4-channel serial-output sampling analog-to-digital converter ADS7841 is used in the onboard dataacquisition system (DAS)

Vibration signal from the perpendicular plane of themotor axis is acquired using a triaxial accelerometerLIS3L02AS4 mounted on a board with the signal condition-ing and antialiasing filtering Sampling frequency is set to3 kHz for vibration acquisitionThe data retrieved by theDASis stored in a regular computer (PC)

Four scenarios have been considered that is the healthycondition HC a bearing failure (BF) condition a half-broken rotor bar (HBRB) condition and full-broken rotor bar(FBRB) The detail of the failures is shown in Figure 5 Thefailure in a 6205-2ZNR bearing has been induced by meansof a hole of 1191mm in the outer race the hole has beenproduced by a tungsten drill bit HBRB failure is artificiallyproduced by drilling a 6mm holewith a depth of 3mm thatcorresponds mostly to the 22 of the section of the rotor barFinally FBRB is produced by a through-hole with a diameterof 6mm and a depth of 14mm which corresponds to thecomplete section of the rotor bar

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 5

Frequency

Signal detailsRaw signalForecasting

outcomeTarget signalT(t)

Delay selection

Delay selection

Delay selection

ANFIS

ANFIS

ANFIS

Windowed RMS Model optimization

Interval finding

Interval finding

Interval finding

Detail of training

Online behavior

Signal recombination

Training procedure

3x RMScalculation

3x RMScalculation

3x optimalGANFIS modeling

Signal recombination

Forecasting outcome

Step 1 Step 2 Step 3 Step 4

Raw signal filtering

Raw signal filtering

Step 5

Correlation based interval finding

Step 6

Step 1 Step 2 Step 3 Step 4 Step 5

3x ANFISprojection

Forecastingoutcome

Z1 Z2 Z3

RMS in Z1

RMS in Z2

RMS in Z3

sum+

Figure 3 Block diagram of the proposed method

(i) First filter band 1198851 is defined as a low pass filter and

covers the low frequency band of the spectrum Thisfilter isolates those frequencies related to the rotatingmechanical frequencies and first harmonics

(ii) Second filter band 1198852 is defined as a bandpass filter

covering the middle frequency band This band isrelated to different mechanical degradations such asbearing defects This filter isolates those componentsin order to gain forecasting resolution in these kindsof failures

(iii) Third filter band 1198853 is a bandpass that covers the

rest of the frequencies till the Nyquist frequencyIt is designed to model high frequency modes thatappear in the vibration signal under incipient failurescenarios

The next step Step 2 deals with the calculation of theenergy as a windowed Root-Mean-Square (RMS) value foreach of the three resulting filtered signals As the method isintended to be used online this calculation is made as shownin (7) that is by means of a sliding window ℎ(119905) with adefinedwidth119908

ℎ and an overlapping factor ovRMS Note that

overlapping is defined to smooth the response of the filterversus new signals Therefore the signals to be modeled toforecast the vibration of the system are the obtained RMSof each filter 119864

119885119894 Note that the temporal duration of 119908

ℎis

configured to be short in comparison with the high dynamicsof the signal For this reason the obtained RMS should beconsidered as a signal giving information of the instantaneousvariation of the vibration RMS instead of a static feature Dueto this fact the resulting RMS presents characteristic andquantifiable dynamics that can be analyzed

119864119885119894(119905) = radic

1

119908ℎ

sdot

119871

sum

119905=1

(119910119911119894(119905) sdot ℎ (119905))

2

(7)

Prior to the model generation the identification of thebest past intervals to enhance the forecasting performanceis proposed as Step 3 The optimization process gets simpleas the search space is being bounded The interval selectionis made by calculating the correlation of the objective signal119864119885119894(119905+119901) with successive delays of the same signal119864

119885119894(119905minus119899)

where 119899 isin [0 10119901]The resulting correlation coefficient is obtained by (8) and

represents a measure of statistical similitude between 119910(119905)and its successive delays represented by 119899 The evolution ofthis coefficient as 119899 increases shows signal oscillation modesand periodicities in which the target signal and its delaysare significantly correlated Then the interval is selectedby setting a correlation threshold 119862th and selecting thoseintervals with the highest accumulated correlation

119862coef (119899) =cov (119864

119911119894(119905 minus 119899) 119864

119911119894(119905 + 119901))

120590 (119864119911119894(119905 minus 119899)) sdot 120590 (119864

119911119894(119905 + 119901))

for 119899 = 0 10119901

(8)

It is common to find modeling situations especially withvibration signals inwhich it is necessary to deal with differenttraining sets or operating conditions In these situations thesearch for the optimal intervals turns into an iterative processthat tries to localize those intervals with a consistent correla-tion and once identified select themaximum common rangethat accumulates the highest correlation

The following step Step 4 consists in the generation andthe training of the ANFIS based models to predict the energyof each filter output being respectively119872

