v14n3a6

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Computacin y Sistemas Vol. 14 No. 3, 2011, 269-282ISSN 1405-5546

Fault Detection in a Heat Exchanger, Comparative Analysisbetween Dynamic Principal Component Analysis and Diagnostic

Observers

Deteccin de Fallas en un Intercambiador de Calor, Anlisis Comparativo entreAnlisis de Componentes Principales Dinmico y Observadores de Diagnstic

Juan C. Tudn Martnez1, Rubn Morales Menndez1, Ricardo A. Ramrez Mendoza1,Luis E. Garza Castan1 and Adriana Vargas Martnez1

1Tecnolgico de Monterrey, Campus MonterreyMonterrey N.L., Mxico

{A00287756, rmm, ricardo.ramirez, legarza, A00777924}@itesm.mx

Article received on September 01, 2009; accepted on February 08, 2010

Abstract. A comparison between the Dynamic PrincipalComponent Analysis (DPCA) method and a set ofDiagnostic Observers (DO) under the same experimentaldata from a shell and tube industrial heat exchanger ispresented. The comparative analysis shows the detectionproperties of both methods when sensors and/oractuators fail online, including scenarios with multiplefaults. Similar metrics are defined for both methods:robustness, quick detection, isolability capacity,explanation facility, false alarm rates and multiple faultsidentifiability. Experimental results show the principaladvantages and disadvantages of both methods. DOshowed quicker detection for sensor and actuator faultswith lower false alarm rate. Also, DO can isolate multiplefaults. DPCA required a minor training effort; however, itcan not identify two or more sequential faults.Keywords: Fault Detection and Diagnosis, ModelClassification, Computer Application, Dynamic PrincipalComponent Analysis, Diagnostic Observers.

Resumen. El artculo presenta una comparacin entre dosmtodos de deteccin de fallas, Anlisis de ComponentesPrincipales Dinmico (DPCA por sus siglas en ingls) yObservadores de Diagnstico (DOpor sus siglas en ingls),bajo los mismos datos experimentales extrados de unintercambiador de calor industrial de tubo y coraza. Elanlisis comparativo muestra las propiedades de deteccinde ambos mtodos cuando sensores y/o actuadores fallanen lnea, incluyendo fallas mltiples. Para ambos mtodosse definen mtricas similares: robustez, tiempo dedeteccin, capacidad de aislamiento y explicacin de

propagacin de fallas, tasa de falsas alarmas y capacidadde identificar fallas mltiples. Los resultados experimentalesmuestran las ventajas y desventajas de ambos mtodos.DOdetecta ms rpido las fallas de sensores y actuadores,presenta menor tasa de falsas alarmas y puede aislar fallasmltiples. DPCA requiere menor esfuerzo de

entrenamiento; sin embargo, no puede identificar 2 o msfallas secuenciales.Palabras clave: Deteccin y Diagnstico de Fallas,Clasificacin de modelos, Aplicacin Computacional,

Anlisis de Componentes Principales Dinmico,Observadores de Diagnstico.

1 Introduction

Early detection and diagnosis of abnormal events inindustrial processes can represent economic, socialand environmental profits. Moreover, when theprocess has a great quantity of sensors or actuators,the Fault Detection and Isolation (FDI) task is very

difficult. Advanced FDI methods can be classifiedinto two major groups [Venkatasubramanian, et al.,2003], those which do not assume any form ofmodel information (process history-based methods)and those which use accurate dynamic processmodels (model-based methods).

Most of the existing FDI approaches tested onHeat Exchangers (HE) are based on quantitativemodel-based methods. In [Habbi, et al., 2008], fuzzymodels based on clustering techniques are used togenerate residuals; the symptom generation candetect leaks in a complex HE. Similarly, a residualgenerator is proposed to create fault signatures in[Krishnan and Pappa, 2005]. An adaptive observer

is used to estimate the overall heat transfercoefficient and detect aperformance degradation ofthe HE in [Astorga, et al., 2008]. In [Sun, et al., 2009], the particle swarm optimization algorithm isapplied to estimate the parameters of a SupportVector Machine (SVM) which is used to predict

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270 Juan C. Tudn Martnez, Rubn Morales Menndez,Ricardo A. Ramrez Mendoza et al.


faults in a HE. An algorithm for predicting theprobability distribution of different faults is proposedin [Morales-Menendez, et al., 2003], the results areused to adjust a process control system.

