Post on 06-Mar-2018
Research ArticleFault Diagnosis of Batch Reactor Using MachineLearning Methods
Sujatha Subramanian1 Fathima Ghouse2 and Pappa Natarajan3
1 Department of Electronics and Instrumentation Engineering Adhiyamaan College of Engineering Hosur KrishnagiriTamil Nadu 635 109 India
2Department of Information Technology Adhiyamaan College of Engineering Hosur Krishnagiri Tamil Nadu 635 109 India3 Department of Instrumentation Engineering Madras Institute of Technology Anna University ChennaiTamil Nadu 600 044 India
Correspondence should be addressed to Sujatha Subramanian saransakthisifycom
Received 3 January 2014 Accepted 4 March 2014 Published 22 April 2014
Academic Editor Azah Mohamed
Copyright copy 2014 Sujatha Subramanian 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
Fault diagnosis of a batch reactor gives the early detection of fault and minimizes the risk of thermal runaway It provides superiorperformance and helps to improve safety and consistency It has becomemore vital in this technical era In this paper support vectormachine (SVM) is used to estimate the heat release (119876
119903) of the batch reactor both normal and faulty conditionsThe signature of the
residual which is obtained from the difference between nominal and estimated faulty119876119903values characterizes the different natures
of faults occurring in the batch reactor Appropriate statistical and geometric features are extracted from the residual signature andthe total numbers of features are reduced using SVM attribute selection filter and principle component analysis (PCA) techniquesartificial neural network (ANN) classifiers like multilayer perceptron (MLP) radial basis function (RBF) and Bayes net are usedto classify the different types of faults from the reduced features It is observed from the result of the comparative study that theproposed method for fault diagnosis with limited number of features extracted from only one estimated parameter (119876
119903) shows that
it is more efficient and fast for diagnosing the typical faults
1 Introduction
Batch and semibatch reactors are extensively used in finechemicals biochemicals pharmaceuticals and food indus-tries for the production of small amounts of products withhigh added value As these processes have become moreautomated and more flexible the demands on their effi-ciency have increased creatingmore complexity in operationand control However the frequency of accidents increasedinvolving important consequences on the human naturaland economic environment [1 2] Therefore fault diagnosishas become a major research topic Batch processes usuallyinvolve a lot of variables that interrelate with one anotherWhen any of these variables diverge away from their specifiedlimits a fault occurs There are a plenty of studies on faultdiagnosis varying from analytical methods to artificial intel-ligence and statistical approaches The approaches of fault
detection are based on the threshold checking in the pastVenkatasubramanian and Chan [3] proposed fault diagnosisto the continuous stirred tank reactors with neural networkand identified six kinds of faults The application of neuralnetworks in fault diagnosis of chemical process focuses onthe following aspects such as using as a classifier usingas a dynamic forecast model and combining with otherdiagnostic methods Later pattern classification and modelidentification [4] EKF based fault detection [5] and faultdiagnosis of ball bearing using machine learning method [6]were used
In this paper SVM model is used to generate theresidual images Fault classification has been done from theextracted image features SVM is a novel machine learningmethod based on statistical learning theoryThe SVMutilizesa hyperplane with maximum margin to produce a goodgeneralization performance by separating different classes As
Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014 Article ID 426402 14 pageshttpdxdoiorg1011552014426402
2 Modelling and Simulation in Engineering
a result SVM has been widely used for many applicationssuch as time series forecasting fault detection modelling ofnonlinear dynamic systems one-class SVM formachine faultdetection and classification [7] SVM for copper clad laminatedefects classification [8] and SVM for fault diagnosis of asteam turbine [9]
For this study different major fault types like actuatorfault sensor fault and process fault are considered Hencethe fault residuals are generated from the output of thenominal model and this faulty model Data based faultdiagnosis method requires a large amount of historical dataTo make this method be more efficient the first step isfeature extraction [10] From the residuals signature themostappropriate statistical and geometrical features are extractedand among these 15 features are selected Through thischaracteristic extraction the data can be transformed to theprior information of fault diagnosis system SVM attributefilter is employed to rank the features in order to reduce theinput data dimension whichmakes the better performance ofthe classifier And its performance is compared based on PCAfeature reduction also
This paper is mainly focused on identifying fault clas-sification of batch reactor from the residual features usingartificial intelligent classifiers such as multilayer perceptron(MLP) radial basis function (RBF) and Bayes net Thepaper is organized as follows Section 2 describes machinelearning methods used in this work Section 3 explains thecase study of the well-known batch reactor Section 4 givesfault identificationmethod Section 5 shows and discusses thesimulation results Finally the conclusion from this work ispresented in Section 6
2 Machine Learning Methods
In this paper the machine learning methods like SVM ANNlike MLP and RBF are used SVM is a supervised learningmethod which is motivated in maximizing the ability togeneralize well from a small number of training samples bymapping the original space into a high dimensional innerproduct space called feature space via a kernel The SVMformulation follows structural risk minimization (SRM)principle in which an upper bound on the generalizationerror is minimized whereas the error risk minimization(ERM) minimizes the prediction error on the training dataThis equips the SVMwith a greater potential to generalize theinput-output relationship learnt during its training phase formaking good predictions for new input data [11]
SVMrsquos solutions are characterized by convex optimizationproblems So it can be applied in settling pattern recogni-tion problems with small samples nonlinearity and higherdimensions SVM can easily be introduced into learningproblems such as function estimation
In the batch reactor the heat released by the reactionaffects the dynamics of the reactor temperature This termdepends on the initial concentration which is usually mea-surable at a very low sampling rate not suitable for real timecontrol or estimation So any fault occurring in the batchreactor will have the impact on the heat release of the reactor
FeedStir Vent controller
Coolantsteam outlet
Coolantsteam inlet
Product
Tr VrQr
Tj
Figure 1 Schematic diagram of a jacketed batch reactor
So a model developed based on the heat release of the reactor(119876119903) which can predict the type of fault occurred But the
quantity of119876119903is not directly measurable one So an estimator
is required to estimate it Here SVM is used to build theestimator model
Similarly for classification of different faults the usualANN classifiers are used in this work There are variousneural network architectures but the application consideredin this work has used MLP with back propagation learningalgorithm RBF and the Bayes net [12ndash16]
3 Case Study
The proposed fault diagnosis scheme is applied to the batchreactor by Cott and Macchietto [17] Aziz et al [18] Mujtabaet al [19] and Sujatha and Pappa [20] The complex reactionscheme of a batch reactor is a representative of manyindustrial reactions as shown in Figure 1 The batch reactoris inherently a dynamic process The reactions I and II of thebatch reactor are given in the following equation