11988511198721198852 and119872

1198853

The structure of themodels is fixed and corresponds to (i) thecurrent value of the energy in the 119894th filter 119864

119885119894(119905) (ii) a past

value of the energy in the 119894th filter delayed 1198991samples 119864

119885119894(119905minus

1198991) and (iii) another past value of the RMS in the 119894th filter

delayed 1198992samples 119864

119885119894(119905 minus 119899

2) The three inputs combined

6 Shock and Vibration

with the ANFIS model give the predicted vibration energy119864(119905 + 119901) as shown in

119864 (119905 + 119901)

=

3

sum

119894=1

ANFIS119885119894(119864119885119894(119905) 119864119885119894(119905 minus 119899

1) 119864119885119894(119905 minus 119899

2))

(9)

Although each model presents the same quantity ofinputs the delayed samples 119899

1and 119899

2could be different for

each filter depending on the optimization results The identi-fied correlation intervals are here introduced as boundariesfor the Genetic Algorithm (GA) The cost function of theoptimization procedure is defined as the Root-Mean-SquareError (RMSE) of the forecasting model that can be seen in(10) The three models are trained independently with allthe available information regarding the different operatingconditions and failure scenariosUltimately in Step 5 the finalforecasting outcome of the vibration is obtained by means ofthe direct combination of three filters models outputs

In order to evaluate the performance of the modelsclassical statistical metrics have been used which are RMSEdefined in (10)MeanAbsolute Error (MAE) in (11) andMeanAbsolute Percentage Error (MAPE) in (12) These metricshave been widely used and accepted from the researchcommunity as indicated in [28] or [29] RMSE is one ofthe most used performance metrics for the development offorecasting models it is a measure of the standard deviationof the differences between predicted values and observedvalues It is useful in order to analyze the global behavior ofthe model but it is very sensitive to the amplitude In thisregard the MAE is used to evaluate the forecast since it is lesssensitive to outliers Finally theMAPEhelps to determine themean deviation of each sample normalized by the amplitudeso it helps to unify the scale and can be used to compare theerrors of signals with different levels of amplitudes

RMSE = radicsum119871

119905=1(119864 (119905) minus (119905))

2

119871

(10)

MAE = radicsum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905))

10038161003816100381610038161003816

119871

(11)

MAPE =sum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905)) 119864 (119905)

10038161003816100381610038161003816

119871sdot 100 (12)

32 Online Behavior One of the primary characteristics ofthe proposed method is that it is prepared to work contin-uously online that is receiving new data from the machineas shown in Figure 3 Therefore after the training procedureof the method vibration signal is acquired periodically fromthe machine under study Then the signal is filtered with thedefined three digital filters and the correspondingRMSvaluesare calculated As the structure of the models and the bestpast inputs are already defined the trained models are usedto project the three energies among the specified 119901 Finallythe output of the three models is combined giving with it thenew forecasted value of the vibration energy

Gearbox

Load

VFD

DAS

Inductionmotor

AccelerometerEncoder

PC

Figure 4 Electromechanical test bench used for experimentalvalidation of the method

4 Experimental Results

The test bench used to obtain experimental vibrations isshown in Figure 4 This test bench consists of a kinematicchain composed of a three-phase 1492 119882 induction motorWEG 00236ET3E145T-W22 whose speed is controlled bya variable frequency drive (VFD) and WEG CFW08 theoperating speed being fixed to 60Hz for all experiments A4 1 ratio gearbox BALDOR GCF4X01AA is used to couplethe drive motor to a DC generator BALDOR CDP3604 TheDC motor is used as a noncontrolled mechanical load thatcomprises around 20 of the nominal torque of the drivingmotor The DAS is a proprietary low-cost design based onfield programable gate array technology The output rota-tional speed is obtained by using a digital encoder the motorstart-up is controlled by a relay in order to automatize thetest run A 12-bit 4-channel serial-output sampling analog-to-digital converter ADS7841 is used in the onboard dataacquisition system (DAS)

Vibration signal from the perpendicular plane of themotor axis is acquired using a triaxial accelerometerLIS3L02AS4 mounted on a board with the signal condition-ing and antialiasing filtering Sampling frequency is set to3 kHz for vibration acquisitionThe data retrieved by theDASis stored in a regular computer (PC)

Four scenarios have been considered that is the healthycondition HC a bearing failure (BF) condition a half-broken rotor bar (HBRB) condition and full-broken rotor bar(FBRB) The detail of the failures is shown in Figure 5 Thefailure in a 6205-2ZNR bearing has been induced by meansof a hole of 1191mm in the outer race the hole has beenproduced by a tungsten drill bit HBRB failure is artificiallyproduced by drilling a 6mm holewith a depth of 3mm thatcorresponds mostly to the 22 of the section of the rotor barFinally FBRB is produced by a through-hole with a diameterof 6mm and a depth of 14mm which corresponds to thecomplete section of the rotor bar

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

with the ANFIS model give the predicted vibration energy119864(119905 + 119901) as shown in