A comparative analysis between two FDIsystems is proposed in this paper. One of them isbased on the Dynamic Principal ComponentAnalysis (DPCA) and one on a set of DiagnosticObservers (DO). In order to detect faults, DPCA onlyrequires process data under normal operatingconditions; whereas, another approaches based onhistorical data (e.g. Artificial Neural Networks, ExpertSystems, etc.) require a priori knowledge undernormal and faulty process conditions. On the otherhand, the FDI system based on DO only needs toverify the model observability; while others model-based methods like parity equations must ensurenullity of matrices, rank of matrices, etc.; and

Kalman filters are frequently used when the faultestimation is desired. Both methods, DPCA and DOwere designed to online detect and isolate faultsrelated to sensor or actuators malfunctions in anindustrial HE.

Recently, DPCA and Correspondence Analysis(CA) have been compared in the FDI task [Detroja,et al., 2005]. CA shows a better efficiency of faultdetection; however, this method needs greatercomputational effort. An adaptive standardization ofthe DPCA has been proposed in [Mina and Verde,2007]; the approach allows detecting faults andavoiding normal variations. In [Perera, et al., 2006],a recursive DPCA algorithm is used to adapt the

model after detecting leakage conditions in achemical-sensing application. Fisher discriminantanalysis is adopted to improve the fault detectionperformance of kernel PCA in [Cui, et al., 2008]. In[Rea, et al., 2008], different types of sensor faultsare detected in an industrial HE using DPCA viastatistical thresholds.

On the other hand, many other approachesbased on DO propose alternatives for detecting andisolating faults in nonlinear systems. Novel robustapproaches look for insensitivityto uncertainties andat the same time are sensitive to faults using somedecoupling method [Chen and Patton, 1999]. Arobust fault detection observer is proposed in [Dai,

et al., 2008], the design of the observer is based onperformance indices and it is optimized with geneticalgorithms. In [Puig, et al., 2008], a passive robustFDI system is proposed; it includes modelinguncertainties using an interval model observer. Anobserver-based fault detection filter is used as

residual generator in [Wu and Ho, 2009]; the faultdetection filters are based on fuzzy-rules. Anadaptive observer for fault diagnosis of nonlineardiscrete-time systems is proposed in [Caccavale and

Villani, 2004]. Using linear models, a dynamicobserver is designed to detect malfunctions causedby measurement and modeling errors [Simmani andPatton, 2008]. In order to detect multiple faults, a setof unknown input-observers are used in [Verde,2001], each one of them is sensitive to a fault whileinsensitive to the remaining faults.

The aforementioned works are tested underdifferent faults and non-uniform process conditions.This paper shows a comparison between DPCA anda set of DO under the same experimental dataprovided from an industrial HE. The comparativeanalysis is made in parallel when sensors and/oractuators fail (soft faults), including scenarios with

multiple faults.This paper is organized as follows: Section 2presents the DPCA formulation, and section 3 thedesigning steps of a set of DO. Section 4 presentsthe experimentation. Section 5 and 6 present theresults of both methods. Section 7 outlines thecomparison analysis. Conclusions are presented insection 8.

2 DPCA Formulation

Let X be a matrix of m observations and n variablesrecorded from a real process. This data setrepresents the normal operating conditions.

X

denotes the scaled data matrix and x is a vectorcontaining the mean () of each variable. Such that,x X1 and X X1xD, whereD is a diagonal matrix containing the standarddeviation () of each variable and 1 is a vector ofelements equal to 1.

When the system has a dynamic behavior, thedata present serial or cross-correlation among thevariables. This violates the assumption of normalityand statistical independence of the samples. Toovercome these limitations, the column space of thematrix X must be augmented for generating a staticcontext of dynamic relations. There is not a

systematic method for determining how many delaysmust be included; however, the number of delaysdepends on the sample time (Ts). If DPCA cannotexplain data variance, Ts can be modified in order toretain the same number of past observations intomatrix X, [Tudn, et al, 2008].