119860 + 119861 997888rarr 119862
119860 + 119862 997888rarr 119863(1)
where 119860 119861 are the raw materials 119862 is the desired productand119863 is the waste product
This benchmark model is given on the basis of reactionequation (1) competent of simulating the reactions like thereactor temperature jacket temperature and heat release ofreactor under nominal operating conditions and also undervarious faulty conditions
These simulations are run under closed loop control withgeneric model controller (GMC) [20 21] The total runningtime of the batch process is 120 minutes (2 hours) The batchreactor model equations are given below
119889119872119860
119889119905= minus 119877
1minus 1198772
Modelling and Simulation in Engineering 3
119889119872119861
119889119905= minus 119877
1
119889119872119862
119889119905= 1198771minus 1198772
119889119872119863
119889119905= 1198772
1198771= 1198961119872119860119872119861
1198772= 1198962119872119860119872119862
1198961= exp(
1198961
1minus 1198962
1
(119879119903+ 27315)
)
1198962= exp(
1198961
2minus 1198962
2
(119879119903+ 27315)
)
119889119879119903
119889119905=(119876119903+ 119876119895)
119872119903119862119901119903
119889119879119895
119889119905=(119879119904119901
119895minus 119879119895)
120591119895
minus119876119895
119881119895120588119895119862119901119895
119876119903= minus Δ119867
11198771minus Δ11986721198772
119872119903= 119872119860+119872119861+119872119862+119872119863
119862119901119903=119862119901119860119872119860+ 119862119901119861119872119861+ 119862119901119862119872119862+ 119862119901119863119872119863
119872119903
119876119895= 119880119860(119879
119895minus 119879119903)
(2)
The initial values of the above mentioned process param-eters of [119872
119860 119872119861 119872119862 119872119863 119879119895 119879119903] are [120 120 00 00
200 200] at 119905 = 0 The reactor temperature is used as thecontrol variable and is bounded between 20∘ and 100∘C andthe jacket temperature is the manipulated variable and it isbounded between 20∘ and 120∘C All the nominal parametersand constant values used in themodel equations (2) are givenin Table 1
4 Fault Diagnosis of the Batch Reactor
Fault can be defined as any nonpermitted deviation of processbehaviour from an acceptable one So fault diagnosis is theproblem of identifying and isolating unanticipated changesin a process Diagnosis is a challenging problem due toseveral factors such as monitoring the number of variablesoccurrences of the process complexity and the variety ofprocess failures The failures can be broadly categorized intothree types such as actuator faults sensor faults and processfaultsThe fault types are inspired from the relevant literature[22] presented in Figure 2
Table 1 Nominal values of the parameters
Constant parameters Values
119862119901119860
Specific heat capacity of component119860
180 kcalkmol∘C
119862119901119861
Specific heat capacity of component119861
400 kcalkmol∘C
119862119901119862
Specific heat capacity of component119862
520 kcalkmol∘C
119862119901119863
Specific heat capacity of component119863
800 kcalkmol∘C
Δ1198671
Heat of reaction of reaction 1 minus100000 kcalkmolΔ1198672
Heat of reaction of reaction 2 minus60000 kcalkmol119862119901
Mass heat capacity of reactant 045 kcalkg∘C119862119901119895
Molar heat capacity of component 119895 045 kcalkg∘C119880 Heat transfer coefficient 976 kcalminm2 ∘C120588119895
Density 10000 kgm3
1198961
1
Preexponential rate constant forreaction 1 209057
1198962
1
Preexponential rate constant forreaction 1 10000
1198961
2
Preexponential rate constant forreaction 2 389057
1198962
2
Preexponential rate constant forreaction 2 17000
119881119895
Jacket volume 06921m3
119860 Heat transfer area 624m2
119872119903
Number of moles of component 1560 kg120591119895
Jacket time constant 30min
Actuator Process Sensor
Faults Faults Faults
Figure 2 Types of faults
Faults can be defined as follows
(i) Process faults processes that occur below a certainlevel of detail are generally represented as lumpedparameters in process models An example of such alumped parameter in this batch reactor is the foulingfactor Changes in these parameters are termed asprocess or parametric faults
(ii) Sensor failure while all sensors have random errorssensor failures refer to gross errors such as biasmeasurement with noise and frozen sensors
Controller and actuator fault the actuator faults aremostly caused by the nonlinear characteristics of the controlvalve by hysteresis stiction friction and poor controllertuning Actuator action in the presence of fault can berepresented as 119906
119886(119905) = 119906(119905) + 119891
119886(119905) where 119891
119886(119905) is the actuator
fault vector Abrupt constant bias has been given via thevector 119891
119886(119905) = 120575119906 so that the actuator action becomes
4 Modelling and Simulation in Engineering
100999897969594939291
0 20 40 60 80 100 120
Actu
ator
inpu
t
Time (min)
Added actuatorbias
(with
bia
s add
ition
)
Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes
Actuator freezing
936
932
928
924
920 20 40 60 80 100 120
Time (min)
Actu
ator
inpu
t(w
ith fr
eezi
ng)
Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)
Tr(k minus 1) Tr(k)
Tj(k)Tj(k minus 1)
Qr(k minus 1)
Tr(k minus 2)
Qr(k)
Input Output
Figure 5 Inputoutput mapping of the SVM heat release estimator
119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing
of the actuator at certain time has been shown as 119891119886(119905) =
minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in
Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor
41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876
119903) which is not ameasurable parameter is estimated
through the SVMmodel
42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which
SVM estimator
Batch reactor y(k)u(k)
zminus1
zminus1
zminus2
zminus2
Qr(k)
Figure 6 Training method for the heat release estimator
0 20 40 60 80 100 120
Time (min)
Predicted (SVM)Actual
1600
1400
1200
1000
800
600
400
200
0
minus200Qr
(kJm
in)
Figure 7 Response of SVM 119876119903estimator under normal condition
the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown
in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is
developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7
The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876
119903) which is
the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers
43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876
119903) Each fault is introduced through simulation and
the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work
431 Process Fault
(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation
Modelling and Simulation in Engineering 5
(nominal)
Faults
Residual (faulty)
Signature window
Features extraction
Feature reduction bySVM attribute
Batch reactor
SVM estimator model (under faulty
condition) SVM estimator model
ANN classifiers
Faults
Qr
Qr (in presenceof fault)
ip
minus
+
Figure 8 Block diagram of fault diagnosis process
Table 2 Fault description
Slnumber
Faulttypes Fault description Category
1 Fault1 Δ119867mdashheat of reactionchange Process fault
2 Fault2119872119886119872119887change (initial
values of input componentfeed change)
Process fault
3 Fault3 Heat transfer coefficientchange (119880) Process fault
4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault
6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault
in 119876119903residual for 10 20 30 and 40 increase
and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value
of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876
119903residual for the heat
of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10
(iii) Change in initial charge of reactants (119872119860 119872119861) a
change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876
119903residual for 10 20
25 and 30 decrease and increase in initial chargeare as shown in Figure 11