119864 (119905 + 119901)

=

3

sum

119894=1

ANFIS119885119894(119864119885119894(119905) 119864119885119894(119905 minus 119899

1) 119864119885119894(119905 minus 119899

2))

(9)

Although each model presents the same quantity ofinputs the delayed samples 119899

1and 119899

2could be different for

each filter depending on the optimization results The identi-fied correlation intervals are here introduced as boundariesfor the Genetic Algorithm (GA) The cost function of theoptimization procedure is defined as the Root-Mean-SquareError (RMSE) of the forecasting model that can be seen in(10) The three models are trained independently with allthe available information regarding the different operatingconditions and failure scenariosUltimately in Step 5 the finalforecasting outcome of the vibration is obtained by means ofthe direct combination of three filters models outputs

In order to evaluate the performance of the modelsclassical statistical metrics have been used which are RMSEdefined in (10)MeanAbsolute Error (MAE) in (11) andMeanAbsolute Percentage Error (MAPE) in (12) These metricshave been widely used and accepted from the researchcommunity as indicated in [28] or [29] RMSE is one ofthe most used performance metrics for the development offorecasting models it is a measure of the standard deviationof the differences between predicted values and observedvalues It is useful in order to analyze the global behavior ofthe model but it is very sensitive to the amplitude In thisregard the MAE is used to evaluate the forecast since it is lesssensitive to outliers Finally theMAPEhelps to determine themean deviation of each sample normalized by the amplitudeso it helps to unify the scale and can be used to compare theerrors of signals with different levels of amplitudes

RMSE = radicsum119871

119905=1(119864 (119905) minus (119905))

2

119871

(10)

MAE = radicsum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905))

10038161003816100381610038161003816

119871

(11)

MAPE =sum119871

119905=1

10038161003816100381610038161003816(119864 (119905) minus (119905)) 119864 (119905)

10038161003816100381610038161003816

119871sdot 100 (12)

32 Online Behavior One of the primary characteristics ofthe proposed method is that it is prepared to work contin-uously online that is receiving new data from the machineas shown in Figure 3 Therefore after the training procedureof the method vibration signal is acquired periodically fromthe machine under study Then the signal is filtered with thedefined three digital filters and the correspondingRMSvaluesare calculated As the structure of the models and the bestpast inputs are already defined the trained models are usedto project the three energies among the specified 119901 Finallythe output of the three models is combined giving with it thenew forecasted value of the vibration energy

Gearbox

Load

VFD

DAS

Inductionmotor

AccelerometerEncoder

PC

Figure 4 Electromechanical test bench used for experimentalvalidation of the method

4 Experimental Results

The test bench used to obtain experimental vibrations isshown in Figure 4 This test bench consists of a kinematicchain composed of a three-phase 1492 119882 induction motorWEG 00236ET3E145T-W22 whose speed is controlled bya variable frequency drive (VFD) and WEG CFW08 theoperating speed being fixed to 60Hz for all experiments A4 1 ratio gearbox BALDOR GCF4X01AA is used to couplethe drive motor to a DC generator BALDOR CDP3604 TheDC motor is used as a noncontrolled mechanical load thatcomprises around 20 of the nominal torque of the drivingmotor The DAS is a proprietary low-cost design based onfield programable gate array technology The output rota-tional speed is obtained by using a digital encoder the motorstart-up is controlled by a relay in order to automatize thetest run A 12-bit 4-channel serial-output sampling analog-to-digital converter ADS7841 is used in the onboard dataacquisition system (DAS)

Vibration signal from the perpendicular plane of themotor axis is acquired using a triaxial accelerometerLIS3L02AS4 mounted on a board with the signal condition-ing and antialiasing filtering Sampling frequency is set to3 kHz for vibration acquisitionThe data retrieved by theDASis stored in a regular computer (PC)

Four scenarios have been considered that is the healthycondition HC a bearing failure (BF) condition a half-broken rotor bar (HBRB) condition and full-broken rotor bar(FBRB) The detail of the failures is shown in Figure 5 Thefailure in a 6205-2ZNR bearing has been induced by meansof a hole of 1191mm in the outer race the hole has beenproduced by a tungsten drill bit HBRB failure is artificiallyproduced by drilling a 6mm holewith a depth of 3mm thatcorresponds mostly to the 22 of the section of the rotor barFinally FBRB is produced by a through-hole with a diameterof 6mm and a depth of 14mm which corresponds to thecomplete section of the rotor bar

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

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Active and Passive Electronic Components

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Acoustics and VibrationAdvances in

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Advances inOptoElectronics

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

Shock and Vibration 7

(a) (b) (c)

Figure 5 Detail of the failures produced in the test bench (a) corresponds to the bearing failure BF (b) corresponds to the 12-broken rotorbar HBRB and (c) to 1 broken rotor bar FBRB

minus4minus2

024

Acce

lera

tion

(g)

500 1000 1500 2000 2500 300025303540

Time (s)