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Fault Detection in a Heat Exchanger, Comparative Analysis between Dynamic Principal 271


, 1, , , , , 1, , (1)By performing PCA on the augmented datamatrix, a multivariate AutoRegressive (AR) model is

extracted directly from data [Ku, et al., 1995]. Inequation (1), w represents the delays quantity toinclude in the AR model. For a multivariate system,the process variables can have different ranges ofvalues, ergo the data matrix X must bestandardized. With the scaled data matrix, a set of asmaller number (r ) of variables is searchedthrough decomposing the data variance, r mustpreserve most of the information given in thesevariances and covariances. The dimensionalityreduction is obtained by a set of orthogonal vectors,called loading vectors (

p), which are obtained by

solving an optimization problem involvingmaximization of the explained variance in the datamatrix by each direction (j); with t Xp, themaximal variance of data t must be computed by:maxmaxmax (2)Such that pp 1. Solving the optimizationproblem through the Singular Value Decomposition(SVD), the eigenvalues of A can be computedfrom, 0 for 1, , (3)where

Arepresents the correlation matrix of the data

matrix X, and I is a n n identity matrix. Using thenew orthogonal coordinate system, the data matrix Xcan be transformed into a new and smaller datamatrix T, called scores matrix, (4)where P represents the obtained loading vectors ofthe SVD with the largest eigenvalues . Eqn (5)computes the back-transformed data matrix X fromthe original data coordination system [Tudn, et al.,2009].

(5)

2.1 Fault detection using DPCA

The normal operating conditions can becharacterized by

Tstatistic [Hotelling, 1993]. Eqn

(6) generates online the T statistic based on thefirst r loading vectors. There is no general fixedcriterion proposed to determine how many PrincipalComponents (PC) should be retained. The SCREEplot is a good choice for showing the quantity ofexplained variance based on the number of retainedPC. The number of retained PC will be determined,when the addition of another one PC does notimprove the quality of data representationsignificantly. (6)where

xis the new measurement vector taken online

and

is a diagonal matrix which contains first

r

eigenvalues of A. If the value of T statistic stayswithin its control limit, then the status of the processis considered normal [Ku, et al., 1995]. Thus, a faultoccurs, when a value of T statistic is greater thanits control limit (T).

1 , (7)where Fr ,mr is the F-distribution with r andm r degrees of freedom with 100% of confidence.

Due T statistic only detects variation in thedirection of the first r PC, [Jackson et al. 1979]propose to monitor the variation in the residual

space (the components associated with the smallestsingular values) using Q statistic for helping to faultdetection.

Both statistics must detect a process fault;however they have not the same resolution in thedeviation when the fault occurs. Similarly to Tstatistic, when a value of Q statistic is greater thanits threshold (Q) a fault has occurred. The values ofQ statistic and its control limit can be calculated by,

(8)

2 1 1

(9)

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where , h 1 and c is thenormal deviate corresponding to (1 ) percentile.

Once a fault is detected, contribution plots areused to isolate the most probable cause of fault[Miller, et al., 1998]. Contribution plots quantify theerror of each process variable when the process ison abnormal status. Process variables with highererror contribution are hypothetically more associatedto the fault. Therefore, these variables are used likeoperator guides for looking to the physical causeswhich are related with these variable deviations.Contribution of each variable to residual vector(Con), can be defined as: (10)where

Rrepresents the residue in the residual

space. Residue R can be computed by subtractingthe back-transformation data (X) to scaled datamatrix (X), (11)where P contains the loading vectors from thesmallest eigenvalues, Figure 1.

2.2 Algorithm

Figure 2 shows the block diagram for getting thecharacterization of the normal operating point using

DPCA. The first step is to standardize the data set.Then, from the correlation matrix of the scaled dataX, the eigenvalues and eigenvectors are computedthrough the SVD method. The SCREE plot is usedto select the number of PC. Finally, the matrix T isback-transformed into the original data coordinationsystem including only the PC variances.Left plot in Figure 3 displays the block diagram forapplying DPCA in the online fault detection task. Thenew measurements are projected onto the loadingvectors, i.e. in the PC space (Hotellings statistic)and residual space (Q statistic). The control limitsare computed from the characterization of thenormal operating point. A fault is correctly detected

when both statistics overshoot their respectivethresholds. Once the fault is detected by bothstatistics, contribution plots are used to isolate themost relevant cause of fault. Right plot in Figure 3shows a block diagram for achieving the faultisolation .Q space is employed to generate theresidue which is used to compute the errorcontributions, because is more sensible to the faultsthan the PC space [Isermann, 2006].