In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed
432 Actuator Fault The actuator fault considered here is asfollows
(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3
(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4
The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13
From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary
433 Sensor Faults The following sensor faults are consid-ered in this work
(i) jacket temperature and reactor temperature measure-ments with the white noise
(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876
119903residual for the sensor faults is shown in
Figure 14The signature of the sensor fault pattern is varying with
respect to the sources of different components and at the timeof fault
From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below
(i) Mean average value of a signal is termed as meanvalue as given in
120583119862=
1
119872119873sum
119894
sum
119895
119875119888
119894119895 (3)
(ii) Standard deviation it is a measure of energy contentin the fault signature shown in
SD = radic119899sum1199092
minus (sum119909)2
119899 (119899 minus 1) (4)
(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in
skewness = 119899
(119899 minus 1) (119899 minus 2)sum(
119909119894minus 119909
119904)
3
(5)
6 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
20
40
Time (min)
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
1400
1600
Time (min)
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Time (min)
minus40
minus20
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
Time (min)
minus1400
minus1200
minus1000
minus800
minus600
minus400
minus200
Qr
resid
ual
(d)
Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876
119903) due to 10 sudden increase in the heat transfer
coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876
119903) due to
40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)
(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in
kurtosis = [119899 (119899 + 1)
(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(
119909119894minus 119909
119904)
4
]
minus 3(119899 minus 1)
2
(119899 minus 2) (119899 minus 3)
(6)
where 119899 is the sample size and 119904 is the standard deviation
5 Results and Discussion
The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware
51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit
52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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International Journal of
2 Modelling and Simulation in Engineering
a result SVM has been widely used for many applicationssuch as time series forecasting fault detection modelling ofnonlinear dynamic systems one-class SVM formachine faultdetection and classification [7] SVM for copper clad laminatedefects classification [8] and SVM for fault diagnosis of asteam turbine [9]
For this study different major fault types like actuatorfault sensor fault and process fault are considered Hencethe fault residuals are generated from the output of thenominal model and this faulty model Data based faultdiagnosis method requires a large amount of historical dataTo make this method be more efficient the first step isfeature extraction [10] From the residuals signature themostappropriate statistical and geometrical features are extractedand among these 15 features are selected Through thischaracteristic extraction the data can be transformed to theprior information of fault diagnosis system SVM attributefilter is employed to rank the features in order to reduce theinput data dimension whichmakes the better performance ofthe classifier And its performance is compared based on PCAfeature reduction also
This paper is mainly focused on identifying fault clas-sification of batch reactor from the residual features usingartificial intelligent classifiers such as multilayer perceptron(MLP) radial basis function (RBF) and Bayes net Thepaper is organized as follows Section 2 describes machinelearning methods used in this work Section 3 explains thecase study of the well-known batch reactor Section 4 givesfault identificationmethod Section 5 shows and discusses thesimulation results Finally the conclusion from this work ispresented in Section 6
2 Machine Learning Methods
In this paper the machine learning methods like SVM ANNlike MLP and RBF are used SVM is a supervised learningmethod which is motivated in maximizing the ability togeneralize well from a small number of training samples bymapping the original space into a high dimensional innerproduct space called feature space via a kernel The SVMformulation follows structural risk minimization (SRM)principle in which an upper bound on the generalizationerror is minimized whereas the error risk minimization(ERM) minimizes the prediction error on the training dataThis equips the SVMwith a greater potential to generalize theinput-output relationship learnt during its training phase formaking good predictions for new input data [11]
SVMrsquos solutions are characterized by convex optimizationproblems So it can be applied in settling pattern recogni-tion problems with small samples nonlinearity and higherdimensions SVM can easily be introduced into learningproblems such as function estimation
In the batch reactor the heat released by the reactionaffects the dynamics of the reactor temperature This termdepends on the initial concentration which is usually mea-surable at a very low sampling rate not suitable for real timecontrol or estimation So any fault occurring in the batchreactor will have the impact on the heat release of the reactor
FeedStir Vent controller
Coolantsteam outlet
Coolantsteam inlet
Product
Tr VrQr
Tj
Figure 1 Schematic diagram of a jacketed batch reactor
So a model developed based on the heat release of the reactor(119876119903) which can predict the type of fault occurred But the
quantity of119876119903is not directly measurable one So an estimator
is required to estimate it Here SVM is used to build theestimator model
Similarly for classification of different faults the usualANN classifiers are used in this work There are variousneural network architectures but the application consideredin this work has used MLP with back propagation learningalgorithm RBF and the Bayes net [12ndash16]
3 Case Study
The proposed fault diagnosis scheme is applied to the batchreactor by Cott and Macchietto [17] Aziz et al [18] Mujtabaet al [19] and Sujatha and Pappa [20] The complex reactionscheme of a batch reactor is a representative of manyindustrial reactions as shown in Figure 1 The batch reactoris inherently a dynamic process The reactions I and II of thebatch reactor are given in the following equation
119860 + 119861 997888rarr 119862
119860 + 119862 997888rarr 119863(1)
where 119860 119861 are the raw materials 119862 is the desired productand119863 is the waste product
This benchmark model is given on the basis of reactionequation (1) competent of simulating the reactions like thereactor temperature jacket temperature and heat release ofreactor under nominal operating conditions and also undervarious faulty conditions
These simulations are run under closed loop control withgeneric model controller (GMC) [20 21] The total runningtime of the batch process is 120 minutes (2 hours) The batchreactor model equations are given below
119889119872119860
119889119905= minus 119877
1minus 1198772
Modelling and Simulation in Engineering 3
119889119872119861
119889119905= minus 119877
1
119889119872119862
119889119905= 1198771minus 1198772
119889119872119863
119889119905= 1198772
1198771= 1198961119872119860119872119861
1198772= 1198962119872119860119872119862
1198961= exp(
1198961
1minus 1198962
1
(119879119903+ 27315)
)
1198962= exp(
1198961
2minus 1198962
2
(119879119903+ 27315)
)
119889119879119903
119889119905=(119876119903+ 119876119895)
119872119903119862119901119903
119889119879119895
119889119905=(119879119904119901
119895minus 119879119895)
120591119895
minus119876119895
119881119895120588119895119862119901119895
119876119903= minus Δ119867
11198771minus Δ11986721198772