500 1000 1500 2000 2500 3000Time (s)

Tem

pera

ture

(∘C)

Figure 6 Evolution of the acceleration signal versus the motortemperature

Two different datasets with the same length have beenacquired the first one is used to train the proposed methodand the second dataset is used to validate the performanceof the method In this regard periodical acquisitions of30 seconds containing 90 ksamples are obtained from theaccelerometer the acquisitions are temporally spaced at 30seconds The average duration of the experiments for alloperating conditions is configured to be 3600 seconds

The selected duration allows obtaining the completeresponse of the vibrations with regard to the thermal stabilityof the electromechanical system This is done in order toconsider the thermal evolution of the vibrations as part ofthe system and facilitate the representation of the failureThe proposed approach brings the experimental validationcloser to the real behavior of complex industrial machineryin which the behavior of the vibration presents a nonconstantdynamic from the starting point till its steady state As aresult the modeling of the vibration considering the thermalevolution represents an additional challenge to the validationof the proposed method Furthermore Figure 6 shows thebehavior of the vibration in healthy condition HC withregard to the temperature of themotor from the starting pointtill the end of the experiment note that the thermal steadystate is reached

Table 1 Design characteristics of the three digital filters used todecompose the vibration signal Calculations made for a samplingfrequency of 3 kHz

Filter Cut-off frequency 1 Cut-off frequency 2 Order1198651198851

0Hz 120Hz 2481198651198852

120Hz 350Hz 1361198651198853

350Hz 1000Hz 120

As can be appreciated in Figure 6 the raw signal ofthe acceleration gives no important information regardingthe condition of the system since it is difficult to detectunderlying patterns such as the affectation of the thermalstabilization since it ismodulated in the oscillatorywaveformof the vibration For this reason the necessity of calculating astatistical feature representative of the condition of the systemis justified after the preprocessing stage

The vibration signal filtering and the correspondingwindowed RMS calculation are carried out by means ofFIR filters and considering the rotating speed the samplingfrequency and also the theoretical background with regardto mechanical failures As a result the cut-off frequenciesof the filters in order to isolate the three primary frequencybands 119885

1 1198852 and 119885

3 are shown in Table 1 The attenuation

is fixed to get minus60 dB in the cutting frequency It should benoticed that as it was expected the order of the filter decreaseswith the bands since the bandwidth of each filter increases

Finally the RMS feature is calculated for each filteroutput the results are 3 RMS signals that summarize theinformation regarding the vibration of the electromechanicalactuator under a concrete failure condition and are the targetsignals to be modeled For this experimental application thetemporal window is configured to be 119908

ℎ= 3000 samples

which corresponds to a window of 1 second of actuatoroperation and an overlapping factor of ovRMS = 25 isselected to smooth the filter responseThe resulting signals tobe predicted are shown in Figure 7 for all considered failuresHow the faulty signal corresponding to a bearing fault ismostly located as it was expected in the second filter 119885

2

from 100 to 500Hz can be appreciatedThe figure justifies thedecomposition of the signal since different spectral behavior

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

005

1RM

S [0

-1]

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

(a)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(b)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(c)

005

1

1000 2000 3000 4000 5000 6000Time (s)

RMS F1RMS F2

RMS F3

RMS

[0-1

]

(d)

Figure 7 RMS of each filter output for all operating conditions (a) HS (b) BF (c) FBRB and (d) HBRB

0 500 1000 1500 2000 2500 3000 350008

1

12

14

16

18

2

Time (s)

RMS

(g)

HCBF

FBRBHBRB

Figure 8 RMS of the vibration signal during the thermal stabiliza-tion period Note that the different failures can be identified duringthis period and as it was expected the BF case shows the highestvibration

can be observed in each filter output with the presence offailure This means that each specific failure focuses its affec-tation to a certain frequency band conclusion that matcheswith the theoretical considerations exposed previously Thenext step in the method deals with the design and thegeneration of the optimal dedicatedANFIS forecastingmodelfor each filter output

Finally to understand the fundamentals of the methodFigure 8 shows the characteristic RMS signature of each faultycondition It demonstrates how the calculated RMS providesthe necessary information to distinguish the different failurespresented in the systemduring the thermal stabilization of theactuator It also justifies the suitability of modeling the RMSof the vibration signal for forecasting and diagnosis purposesIt should be remarked that these RMS are the target signals tobe obtained by the models in the defined forecasting horizon119901 the final result of the proposed method

41 Study of Forecasting Horizon Selection The selection ofthe forecasting horizon is a crucial step that needs to be facedbefore the modeling Most of the related literature selects theforecasting horizon simply by application requirements Yetthe procedure to analyze the behavior of the target signalto find the optimal forecasting horizon is not established inthe literature It is proposed then in this work to selectthe optimal horizon by analyzing the performances of themethod at different horizon values