Fig. 1. FDI system using DPCA

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Fig. 2. DPCA algorithm

Fig. 3. Fault detection algorithm using DPCA (left), fault isolation using contribution plots (right)

3 Design of a Set of DO

As the state observer computes the errorbetween the process states and adjustable modelstates, it can be used as a further alternative formodel-based fault detection. The discrete statespace model is defined as, 1 (12)

(13)where vk and zk represent the inherent noise inthe process states and output, respectively. In thiscaseV and Z are considered zero. A state observerfor unmeasurable state variables can berepresented as,

xk 1 Gxk Huk yk yk (14)yk Cxk (15)

where K is the observer feedback matrix, which isused to reduce the differences between the dynamicmodel and the process. Furthermore, K must bedesigned to ensure the observer stability, i.e. K ischosen such that the eigenvalues of

G KCbe the

poles of the desired closed loop system, in thismanner the eigenvalues of G KC, called observerpoles, can be controlled by the states feedback. Kmatrix in each observer is designed via poleplacementwith observer poles close to origin in thediscrete space. The pole placement method is used

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to find K which guarantees the convergence speedand observer stability.

3.1 FDD using a Set of DO

The error of the observer can be computed as,xk 1 xk 1 G KCx x (16)Defining ek xk xk as the error vector,the predicted error can be calculated as,ek 1 G KCek (17)

The dynamic behavior of the error signal ek isdetermined by the eigenvalues of G KC. If thematrix G KC is a stable matrix, the error vector willconverge to zero for any initial error e0. In order toensure the stability of the matrix

G K

C, the

observer feedback matrix

Kmust be computed

properly to achieve pole placement. The design of aset of DO can be reviewed in detail in [Tudn, 2008].

When an unknown fault changes the process,the error signal called residual, should be different tozero. Therefore, if the residual is close to zero (i.e.noise with 0 and 1), the process variableis into its normal operating condition, called nominalbehavior. If the process is affected by several faults,it is possible to use a set of DO for identification ofdifferent faults. All DO are designed from differentfault models and they are sensitive to any faultexcept the used fault for their design. Therefore, theresidual which does not change its past behavior willbe isolated and associated as the most relevant tothe occurred fault.

3.2 Algorithm

Left plot in Figure 4 exhibits the block diagram fordesigning a state observer. From each faulty

condition, a state observer is obtained. On the otherhand, right plot in Figure 4 shows the FDI algorithmusing a set of DO. At each sample time, a newmeasurement vector is projected onto all observers;since all DO are sensitive to any fault except theconsidered fault for their design, the FDI task isachieved.

4 Experimentation

Experimental Set Up. HE are widely used in industryboth for cooling and heating large scale industrialprocesses. An industrial shell and tube HE was thetest bed for designing and testing both FDI systems.

The non-linearity of the process and its slowtransient response are the most relevant features ofthe system. In this case, the experimental set up hasall desirable characteristics for testing a faultdetection scheme due to its components are reallyof industrial type with its implications: waste, lost ofcalibration, non-linearity, mechanical failures, etc. Atthe left side of Figure 5, a photo of the system isshowed; while right side displays a conceptualdiagram of the main instrumentation: 2 temperaturesensor/transmitters.TT, TT,.2.flow.sensor/transmitters FT, FT and their control valvesFV

, FV

. The instrumentation is connected to a

data acquisition (NI USB-6215) system that iscommunicated with a computer, in bidirectional form.

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Fig. 4. Design algorithm of a state observer (left figure). FDI algorithm of a set of DO (right figure)

Fig. 5. Experimental System

Design of Experiments. Four types of additive softfaults were implemented into the industrial HE:abrupt and gradual faults in sensors, abrupt faults inactuators and multiple faults in sensors. A sensorfault simulates a transmitter bias. The conditions ofthe implemented sensor faults are described in theTable 1.