119872119903= 119872119860+119872119861+119872119862+119872119863
119862119901119903=119862119901119860119872119860+ 119862119901119861119872119861+ 119862119901119862119872119862+ 119862119901119863119872119863
119872119903
119876119895= 119880119860(119879
119895minus 119879119903)
(2)
The initial values of the above mentioned process param-eters of [119872
119860 119872119861 119872119862 119872119863 119879119895 119879119903] are [120 120 00 00
200 200] at 119905 = 0 The reactor temperature is used as thecontrol variable and is bounded between 20∘ and 100∘C andthe jacket temperature is the manipulated variable and it isbounded between 20∘ and 120∘C All the nominal parametersand constant values used in themodel equations (2) are givenin Table 1
4 Fault Diagnosis of the Batch Reactor
Fault can be defined as any nonpermitted deviation of processbehaviour from an acceptable one So fault diagnosis is theproblem of identifying and isolating unanticipated changesin a process Diagnosis is a challenging problem due toseveral factors such as monitoring the number of variablesoccurrences of the process complexity and the variety ofprocess failures The failures can be broadly categorized intothree types such as actuator faults sensor faults and processfaultsThe fault types are inspired from the relevant literature[22] presented in Figure 2
Table 1 Nominal values of the parameters
Constant parameters Values
119862119901119860
Specific heat capacity of component119860
180 kcalkmol∘C
119862119901119861
Specific heat capacity of component119861
400 kcalkmol∘C
119862119901119862
Specific heat capacity of component119862
520 kcalkmol∘C
119862119901119863
Specific heat capacity of component119863
800 kcalkmol∘C
Δ1198671
Heat of reaction of reaction 1 minus100000 kcalkmolΔ1198672
Heat of reaction of reaction 2 minus60000 kcalkmol119862119901
Mass heat capacity of reactant 045 kcalkg∘C119862119901119895
Molar heat capacity of component 119895 045 kcalkg∘C119880 Heat transfer coefficient 976 kcalminm2 ∘C120588119895
Density 10000 kgm3
1198961
1
Preexponential rate constant forreaction 1 209057
1198962
1
Preexponential rate constant forreaction 1 10000
1198961
2
Preexponential rate constant forreaction 2 389057
1198962
2
Preexponential rate constant forreaction 2 17000
119881119895
Jacket volume 06921m3
119860 Heat transfer area 624m2
119872119903
Number of moles of component 1560 kg120591119895
Jacket time constant 30min
Actuator Process Sensor
Faults Faults Faults
Figure 2 Types of faults
Faults can be defined as follows
(i) Process faults processes that occur below a certainlevel of detail are generally represented as lumpedparameters in process models An example of such alumped parameter in this batch reactor is the foulingfactor Changes in these parameters are termed asprocess or parametric faults
(ii) Sensor failure while all sensors have random errorssensor failures refer to gross errors such as biasmeasurement with noise and frozen sensors
Controller and actuator fault the actuator faults aremostly caused by the nonlinear characteristics of the controlvalve by hysteresis stiction friction and poor controllertuning Actuator action in the presence of fault can berepresented as 119906
119886(119905) = 119906(119905) + 119891
119886(119905) where 119891
119886(119905) is the actuator
fault vector Abrupt constant bias has been given via thevector 119891
119886(119905) = 120575119906 so that the actuator action becomes
4 Modelling and Simulation in Engineering
100999897969594939291
0 20 40 60 80 100 120
Actu
ator
inpu
t
Time (min)
Added actuatorbias
(with
bia
s add
ition
)
Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes
Actuator freezing
936
932
928
924
920 20 40 60 80 100 120
Time (min)
Actu
ator
inpu
t(w
ith fr
eezi
ng)
Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)
Tr(k minus 1) Tr(k)
Tj(k)Tj(k minus 1)
Qr(k minus 1)
Tr(k minus 2)
Qr(k)
Input Output
Figure 5 Inputoutput mapping of the SVM heat release estimator
119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing
of the actuator at certain time has been shown as 119891119886(119905) =
minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in
Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor
41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876
119903) which is not ameasurable parameter is estimated
through the SVMmodel
42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which
SVM estimator
Batch reactor y(k)u(k)
zminus1
zminus1
zminus2
zminus2
Qr(k)
Figure 6 Training method for the heat release estimator
0 20 40 60 80 100 120
Time (min)
Predicted (SVM)Actual
1600
1400
1200
1000
800
600
400
200
0
minus200Qr
(kJm
in)
Figure 7 Response of SVM 119876119903estimator under normal condition
the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown
in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is
developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7
The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876
119903) which is
the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers
43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876
119903) Each fault is introduced through simulation and
the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work
431 Process Fault
(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation
Modelling and Simulation in Engineering 5
(nominal)
Faults
Residual (faulty)
Signature window
Features extraction
Feature reduction bySVM attribute
Batch reactor
SVM estimator model (under faulty
condition) SVM estimator model
ANN classifiers
Faults
Qr
Qr (in presenceof fault)
ip
minus
+
Figure 8 Block diagram of fault diagnosis process
Table 2 Fault description
Slnumber
Faulttypes Fault description Category
1 Fault1 Δ119867mdashheat of reactionchange Process fault
2 Fault2119872119886119872119887change (initial
values of input componentfeed change)
Process fault
3 Fault3 Heat transfer coefficientchange (119880) Process fault
4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault
6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault
in 119876119903residual for 10 20 30 and 40 increase
and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value
of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876
119903residual for the heat
of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10
(iii) Change in initial charge of reactants (119872119860 119872119861) a
change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876
119903residual for 10 20
25 and 30 decrease and increase in initial chargeare as shown in Figure 11
In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed
432 Actuator Fault The actuator fault considered here is asfollows
(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3
(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4
The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13
From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary
433 Sensor Faults The following sensor faults are consid-ered in this work
(i) jacket temperature and reactor temperature measure-ments with the white noise
(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876
119903residual for the sensor faults is shown in
Figure 14The signature of the sensor fault pattern is varying with
respect to the sources of different components and at the timeof fault
From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below
(i) Mean average value of a signal is termed as meanvalue as given in
120583119862=
1
119872119873sum
119894
sum
119895
119875119888
119894119895 (3)
(ii) Standard deviation it is a measure of energy contentin the fault signature shown in
SD = radic119899sum1199092
minus (sum119909)2
119899 (119899 minus 1) (4)
(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in
skewness = 119899
(119899 minus 1) (119899 minus 2)sum(
119909119894minus 119909
119904)
3
(5)
6 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
20
40
Time (min)
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
1400
1600
Time (min)
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Time (min)
minus40
minus20