The proposed analysis interval comprises from 119901 = 1

sample 1 sec to 119901 = 600 samples with an increase ratioof 119875inc = 5 Once the evaluation range is established theproposed models are trained and evaluated iteratively for allthe specified horizons The forecasted outcome of the threemodels is evaluated by the proposed performance metricsconsidering the four operating conditions As a result themean performance of all operating conditions with regardto the metric used and the evaluated model is shown inFigure 9 Nevertheless the error of the model depends onthe performance of the optimization algorithm used to selectthe best past inputs for this reason a smoothed response ofthe error has been generated in order to estimate the averageexpected error with the selected horizon

The general results show that as it was expected in timeseries forecasting applications in which the forecasted signaldoes not present a periodic pattern the lowest error can befound in the initial area that comprises 119901 = [1ndash50] Thenthe error increases for all the models especially the modelof the first frequency band that exhibits a linear behavior byincreasing gradually with the forecasting horizon Howeverfor the model of the second and third frequency bands thereis a second decay of error growth around 119901 = 200 Thisarea also represents a low error region that can be utilized todevelop the forecasting models and thus 119901 = 200 is selectedfor the current application

In specific conclusions it should be noticed that lowfrequency dynamics are easier to be modeled independentlyof the selected forecasting horizon since they represent

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

0

05

1

0 200 400 600Forecasting horizon

RMSE

0 200 400 600Forecasting horizon

0

05

1

RMSE

0 200 400 600Forecasting horizon

0

05

1RM

SERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(a)

0 200 400 600Forecasting horizon

0

50

100M

APE

0 200 400 600Forecasting horizon

0

50

100

MA

PE

0 200 400 600Forecasting horizon

0

50

100

MA

PERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(b)

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

E

0 200 400 600Forecasting horizon

0

05

1

MA

ERM

S of

Fz1

RMS

ofFz2

RMS

ofFz3

(c)

Figure 9 Study of the affectation of the forecasting horizon to the forecasting performance

the tendency of the vibration and thus they suffer slowerchanges among time It should be observed how errorincreases in the higher frequency bands since fast dynamicsare more punctual and closely related to adjacent samples ofthe current vibration value

42 Competency of theMethod Theproposedmethod beginsonce the forecasting horizon is selected and the RMS of thethree filter outputs is calculated The structure of the threemodels 119872

1198851 1198721198852 and 119872

1198853 is fixed by a single output

119864119885119894(119905 + 119901) and three inputs (i) 119864

119885119894(119905) (ii) 119864

119885119894(119905 minus 119899

1119894) and

(iii) 119864119885119894(119905 minus 1198992119894)

At this point the problem derives to the selection of thebest past values 119899

1119894and 119899

2119894 for each frequency band To do

so a generic GA based optimization algorithmhas been usedYet in order to increase the effectiveness of the optimizationand reduce the associated computational cost in terms ofsearch iterations the method proposes a prior past indexinterval finding step The correlation coefficient (8) has beencalculated for each filter considering the average correlationbetween all the considered scenarios

Due to the fast dynamics of the acquired vibrationsignal the delayed signals of more than 20 acquisitions areconsidered to be nonsignificant for the application thereforethe total number of delayed signals is set to 600 Theamount of necessary correlation to consider a strong relationbetween the target signal and its self-delayed signals is notdefined Thus the experimental results show that usefulintervals are considered with a correlation threshold above40 (119862th gt 04) Additionally in order to avoid finding emptyintervals in which only few indexes are found intervals witha length lower than 5 indexes are discarded The interval thataccumulates the highest 119862th value is selected as the upperand lower values constraints of the optimization algorithm

Figure 10 shows the average correlation coefficient for theexperimental set-up

The correlation of the target signal in 1198851shows a quick

drop in the correlation coefficient in the first 20 delays thisbehavior is characteristic of vibration forecasting applica-tions such as the used test bench since the dependenceof the target signal with the correlative delays is high Thecorrelation coefficient decreases continuously until delay 200where there is an area between delays 200 to 400 in which thecoefficient increases moderately This coefficient increase isdue to a certain similarity that can be found in the signalThisinterval can be exploded by the GA in order to find the bestindex for119872

1198851This fact confirms the previous selection of the

forecasting horizon for 1198851since the correlation increases in

the same area that the selected horizon doesThe correlation of119885

2presents a smoother decrease of the

coefficient as the delay time increases Moreover it presentssome oscillations as the delay increases this resonancecorresponds to signal periodicities that are characteristicof the dynamics of the signal These periodicities can beused to enhance the forecasting capabilities of the modelsince the past signals introduced are more correlated to thetarget signal In this regard the selected interval in 119872

1198852to

exploit these periodicities is set at 1198681198852= [200 350] seconds

Note that another time the periodicity also matches withthe selected horizon extracted from the proposed methoderror analysis Additionally notice that the correlation inthe second band is the highest with regard to the othersThis happens because the fundamental harmonic of theoperating speed is allocated primarily in the second bandand therefore it presents a softdynamic easier to bemodeled