Table 1. Types of faults in sensors/transmitters

Tag name Abrupt fault Gradual fault (slope)FT 6% (5) 0.1%/secFT

8% (

5) 0.1%/sec

TT 2C (8) 0.1C/secTT 2C (8) 0.1C/secOn the other hand, the actuator faults are

considered like low or high pressure in thepneumatic valves (10%). Four different cases ofactuator faults have been designed. The case 0 is

considered as the normal operating point: steamvalve in 70% and water valve in 38%. The rest of thecases can be reviewed in the Table 2. Finally, theFDI systems were tested with multiple sensor faultsintroduced in sequence.

Table 2. Faults implemented in actuators

Case Status of thesteam valve

Status of thewater valve0 normal normal1 low pressure normal

2 high pressure normal

3 normal low pressure

4 normal high pressure

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For comparison, same metrics have been monitoredin both approaches: quick detection, isolabilitycapacity, explanation facility, false alarm rates,robustness for detecting different faults and multiple

faults identifiability.

5 Results for DPCA

Training Stage. DPCA uses 1 second of sampletime for this step; and 1900 measurement data ofeach sensor were taken. Thus, the data vector isdefined by, (18)

By taking 1 past observation of eachmeasurement, it is possible to explain a highquantity of variance including the possible auto and

cross correlations. Table 3 shows thecharacterization of the normal operating point usingDPCA; with 5 PC, it can be explained the 99.94% oftotal variance and 1 more PC does not improve thequality of data representation.

Table 3. Process characterization

PC Eigenvalue Explainedvariance (%)

CumulativeExplained

Variance (%)1 3.1361 39.20 39.202 2.0643 25.80 65.003 1.3861 17.32 82.334 0.9925 12.40 94.735 0.4167 5.20 99.946 0.0013 0.01 99.967 0.0003 0.00 99.968 0.0002 0.00 99.96

Testing Stage. When an abrupt fault isimplemented in the TT sensor at time 105, Q and Tstatistics clearly overshoot their control limits. Rightplot in Figure 6.a demonstrates how the contributionplot helps correctly to isolate the fault. The 78% oftotal error corresponds to outlet temperature signal.Commonly, the sensors are exposed to calibrationerrors or degradation by wear. This measurementdeviation can be emulated as a soft and gradualfault. Figure 6.b (left plot) shows the gradual fault

a) b)

Fig. 6. FDI analysis for an abrupt fault (left plot) and gradual fault (right plot) in the TTsensor using DPCAdetection in the TT sensor, when Q and T statisticsovershoot their thresholds after 14 and 10 secondsrespectively. As it is evident, the behavior of bothstatistics corresponds to the fault behavior whichwas activated. Figure 6.b (right plot) exhibits that

64% of total error corresponds to outlet temperaturesignal.

A similar result to Figure 6 is obtained foractuator faults. No matter if the bias is positive ornegative, both statistics overshoot their control limitswhen a fault is detected. For the cases 1 and 2, the

steam flow signal has the greatest error contributionbecause these faults are associated to changes inthe pressure of the steam valve. Similarly, the waterflow has the greatest error contribution when thewater valve fails (cases 3 -4). Details can be

reviewed in [Tudn, et al., 2009].Under sequential and multiple faults, left plot inFigure 7 demonstrates that both statistics overshootand move more away from their thresholds when thefaults are introduced. None of the statistics comesback to its normal status since none of the faults is

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deactivated. After the fault 1, contribution plots cannot associate the error to a specific fault.

6 Results for DO

Training Stage. 5 seconds of sample time are usedto obtain the state space model for each faultcondition. The process identification is based on theRecursive Least Squares (RLS) method using arandom binary signal (RBS) above the actuators.For each faulty model, the system has 4 statevariables (x ). Each state variable is associatedwith a fault signal in the steam flow, water flow,outlet temperature or inlet temperature. The residue

is defined as the square of the error signal ek. Thesteam and water control valve, their respective flowsand the inlet temperature are the inputs (u );whereas, the outlet temperature is the process

output.Table 4 shows the numerical discrete state spacemodels obtained from the process identification. Thenormal and faulty models of the HE are incompanion form. It is important to consider that theorder of the model is defined according to theminimal expression required for a correctrepresentation. The non-fault state space model,considered in the normal operating