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
Time (min)
minus1400
minus1200
minus1000
minus800
minus600
minus400
minus200
Qr
resid
ual
(d)
Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876
119903) due to 10 sudden increase in the heat transfer
coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876
119903) due to
40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)
(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in
kurtosis = [119899 (119899 + 1)
(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(
119909119894minus 119909
119904)
4
]
minus 3(119899 minus 1)
2
(119899 minus 2) (119899 minus 3)
(6)
where 119899 is the sample size and 119904 is the standard deviation
5 Results and Discussion
The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware
51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit
52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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DistributedSensor Networks
International Journal of
Modelling and Simulation in Engineering 3
119889119872119861
119889119905= minus 119877
1
119889119872119862
119889119905= 1198771minus 1198772
119889119872119863
119889119905= 1198772
1198771= 1198961119872119860119872119861
1198772= 1198962119872119860119872119862
1198961= exp(
1198961
1minus 1198962
1
(119879119903+ 27315)
)
1198962= exp(
1198961
2minus 1198962
2
(119879119903+ 27315)
)
119889119879119903
119889119905=(119876119903+ 119876119895)
119872119903119862119901119903
119889119879119895
119889119905=(119879119904119901
119895minus 119879119895)
120591119895
minus119876119895
119881119895120588119895119862119901119895
119876119903= minus Δ119867
11198771minus Δ11986721198772
119872119903= 119872119860+119872119861+119872119862+119872119863
119862119901119903=119862119901119860119872119860+ 119862119901119861119872119861+ 119862119901119862119872119862+ 119862119901119863119872119863
119872119903
119876119895= 119880119860(119879
119895minus 119879119903)
(2)
The initial values of the above mentioned process param-eters of [119872
119860 119872119861 119872119862 119872119863 119879119895 119879119903] are [120 120 00 00
200 200] at 119905 = 0 The reactor temperature is used as thecontrol variable and is bounded between 20∘ and 100∘C andthe jacket temperature is the manipulated variable and it isbounded between 20∘ and 120∘C All the nominal parametersand constant values used in themodel equations (2) are givenin Table 1
4 Fault Diagnosis of the Batch Reactor
Fault can be defined as any nonpermitted deviation of processbehaviour from an acceptable one So fault diagnosis is theproblem of identifying and isolating unanticipated changesin a process Diagnosis is a challenging problem due toseveral factors such as monitoring the number of variablesoccurrences of the process complexity and the variety ofprocess failures The failures can be broadly categorized intothree types such as actuator faults sensor faults and processfaultsThe fault types are inspired from the relevant literature[22] presented in Figure 2
Table 1 Nominal values of the parameters
Constant parameters Values
119862119901119860
Specific heat capacity of component119860
180 kcalkmol∘C
119862119901119861
Specific heat capacity of component119861
400 kcalkmol∘C
119862119901119862
Specific heat capacity of component119862
520 kcalkmol∘C
119862119901119863
Specific heat capacity of component119863
800 kcalkmol∘C
Δ1198671
Heat of reaction of reaction 1 minus100000 kcalkmolΔ1198672
Heat of reaction of reaction 2 minus60000 kcalkmol119862119901
Mass heat capacity of reactant 045 kcalkg∘C119862119901119895
Molar heat capacity of component 119895 045 kcalkg∘C119880 Heat transfer coefficient 976 kcalminm2 ∘C120588119895
Density 10000 kgm3
1198961
1
Preexponential rate constant forreaction 1 209057
1198962
1
Preexponential rate constant forreaction 1 10000
1198961
2
Preexponential rate constant forreaction 2 389057
1198962
2
Preexponential rate constant forreaction 2 17000
119881119895
Jacket volume 06921m3
119860 Heat transfer area 624m2
119872119903
Number of moles of component 1560 kg120591119895
Jacket time constant 30min
Actuator Process Sensor
Faults Faults Faults
Figure 2 Types of faults
Faults can be defined as follows
(i) Process faults processes that occur below a certainlevel of detail are generally represented as lumpedparameters in process models An example of such alumped parameter in this batch reactor is the foulingfactor Changes in these parameters are termed asprocess or parametric faults
(ii) Sensor failure while all sensors have random errorssensor failures refer to gross errors such as biasmeasurement with noise and frozen sensors
Controller and actuator fault the actuator faults aremostly caused by the nonlinear characteristics of the controlvalve by hysteresis stiction friction and poor controllertuning Actuator action in the presence of fault can berepresented as 119906
119886(119905) = 119906(119905) + 119891
119886(119905) where 119891
119886(119905) is the actuator
fault vector Abrupt constant bias has been given via thevector 119891
119886(119905) = 120575119906 so that the actuator action becomes
4 Modelling and Simulation in Engineering
100999897969594939291
0 20 40 60 80 100 120
Actu
ator
inpu
t
Time (min)
Added actuatorbias
(with
bia
s add
ition
)
Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes
Actuator freezing
936
932
928
924
920 20 40 60 80 100 120
Time (min)
Actu
ator
inpu
t(w
ith fr
eezi
ng)
Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)
Tr(k minus 1) Tr(k)
Tj(k)Tj(k minus 1)
Qr(k minus 1)
Tr(k minus 2)
Qr(k)
Input Output
Figure 5 Inputoutput mapping of the SVM heat release estimator
119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing
of the actuator at certain time has been shown as 119891119886(119905) =
minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in
Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor
41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876
119903) which is not ameasurable parameter is estimated
through the SVMmodel
42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which
SVM estimator
Batch reactor y(k)u(k)
zminus1
zminus1
zminus2
zminus2
Qr(k)
Figure 6 Training method for the heat release estimator
0 20 40 60 80 100 120
Time (min)
Predicted (SVM)Actual
1600
1400
1200
1000
800
600
400
200
0
minus200Qr
(kJm
in)
Figure 7 Response of SVM 119876119903estimator under normal condition
the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown
in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is
developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7
The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876
119903) which is
the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers
43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876
119903) Each fault is introduced through simulation and
the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work
431 Process Fault
(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation
Modelling and Simulation in Engineering 5
(nominal)
Faults
Residual (faulty)
Signature window
Features extraction
Feature reduction bySVM attribute
Batch reactor
SVM estimator model (under faulty
condition) SVM estimator model
ANN classifiers
Faults
Qr
Qr (in presenceof fault)
ip
minus
+
Figure 8 Block diagram of fault diagnosis process
Table 2 Fault description
Slnumber
Faulttypes Fault description Category
1 Fault1 Δ119867mdashheat of reactionchange Process fault
2 Fault2119872119886119872119887change (initial
values of input componentfeed change)
Process fault
3 Fault3 Heat transfer coefficientchange (119880) Process fault
4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault
6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault
in 119876119903residual for 10 20 30 and 40 increase
and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value
of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876
119903residual for the heat
of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10