Finally 1198853exhibits a lower correlation coefficient for

the entire analyzed interval This behavior is expected sinceit corresponds to the highest frequency band In vibration

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

0 100 200 300 400 500 600

07

08

09

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(a)

0 100 200 300 400 500 60002

04

06

08

1

Delayed signals (s)

Cor

relat

ion

coeffi

cien

t

(b)

0 100 200 300 400 500 600Delayed signals (s)

0

05

1C

orre

latio

n co

effici

ent

(c)

Figure 10 Correlation coefficient for each target RMS (a) corresponds to the correlation in the first band RMS1198851 (b) to RMS

1198852 and (c) to

RMS1198853

Table 2 Selected past index as a result from the constrained GAbased optimization

1198991

1198992

1198721198851

217 3891198721198852

285 3971198721198853

247 348

forecasting the high frequency band is closely related tonoise while the system is working in proper condition butit is modified with the apparition of incipient failures Thisbehavior near the noise makes the signal chaotic and onlydependent to adjacent past values this causes the coefficientto drop quickly as the delay increases Despite this fact thereis an increase of the coefficient in the interval of 119868

1198852=

[200 350] that could be taken advantage of by the model1198721198853In the proposed ANFIS modeling structure each input is

normalized with the minndashmax method in order to obtain arange from 0 to 1 The inputs are fuzzified by means of threegeneralized bell-shaped membership functions The modelis trained for 15 epochs by means of the classical hybridlearning algorithm which is the combination of the least-squares method and the backpropagation gradient descentmethodThe resulting past value indexes after 20 generationsof the GA are shown in Table 2 Note that the indexes arereferenced to the absolute delay to get the relative indexes119901 value must be subtracted

As a result the forecasting models have been trained andvalidated using the validation set The performance of themodel for all operating conditions is quantitatively analyzed

by means of RMSE MAE and MAPE coefficients shown inTable 3

The modeling of each frequency band vibration presentsremarkable results for all operating conditions as it achievesa MAPE lower than 5 in all operating conditions Nev-ertheless the healthy condition presents a dynamic that ismore difficult to model in comparison with the others Thebehavior of the vibration in healthy condition presents asteady pattern since there is an absence of a strong signaturerelated to the failure such as the BF case This healthy patternshould seem a priori easier to be modeled however as themodel is being forced to learn different dynamics it dedicatesmore efforts to those datasets that are similar to each other

As a consequence the healthy state presents a differentdynamic with regard to the faulty scenarios and thereforethe modeling error slightly increases around 2 of errorincrease in terms of MAPE The learning ability of themodel is finite thus there should be a trade-off betweenthe number of different dynamics that the model needs toconsider and the performance achieved by the model versusa single set Furthermore regarding the models the bestperformance is achieved by119872

1198853 since it presents the lowest

RMSE for all datasets This means that the model does notpresent outliers and the forecasted outcome follows the targetsignal in its mean value Regarding the operating conditionthe bearing failure is the easiest scenario to be modeledin bands 1198851 and 1198852 since the fault signature presents amonotonic dynamic easily to be captured by the modelThe outputs of three models are combined to obtain thefinal forecasting information In this regard the predictionperformance during the validation can be seen in Figure 11The adjustment of the models can be appreciated in Figure 11and in the performance metrics shown in Table 4

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

Table 3 Error achieved by the model with the four different sets used in the experimental validation 1198641corresponds to RMSE 119864

2to MAPE

and 1198643to MAE

1198721198851

HC1198641

00141198721198852

HC1198641

00201198721198853

HC1198641

00071198642

3654 1198642

4120 1198642

12121198643

01 1198643

0127 1198643

0075

1198721198851

BF1198641

00101198721198852

BF1198641

00141198721198853

BF1198641

00051198642

1699 1198642

1213 1198642

07841198643

009 1198643

0097 1198643

0065

1198721198851

HBRB1198641

00991198721198852

HBRB1198641

00171198721198853

HBRB1198641

00051198642

1625 1198642

2245 1198642

07451198643

0084 1198643

0116 1198643

0063

1198721198851

FBRB1198641

00181198721198852

FBRB1198641

00141198721198853

FBRB1198641

00071198642

3397 1198642

2815 1198642

10021198643

0118 1198643

0105 1198643

0073

1198721198851

Mean1198641

00131198721198852

Mean1198641

00161198721198853

Mean1198641

00061198642

25937 1198642

25981 1198642

09361198643

00982 1198643

0111 1198643

0069

0 500 1000 1500 2000 2500 30001

111213

Time (s)

RMS

(g)

TargetPredicted

(a)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

1314151617

RMS

(g)

(b)

0 500 1000 1500 2000 2500 3000Time (s)

TargetPredicted

121314

RMS

(g)

(c)

0 500 1000 1500 2000 2500 3000Time (s)

1516171819

RMS

(g)

TargetSingle model

Predicted

(d)