Fig. 7. FDI analysis for multiple faults using DPCA

Table 4. Decoupled faulty discrete state-space models

Model

Non Fault 0.96 1 00 0 10 0 00 0 0 001 0 0.01 0.03 0.010 0.01 00 0 0.020 0 0. 03 0.01 0.020.01 00 0.010 0.01 1 0 0 0 0.560.060.0040.0001Fault 1 0.97 1 00.01 0 10 0 00 0 0

001 0 0.01 0.03 0.020 0.01 0.040 0 0.020 0 0. 03

0.01 0.020.01 00 0.010 0.01 1 0 0 0 0.570.050.0040.0001

Fault 6 1.02 1 00.01 0 10.01 0 00.05 0 0 001 0

0.01 0.05 0.030 0.03 00 0.01 0.020 0 0. 030.01 0.040.01 0.030 0.060 0.01 1 0 0 0

0.620.050.0140.049conditions, is obtained when the steam and water

control valves have 70% and 38% of openingrespectively; the inlet temperature is 23Capproximately and the outlet temperature is aroundof 36C, the steam flow oscillates in 58% and thewater flow in 30%. Fault 1 is considered when thesensor signal of the inlet temperature, changes.

Faults 2 and 3 are obtained from the measurement

deviation in the water and steam flow sensorrespectively. Fault 4 is related to a change in theoutlet temperature sensor. Finally, the faults 5 and 6correspond to malfunctions in the water and steamcontrol valves respectively.

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Figure 8 presents the model reliability at normaloperating conditions; the process model followscorrectly to real process value (outlet temperature).

Fig. 8. Model reliability

In order to design the set of DO, multiple modelsof the process are obtained, one state-space model

for each fault condition. Once all faulty models areknown, a state-observer is designed for each faultcondition. An individual observer will be sensible toall faults except to the fault which was used todesign the observer. A schematic block diagramrepresentation of the design of an individualobserver from the set of DO is shown in Figure 9.

Fig. 9. Design of an individual DO

In this manner, the set of DO is designed todistinguish different fault conditions. The observerfeedback matrix in each observer is designed viapole placement with poles of the stability matrixG KC close to origin in the discrete space (z =0.1). The pole placement method is used to find

K

which guarantees the convergence speed andobserver stability. Table 4 shows the observer gainsobtained for each faulty model. For the system innormal operating conditions, the observer feedbackmatrix K is computed as:

det|zI G KC| z 0 . 1 (19)K 0.56 0.06 0.004 0.0001 (20)

Testing Stage. When an abrupt fault is implementedin the TT sensor, the outlet temperature residue isthe unique signal which does not change its nominalbehavior whereas the remainder residues arenegatively deviated 1.5 units at time 10 (fault time),see the top plot in Figure 10. Thus, it is possible toassociate this fault to the TT sensor. A similar resultoccurs when a gradual fault is implemented. Bottomplot in Figure 10 shows the fault detection after 5seconds once the fault has occurred. Similarly, whena control valve has a pressure failure (low or highpressure), the flow residue associated to this valvedoes not change its behavior from its nominal value;whereas, the remainder residues are deviated.

Fig. 10. FDI analysis for an abrupt fault (top plot) and

gradual fault (bottom plot) in the TTsensor using DOUsing the sequence of multiple faults, Figure 11shows that only one signal is not deviated from itsbehavior when is introduced any abrupt sensor fault.In this case, the residual which does not change itsbehavior is associated to the occurred fault.

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Fig. 11. FDI analysis using DO for multiple faults

7 Comparison of the methods

It is important to specify that in all cases, theimplemented faults in both methods have the sameconditions. Therefore, the comparison betweenDPCA and DO can be specified under same metrics.According to Table 5, DO expose a quickerdetection than DPCA when a gradual fault isimplemented in a sensor signal. In all fault cases, itis easy to explain the fault propagation using bothmethods, i.e. the explanation facility metric isachieved.

The false alarm rate is the index of false eventswhich occurs when: (1) the FDI system does notdetect an occurred fault or (2) the FDI systemdetects a fault which did not happen. In actuator

faults, DO present a lower false alarm rate thanDPCA.

The sample time must be selected according tothe FDI requirements. DPCA does not require agreater sample time because with 1 pastobservation, taking 1 second as sample time, it ispossible to detect any abnormal event. On the otherhand, in the design of DO, the sample time can notbe greater than the dead time of the process (15seconds).