(iii) Change in initial charge of reactants (119872119860 119872119861) a
change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876
119903residual for 10 20
25 and 30 decrease and increase in initial chargeare as shown in Figure 11
In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed
432 Actuator Fault The actuator fault considered here is asfollows
(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3
(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4
The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13
From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary
433 Sensor Faults The following sensor faults are consid-ered in this work
(i) jacket temperature and reactor temperature measure-ments with the white noise
(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876
119903residual for the sensor faults is shown in
Figure 14The signature of the sensor fault pattern is varying with
respect to the sources of different components and at the timeof fault
From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below
(i) Mean average value of a signal is termed as meanvalue as given in
120583119862=
1
119872119873sum
119894
sum
119895
119875119888
119894119895 (3)
(ii) Standard deviation it is a measure of energy contentin the fault signature shown in
SD = radic119899sum1199092
minus (sum119909)2
119899 (119899 minus 1) (4)
(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in
skewness = 119899
(119899 minus 1) (119899 minus 2)sum(
119909119894minus 119909
119904)
3
(5)
6 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
20
40
Time (min)
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
1400
1600
Time (min)
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Time (min)
minus40
minus20
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
Time (min)
minus1400
minus1200
minus1000
minus800
minus600
minus400
minus200
Qr
resid
ual
(d)
Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876
119903) due to 10 sudden increase in the heat transfer
coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876
119903) due to
40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)
(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in
kurtosis = [119899 (119899 + 1)
(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(
119909119894minus 119909
119904)
4
]
minus 3(119899 minus 1)
2
(119899 minus 2) (119899 minus 3)
(6)
where 119899 is the sample size and 119904 is the standard deviation
5 Results and Discussion
The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware
51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit
52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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DistributedSensor Networks
International Journal of
4 Modelling and Simulation in Engineering
100999897969594939291
0 20 40 60 80 100 120
Actu
ator
inpu
t
Time (min)
Added actuatorbias
(with
bia
s add
ition
)
Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes
Actuator freezing
936
932
928
924
920 20 40 60 80 100 120
Time (min)
Actu
ator
inpu
t(w
ith fr
eezi
ng)
Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)
Tr(k minus 1) Tr(k)
Tj(k)Tj(k minus 1)
Qr(k minus 1)
Tr(k minus 2)
Qr(k)
Input Output
Figure 5 Inputoutput mapping of the SVM heat release estimator
119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing
of the actuator at certain time has been shown as 119891119886(119905) =
minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in
Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor
41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876
119903) which is not ameasurable parameter is estimated
through the SVMmodel
42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which
SVM estimator
Batch reactor y(k)u(k)
zminus1
zminus1
zminus2
zminus2
Qr(k)
Figure 6 Training method for the heat release estimator
0 20 40 60 80 100 120
Time (min)
Predicted (SVM)Actual
1600
1400
1200
1000
800
600
400
200
0
minus200Qr
(kJm
in)
Figure 7 Response of SVM 119876119903estimator under normal condition
the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown
in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is
developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7
The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876
119903) which is
the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers
43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876
119903) Each fault is introduced through simulation and
the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work
431 Process Fault
(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation
Modelling and Simulation in Engineering 5
(nominal)
Faults
Residual (faulty)
Signature window
Features extraction
Feature reduction bySVM attribute
Batch reactor
SVM estimator model (under faulty
condition) SVM estimator model
ANN classifiers
Faults
Qr
Qr (in presenceof fault)
ip
minus
+
Figure 8 Block diagram of fault diagnosis process
Table 2 Fault description
Slnumber
Faulttypes Fault description Category
1 Fault1 Δ119867mdashheat of reactionchange Process fault
2 Fault2119872119886119872119887change (initial
values of input componentfeed change)
Process fault
3 Fault3 Heat transfer coefficientchange (119880) Process fault
4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault
6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault
in 119876119903residual for 10 20 30 and 40 increase
and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value
of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876
119903residual for the heat
of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10
(iii) Change in initial charge of reactants (119872119860 119872119861) a
change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876
119903residual for 10 20
25 and 30 decrease and increase in initial chargeare as shown in Figure 11
In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed
432 Actuator Fault The actuator fault considered here is asfollows
(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3
(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4
The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13
From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary
433 Sensor Faults The following sensor faults are consid-ered in this work
(i) jacket temperature and reactor temperature measure-ments with the white noise
(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876
119903residual for the sensor faults is shown in
Figure 14The signature of the sensor fault pattern is varying with
respect to the sources of different components and at the timeof fault
From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below
(i) Mean average value of a signal is termed as meanvalue as given in
120583119862=
1
119872119873sum
119894
sum
119895
119875119888
119894119895 (3)
(ii) Standard deviation it is a measure of energy contentin the fault signature shown in
SD = radic119899sum1199092
minus (sum119909)2
119899 (119899 minus 1) (4)
(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in
skewness = 119899
(119899 minus 1) (119899 minus 2)sum(
119909119894minus 119909
119904)
3
(5)
6 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
20
40
Time (min)
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
1400
1600
Time (min)
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Time (min)
minus40
minus20
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
Time (min)
minus1400
minus1200
minus1000
minus800
minus600
minus400
minus200
Qr
resid
ual
(d)
Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876
119903) due to 10 sudden increase in the heat transfer
coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876
119903) due to
40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)
(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in
kurtosis = [119899 (119899 + 1)
(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(
119909119894minus 119909
119904)
4
]
minus 3(119899 minus 1)
2
(119899 minus 2) (119899 minus 3)
(6)
where 119899 is the sample size and 119904 is the standard deviation
5 Results and Discussion