Figure 11 Results of the forecasting method (a) Combined output applied to HC (b) Combined output applied to HBRB (c) Combinedoutput applied to FBRB (d) Combined output applied to BF versus the output of the single model method to the same scenario

Table 4 Performance of the statistical error metrics applied to thecombination of all model outputs Also the performance of theforecasting without the frequency decomposition is also shown inthe table

Method Single modelingRMSE MAPE MAE RMSE MAPE MAE

HC 0013 169 0135 0203 345 0129BF 0020 227 0125 0275 677 0265HBRB 0022 282 0133 0478 692 0184FBRB 0025 344 0139 0394 893 0192

The results show that when the outputs of the threemodels are combined the obtained signals outperform interms of error the individual results of all models In this

regard low error is achieved in all the considered scenariosThe method is capable of obtaining a MAPE lower than 2in all the cases studied Also the MAE shows the stability ofthe output by maintaining the absolute error near 0125 in allcases Additionally as can be seen in the figure and by termsof RMSE the proposed method presents a smooth responsethat presents a marginal number of outliers

To conclude the results the performance of the proposedmethod is tested versus a forecasting approach in whichthe vibration signal is not decomposed The performanceachieved by the secondmethod is named singlemodeling thatcan be also seen in Table 4

The main limitation of the single model approach is thatdespite the fact that the model is able to learn the firstscenario HC with virtually fewer errors than the proposed

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

method it is not capable of modeling additional dynamicscontained in the other scenarios For example as it can beseen in Figure 11(d) themodel gets lostwith theBF set whichfurthermore was the easiest to be modeled with the methodThe point here is that the amount of signal dynamic eachforecasting model can face is limited and thus by filteringthe vibration signal and facing the forecasting problem froma signal decomposition point of view the final performanceand the adaptability of themodels towards different behaviorsand operating condition increase

5 Conclusions

This paper presents a novel vibration signal modelingmethodology applied to a kinematic chain under differentfailure conditions First it should be pointed that the RMSvalues of the vibration have been proved to be a representativefeature regarding the health condition of the electromechan-ical actuator

Furthermore there are three important aspects in thisnew method having a strong implication in the vibrationforecasting field The first one is the application of a sig-nal decomposition strategy It has been proved that signaldecomposition allows a better characterization of the signaldynamics and improves the forecasting accuracy by reducingthe amount of dynamic that each model should face Thesecond is the optimal model configuration by means ofthe proposed analysis of the prediction horizon and timedelays This analysis leads to an optimal configuration ofthe optimization and thus the simplification of the processassuring the convergence to a reliable and robust forecastingThe third is the calculation of the forecasting value bymeans of the linear combination of the models How thecombination of the three individual models concludes ina better performance when facing the original forecastingmethod has been seen this fact is evidenced when theproposed method is compared with the classical approachwith only one model

For the experimental validation of the method fourdifferent operating conditions have been considered whichrepresent an important range of system condition possi-bilities Under these experimental conditions the proposedprognosismethodology achieves reliable results with an errorlower than 2 in all the exposed scenarios Moreover con-sidering the analyzed model error parameters the prognosismethodology shows still enough dynamic range to includeadditional patterns

The aim of the study has been to propose a new reliableprognosismethodology for diagnosis analysis undermultiplefailure conditions The study is based on different motorfaults scenarioTherefore it should be pointed that the resultsobtained in this work suggest that this methodology may bealso useful for any other component in the kinematic chain

A limitation of this study is that the affectation of othersources of information such as the temperature of the motoror the stator current has not been consideredThis additionalinformation should be correlated with the vibration of thesystem and thus may help to increase the response and

adaptation capabilities of the models towards new scenariosIn this regard further research can be focused on investigat-ing information management methods such as informationcompression or topology preservation to exploit and addother information available in the kinematic chain in thedesign of the forecasting models

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the Spanish Ministryof Education Culture and Sport under Grant FPU1300589The authors also wish to acknowledge financial support fromthe Generalitat de Catalunya (GRC MCIA Grant no SGR2014-101)

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] G Medina-Oliva P Weber and B Iung ldquoIndustrial systemknowledge formalization to aid decision making in mainte-nance strategies assessmentrdquo Engineering Applications of Arti-ficial Intelligence vol 37 pp 343ndash360 2015

[3] B Liu S F Ling and R Gribonval ldquoBearing failure detectionusing matching pursuitrdquo NDT amp E International vol 35 no 4pp 255ndash262 2002

[4] Z F Ninoslav B Rusmir and D Cvetkovic ldquoVibration featureextraction methods for gear faults diagnosismdasha reviewrdquo FactaUniversitatis Series Working and Living Environmental Protec-tion vol 12 no 1 pp 63ndash72 2015

[5] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[6] H Ozturk I Yesilyurt andM Sabuncu ldquoInvestigation of effec-tiveness of some vibration-based techniques in early detectionof real-time fatigue failure in gearsrdquo Shock and Vibration vol 17no 6 pp 741ndash757 2010