In fault isolation, contribution plots indicate whichvariables are hypothetically more associated to the

fault since it is possible that more fault cases areinvolved; while, a set of DO can correctly isolate afault if all fault models and the model of the normaloperating condition, are known with high reliability.

For faults in actuators, the normal operatingconditions change in more of two sensors and thediagnosis task can be complicated. When this kindof actuator faults are implemented, the detectiontime is not instantaneous even when these faults areabrupt. DO demonstrated a faster detection time (i.e.almost the half of detection time) than the DPCAmethod when faults in both actuators areimplemented.

Both methods can detect multiple sensor faults;however, DPCA cannot isolate correctly when two ormore faults have been implemented. According tocomputational efforts, the training stage of DO ismore complicated than the DPCA training; because

it requires a reliable ARX model which must betranslated to a discrete state space model.Furthermore, each fault case must be modeled in aparticular state space model. Once the fault model isknown with high reliability, a state observer isdesigned; particularly in this work all models (normaland faulty) are obtained in parallel. On the otherhand, DPCA training is executed faster once historicdata of the normal operating point are known.

When new and unknown soft faults arepresented, the performance of DO can bedeteriorated; while DPCA does not suffer thislimitation. The FDI system based on DO needs tomodel the new faults, thus, the set of DO will

increase. On the other hand, DPCA does not requiremore training effort because only deviations fromnormal operating point are considered. Therefore,DPCA is easier to implement under several faultsbecause the characterization under normalconditions does not change. Both methods aredeteriorated when the process is time-variant;however, DPCA can be easily retrained in any timewindow.

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Table 5. Comparison of DPCA and DO approaches

In case of DO, the maintenance of the model ismore complicated because all faulty models must becomputed again

8 Conclusions

A comparison between the Dynamic PrincipalComponent Analysis (DPCA) and a set of DiagnosticObservers (DO) under the same experimental dataprovided from a heat exchanger HE is presented.DPCA, which performs very well on fast detection ofabnormal situations, is easier to implement inindustrial applications. It results very attractive touse DPCA in industrial applications when practicallythe 100% of the system operation is around aspecific operating point. In this case, only data of thenormal operating conditions are required, while DOmust include information about faulty processbehavior.When an accurate process model is complicated toobtain due to nonlinearity, process disturbances,model uncertainties, etc., the use of Fault Detectionand Isolation (FDI)approaches based on DPCA canbe implemented. However, FDI approaches basedon modeling demonstrate better performance.Detection results shows that DPCA had 42% moreof false alarms than DO under actuator faults. DOpresent a faster detection time than the DPCA

method in every test ([4 1 0] seconds lower).Finally, DPCA can not identify multiple faultswhereas quantitative model- based methods, as DO,have the multiple-fault identifiability property.

Under new and unknown faults, the maintenanceof the FDI system is more complicated in DObecause new faulty models must be computed;

while, DPCA does not need more training effortbecause only deviations from the normal operatingpoint are considered.

References

1. Astorga-Zaragoza, C. M., Alvarado-Martnez, V. M.,Zavala-Ro, A. & Mndez-Ocaa R. M. (2008).Observer-based monitoring of heat exchangers. ISATransactions, 47(1), 1524.

2. Caccavale, F. & Villani, L. (2004). An adaptiveobserver for fault diagnosis in nonlinear discrete-timesystems. American Control Conference 2004, BostonMassachusetts, USA, 3, 24632468.

3. Cui, P., Li, J. & Wang, G. (2008). Improved kernelprincipal component analysis for fault detection. ExpertSystems with Applications, 34(2), 12101219.

4. Chen, J. & Patton R. J. (1999). Robust model-basedfault diagnosis for dynamic systems. Boston: KluwerAcademic Publishers.

5. Dai, X., Liu G.&Long, Z. (2008).Discrete-time robustfault detection observer design: a genetic algorithmapproach. 7th World Congress Intelligent Control &Automation, Chongqing, China, 28432848.

6. Detroja, K. P., Gudi, R.D.&Patwardhan, S. C. (2007).Plant-wide detection and diagnosis usingcorrespondence analysis. Control Engineering Practice,15(12), 1468-1483.