The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware
51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit
52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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International Journal of
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DistributedSensor Networks
International Journal of
Modelling and Simulation in Engineering 5
(nominal)
Faults
Residual (faulty)
Signature window
Features extraction
Feature reduction bySVM attribute
Batch reactor
SVM estimator model (under faulty
condition) SVM estimator model
ANN classifiers
Faults
Qr
Qr (in presenceof fault)
ip
minus
+
Figure 8 Block diagram of fault diagnosis process
Table 2 Fault description
Slnumber
Faulttypes Fault description Category
1 Fault1 Δ119867mdashheat of reactionchange Process fault
2 Fault2119872119886119872119887change (initial
values of input componentfeed change)
Process fault
3 Fault3 Heat transfer coefficientchange (119880) Process fault
4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault
6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault
in 119876119903residual for 10 20 30 and 40 increase
and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value
of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876
119903residual for the heat
of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10
(iii) Change in initial charge of reactants (119872119860 119872119861) a
change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876
119903residual for 10 20
25 and 30 decrease and increase in initial chargeare as shown in Figure 11
In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed
432 Actuator Fault The actuator fault considered here is asfollows
(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3
(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4
The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13
From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary
433 Sensor Faults The following sensor faults are consid-ered in this work
(i) jacket temperature and reactor temperature measure-ments with the white noise
(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876
119903residual for the sensor faults is shown in
Figure 14The signature of the sensor fault pattern is varying with
respect to the sources of different components and at the timeof fault
From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below
(i) Mean average value of a signal is termed as meanvalue as given in
120583119862=
1
119872119873sum
119894
sum
119895
119875119888
119894119895 (3)
(ii) Standard deviation it is a measure of energy contentin the fault signature shown in
SD = radic119899sum1199092
minus (sum119909)2
119899 (119899 minus 1) (4)
(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in
skewness = 119899
(119899 minus 1) (119899 minus 2)sum(
119909119894minus 119909
119904)
3
(5)
6 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
20
40
Time (min)
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
1400
1600
Time (min)
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Time (min)
minus40
minus20
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
Time (min)
minus1400
minus1200
minus1000
minus800
minus600
minus400
minus200
Qr
resid
ual
(d)
Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876
119903) due to 10 sudden increase in the heat transfer
coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876
119903) due to
40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)
(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in
kurtosis = [119899 (119899 + 1)
(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(
119909119894minus 119909
119904)
4
]
minus 3(119899 minus 1)
2
(119899 minus 2) (119899 minus 3)
(6)
where 119899 is the sample size and 119904 is the standard deviation
5 Results and Discussion
The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware
51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit
52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
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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
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
6 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
20
40
Time (min)
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
1400
1600
Time (min)
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Time (min)
minus40
minus20
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
Time (min)
minus1400
minus1200
minus1000
minus800
minus600
minus400
minus200
Qr
resid
ual
(d)
Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876
119903) due to 10 sudden increase in the heat transfer
coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876
119903) due to
40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)
(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in
kurtosis = [119899 (119899 + 1)
(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(
119909119894minus 119909
119904)
4
]
minus 3(119899 minus 1)
2
(119899 minus 2) (119899 minus 3)
(6)
where 119899 is the sample size and 119904 is the standard deviation
5 Results and Discussion
The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware
51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit
52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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
Modelling and Simulation in Engineering 7
Table3Ex
tractedfeatures
from119876119903resid
ual
Class
Area
Mean
StdD
ev119883
119884119883119872
119884119872
Major
Minor
Feret
IntD
enSkew
Kurt
fArea
RawIntD
enFA
ULT
15344
652499
83542
6645
3165
66570
31624
112725
60368
113323
133605465
minus6915
45815
98031
133605465
FAULT
15396
4825032
3422
6650
3090
66569
3091
8111935
61383
113137
135084975
minus7177
49512
9816
5135084975
FAULT
1547120
2516
12918
6605
2970
6615
429830
110242
6318
9112611
137664
045
minus8507
70364
98673
137664
045
FAULT
2502824
2514
13001
6620
3205
66289
32061
111032
57660
110877
1264
18800
minus8258
6619
598595
1264
18800
FAULT
2511160
2514
82974
6655
3170
66639
3170
7110919
58675
111206
128548050
minus8338
67519
98621
128548050
FAULT
2543240
25056
3335
6690
3080
67012
30825
113514
6093
2114
176
136114410
minus7379
52455
98259
136114410
FAULT
2543510
25041
3390
6630
3235
66415
32340
111709
6194
8113203
136100130
minus725
50569
982
136100130
FAULT
2506430
2512
03087
6605
3170
6619
131695
112048
57547
111631
127218225
minus8014
62225
98512
127218225
FAULT
3522080
25093
3193
6700
3180
67070
31860
113289
58675
113067
131008800
minus7731
5776
698406
131008800
FAULT
3524365
25023
3454
6625
3125
66383
31287
112273
59465
112594
1312117
80minus7105
48477
9812
91312117
80FA
ULT
3523566
25079
3246
6590
3115
66066
31211
111258
5991
6111989
131309190
minus7596
55699
98352
131309190
FAULT
3525616
25086
3220
6620
3110
66303
3112
8111483
60029
112212
131858715
minus7661
56687
9837
8131858715
FAULT
4493968
2498
53583
6610
3270
6595
33274
8111032
56644
110465
123422550
minus6828
44626
97984
123422550
FAULT
4516780
24875
3941
6630
3150
6599
031550
111709
5890
1111918
128551365
minus6153
35855
97551
128551365
FAULT
4490539
2491
53815
6625
3205
6615
03214
8111371
56080
110506
122220990
minus6377
38662
97708
122220990
FAULT
4503296
25023
3453
6605
3240
6590
532492
110919
5777
3110834
125941950
minus7108
4852
79813
1125941950
FAULT
55144
8525000
3535
6655
3155
66409
31753
112725
58111
112393
12862200
0minus6931
46035
9804
12862200
0FA
ULT
5502892
25090
3205
6620
3225
6613
532334
111483
57434
111140
126178590
minus7701
57302
9839
4126178590
FAULT
5520676
25065
3301
6640
3165
66356
31526
111483
59465
111976
130508235
minus746
53659
98295
130508235
FAULT
5515840
25095
3186
6640
3180
66258
31858
111935
58675
112002
129452025
minus7748
58039
98413
129452025
FAULT
5519024
23486
6876
6685
3120
67091
31267
11091
959578
111582
121902750
minus3123
7753
9210
6121902750
FAULT
6518000
2414
35722
6540
3230
65845
32111
112837
58450
112619
125065515
minus3983
1386
94682
125065515
FAULT
6517443
24400
5179
6545
3135
66061
31644
112499
58562
112399
126258915