[7] R B Randall and J Antoni ldquoRolling element bearingdiagnosticsmdasha tutorialrdquoMechanical Systems and Signal Process-ing vol 25 no 2 pp 485ndash520 2011

[8] H Taplak S Erkaya and I Uzmay ldquoExperimental analysison fault detection for a direct coupled rotor-bearing systemrdquoMeasurement vol 46 no 1 pp 336ndash344 2013

[9] R Jiang J Chen G Dong T Liu andW Xiao ldquoThe weak faultdiagnosis and condition monitoring of rolling element bearingusingminimum entropy deconvolution and envelop spectrumrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 227 no 5 pp1116ndash1129 2013

[10] M E H Benbouzid ldquoA review of induction motors signatureanalysis as a medium for faults detectionrdquo IEEE Transactions onIndustrial Electronics vol 47 no 5 pp 984ndash993 2000

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

[11] B T Holm-Hansen and R X Gao ldquoVibration analysis ofa sensor-integrated ball bearingrdquo Journal of Vibration andAcoustics vol 122 no 4 pp 384ndash392 2000

[12] A Heng S Zhang A C C Tan and J Mathew ldquoRotatingmachinery prognostics state of the art challenges and oppor-tunitiesrdquo Mechanical Systems and Signal Processing vol 23 no3 pp 724ndash739 2009

[13] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptiveneuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[14] H Henao G-A Capolino M Fernandez-Cabanas et alldquoTrends in fault diagnosis for electrical machines a review ofdiagnostic techniquesrdquo IEEE Industrial Electronics Magazinevol 8 no 2 pp 31ndash42 2014

[15] J Ben Ali N Fnaiech L Saidi B Chebel-Morello and FFnaiech ldquoApplication of empirical mode decomposition andartificial neural network for automatic bearing fault diagnosisbased on vibration signalsrdquo Applied Acoustics vol 89 pp 16ndash272015

[16] J Lee FWuW ZhaoM Ghaffari L Liao andD Siegel ldquoProg-nostics and health management design for rotary machinerysystemsmdashreviews methodology and applicationsrdquo MechanicalSystems and Signal Processing vol 42 no 1-2 pp 314ndash334 2014

[17] T Khan L Udpa and S Udpa ldquoParticle filter based prognosisstudy for predicting remaining useful life of steam generatortubingrdquo in Proceedings of the 2011 IEEE International Conferenceon Prognostics and Health Management (PHM rsquo11) pp 1ndash6IEEE Montreal Canada June 2011

[18] Z Fan G Liu X Si Q Zhang and Q Zhang ldquoDegradationdata-driven approach for remaining useful life estimationrdquoJournal of Systems Engineering and Electronics vol 24 no 1 pp173ndash182 2013

[19] C Chen B ZhangGVachtsevanos andMOrchard ldquoMachinecondition prediction based on adaptive neuro-fuzzy and high-order particle filteringrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 9 pp 4353ndash4364 2011

[20] D Wang C Li A Widodo P K Kankar and W CaesarendraldquoFault diagnosis and prognosis of critical componentsrdquo Shockand Vibration vol 2016 Article ID 9597656 3 pages 2016

[21] Q Zhang F Liu X Wan and G Xu ldquoAn adaptive supportvector regressionmachine for the state prognosis of mechanicalsystemsrdquo Shock and Vibration vol 2015 Article ID 469165 8pages 2015

[22] A C Chasalevris P G Nikolakopoulos and C A Papadopou-los ldquoDynamic effect of bearing wear on rotor-bearing systemresponserdquo Journal of Vibration and Acoustics vol 135 no 1Article ID 011008 12 pages 2013

[23] C Bianchini F Immovilli M Cocconcelli R Rubini and ABellini ldquoFault detection of linear bearings in brushlessAC linearmotors by vibration analysisrdquo IEEE Transactions on IndustrialElectronics vol 58 no 5 pp 1684ndash1694 2011

[24] J A Carino D Zurita M Delgado J A Ortega and R JRomero-Troncoso ldquoHierarchical classification scheme basedon identification isolation and analysis of conflictive regionsrdquoin Proceedings of the 19th IEEE International Conference onEmerging Technologies and Factory Automation (ETFA rsquo14) pp1ndash8 IEEE Barcelona Spain September 2014

[25] P Girdhar and C Scheffer Practical Machinery VibrationAnalysis and Predictive Maintenance Elsevier 2004

[26] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[27] D Wijayasekara O Linda M Manic and C Rieger ldquoFN-DFE fuzzy-neural data fusion engine for enhanced resilientstate-awareness of hybrid energy systemsrdquo IEEETransactions onCybernetics vol 44 no 11 pp 2065ndash2075 2014

[28] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[29] A Davydenko and R Fildes ldquoMeasuring forecasting accuracythe case of judgmental adjustments to SKU-level demandforecastsrdquo International Journal of Forecasting vol 29 no 3 pp510ndash522 2013

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of