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Approach Type

of fault

Location Detection

time (s)

Isolability Explanation

facility

False

alarm rate

(%)

DPCA

AbruptGradualAbruptAbrupt

Actuators

Multiple sensors

Instantaneous10 149 18

Instantaneous 0

014.13

0

DO

AbruptGradualAbrupt

Abrupt

Actuators

Multiple sensors

Instantaneous5

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11. Krishnan, R. A. & Pappa, N. (2005). Real time faultdiagnosis for a heat exchanger - a model basedapproach. 2005 Annual IEEE INDICON, Chennai, India,7882.

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13. Lingfang, S., Yingying, Z.&Rina, S. (2009).Researchon the fouling prediction of heat exchanger based onSupport Vector Machine optimized by particle swarmoptimization algorithm. International Conference onMechatronics and Automation, Changchun, China,20022007.

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2007, New York, USA, 32343239.16. Morales-Menendez, R., de Freitas, N., & Poole, D.(2003). Estimation and control of industrial processeswith particle filters. American ControlConference 2003,Denver Colorado, USA, 579584.

17. Parera, A., Papamichail, N., Barsan, N., Weimar, U.&Marco, S. (2006). On-line novelty detection by recursivedynamic principal component analysis and gas sensorarrays under drift conditions. IEEE Sensors Journal,6(3), 770783.

18. Puig, V., Quevedo, J., Escobet T., Nejjari F. &de lasHeras, S. (2008). Passive robust fault detection ofdynamic processes using interval models. IEEETransactions on Control Systems Technology, 16(5),10831089.

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Juan Carlos TudnMartnez

Obtained the degree of B.Sc. in Chemical Engineering withhonors on May2006 and the M. Sc. degree in Automationon December 2008 from Tecnolgico de Monterrey.

Actually, he is studying a PhD in Sciences of Engineering.His research is focused in Fault Diagnosis and FaultTolerant Control.

Rubn MoralesMenndez

Received the B.Sc. in Chemical Engineering and Systemsand two M.Sc. degrees in Process Systems andAutomation in 1984, 1986 and 1992, respectively. He hasa PhD degree in Artificial Intelligence from Tecnolgico deMonterrey in 2003. From 2000 to 2003, he was aVisitingScholar with the Laboratory of Computational Intelligenceat University of British Columbia, Canada. He is aconsultant specializing in the analysis and design ofautomatic control systems for continuous processes formore than 22 years. He is member of the NationalResearchers System of Mexico (level I), and member ofIFAC TC 9.3.

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Ricardo A. RamrezMendoza

Received the B.Sc. in Mechanical and ElectricalEngineering and the M.Sc. degrees in Automation in 1988and 1992, respectively. He has a PhD degree in AutomaticControl from Grenoble Institute of Technology in France in1997. From 1997 to 2004, he was a Associated Professorwith the Departament of Mechatronics at Tecnologico deMonterrey Campus Monterrey, Mexico. He is a seniorconsultant in Vehicle Dynamics and Automotive Control formore than 15 years. He is member of the NationalResearchers System of Mexico (level I). Currently, he isDean of Engineering and Architecture at Tecnologico deMonterrey Campus Mexico City.

Luis E. Garza Castan

Was born on December 15th, 1963, in Monclova,Coahuila. He holds a PhD in Artificial Intelligence fromITESM, Monterrey since 2001, and graduated from themaster degree in Control Engineering in 1988, and from

Electronic Systems Engineering in 1986. He worked, forabout 10 years, in the Control and Automation area inMetallurgical and Metal-mechanic industry. Now, he is afull time professor in the Mechatronics and Automationdepartment at ITESM Monterrey, and is a level 1 memberof the Sistema Nacional de Investigadores (SNI). He haspublished more than 40 articles in Biometrics, FaultDiagnosis and FTC.

Adriana Vargas Martnez

Was born in 1983, and received the B.Sc. in ChemicalEngineering with minor in Industrial Systems in 2005 andgraduated from a M.Sc. degree in Environmental Systemsin 2007. Since 2007 she is a formal student of the PhD inMechatronics in the Tecnolgico de Monterrey. Herresearch fields include Artificial Intelligence Methods forFault Tolerant Control.

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