minus4499
18238
95688
126258915
FAULT
6524160
24489
4974
6570
3210
66489
31861
1137406
58675
113422
128365215
minus472
20281
96038
128365215
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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
8 Modelling and Simulation in Engineering
0 20 40 60 80 100 1200
50
100
150
200
250
300
350
400
Time (min)
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
Time (min)
minus150
minus100
minus50
Qr
resid
ual
(c)
Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876
119903) due to 25 decrease in heat of reaction
(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876
119903) due to 10 increase in heat of reaction
Table 4 SVM ranking table
Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1
Table 5 Confusion matrix for different classifier
Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6
the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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Shock and Vibration
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Civil EngineeringAdvances in
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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DistributedSensor Networks
International Journal of
Modelling and Simulation in Engineering 9
0 20 40 60 80 100 120
0
100
Time (min)
minus500
minus400
minus300
minus200
minus100
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time (min)
minus100
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
50
100
150
200
250
300
350
400
450
Time (min)
minus50
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
50
Time (min)
minus100
minus150
minus50
minus200
minus250
Qr
resid
ual
(d)
Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872
119860119872119861) (a) Residual (in terms of 119876
119903) due to 25
increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876
119903) due to 30 decrease in the initial values of the raw
material (119872119860 119872119861) (c) Residual (in terms of 119876
119903) due to 20 decrease in the initial values of the raw material (119872
119860 119872119861) (d) Residual (in
terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872
119860119872119861)
Table 6 Results for training of fault features
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1
From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier
The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea
The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net
Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative
10 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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 Modelling and Simulation in Engineering
Table 7 Performance criteria of the classifiers
Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features
Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011
Total number of instances 24
Table 8 Correlation matrix (PCA)
Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1
Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025
StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038
119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099
119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1
119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098
Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099
Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099
Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1
IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044
Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052
fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1
RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1
Table 9 Eigen vectors for each feature
Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen
Table 10 PCA ranked attributes
Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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
Modelling and Simulation in Engineering 11
0 20 40 60 80 100 120
0
10
20
30
40
Time (min)
minus10
minus30
minus20
Qr
resid
ual
(a)
0 20 40 60 80 100 120Time (min)
0
10
20
30
40
minus10
minus30
minus20
Qr
resid
ual
(b)
Time (min)0 20 40 60 80 100 120
0
20
40
60
minus80
minus60
minus40
minus20
Qr
resid
ual
(c)
Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876
119903) due to actuator freezing
at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in
terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)
Table 11 Classifier performance comparison based on PCA and SVM
Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA
Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031
square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy
From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are
poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data
The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value
12 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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 Modelling and Simulation in Engineering
0 20 40 60 80 100 120
0
50
Time (min)
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
20
Time (min)
minus160
minus140
minus120
minus100
minus80
minus60
minus40
minus20
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
100
200
300
Time (min)
minus400
minus500
minus600
minus300
minus200
minus100
Qr
resid
ual
(c)
0 20 40 60 80 100 120
0
100
Time (min)
minus400
minus500
minus600
minus700
minus300
minus200
minus100
Qr
resid
ual
(d)
Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876
119903) due to actuator biasing at the
time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876
119903) due to
actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)
for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed
The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10
Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA
6 Conclusion
This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter
estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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
Modelling and Simulation in Engineering 13
0 20 40 60 80 100 120
0
5
10
15
Time (min)
minus15
minus10
minus5
Qr
resid
ual
(a)
0 20 40 60 80 100 120
0
10
20
Time (min)
minus40
minus30
minus20
minus10
Qr
resid
ual
(b)
0 20 40 60 80 100 120
0
2
4
6
8
10
Time (min)
minus4
minus6
minus2
Qr
resid
ual
(c)
Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876
119903) due to reactor temperature sensor measurement with
white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876
119903) due
to bias in jacket temperature sensor measurement
classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge
based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009
[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000
[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989
[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005
[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010
[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011
[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005
[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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
14 Modelling and Simulation in Engineering
[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010
[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011
[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999
[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002
[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989
[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988
[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005
[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999
[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989
[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000
[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006
[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011
[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988
[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008
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
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