Data-Driven Fault Diagnosis in a Chemical Process

Thomas W. Rauber 'Celso J. Munaro-

'Depar tamen to de Informát icaUniversidade Federal do Espíri to Santo - UFESAv. F. Ferrari, 29065-900 Vitória - ES, BRASIL

thom as@in f.u fes.br

de Enge nha ria Elét ricaUniv ersid ade Federal do Espírito Santo - UFES

Cai xa Postal O1-90 I I, 29065-900 Vitória - ES , BRASILmunaro@ele .ufes.br

Abstract: The objec tive of th is paper is the present ation of sophist icate d pattern recogn ition techniquesfor model-free fault de tec tion and diagnosis in an indus trial product ion processoWe argue tha t effectiveprocess supervision can be achieved by example-based learn ing of the d ifferent situa tions of theprocessoResult s for a simulated co ntinuous ly stirred tank reac tor process are presented .

Resumo: O objetivo des se tex to e a apresen tação de técnicas sofis ticadas de reconhecimento depadrões para a detecção e diagnós tico de falhas em um processo de produção ind ustrial.Argumentamos que e possíve l real izar uma supervisão de processos efic iente por aprend izagembaseado em exemplos das d iferentes situações do pro cesso. Apresentam-se resultados para um reatorquímico simulado.

1. IntroductionThe topic of fault det ection (rnonitori ng) and diagnosi shas been the theme of inten sive research over the lastyears. It is an interdisciplin ary field, incorporating thework from contro l, e lect rica l eriginceri ng, co rn pute rsc ience and the area of app licat ion. for instance chcm i-ca l eng inee ring. A broad range of other appli cat ionareas require these me thods which are ablc to decide ira system is wo rking co rrec tly or erroneo us ly and reportthe nature of the faul t, e .g. ai rp lanes , power plants.medi cai systems, rnanu facturing, etc . Mo nitoring anddiagnosis ca n prevent damage to a system and its envi-ronme nt and can avo id cos ts associated with the abnor-mal operation 01' a system . Sophisticated mon itorin gand di agnosis ca n extend the capability and increasethe accuracy of simpler techniques.

Th er e are two principa l approac hes to iden tify afault: model -based techniques and model- free tech-niques. The model-based method rely on a mathem ati -ca l representation of the process dynamics. A tault isidentified if intern ai variables (pa rame ters, proces sstate var iables) o f the model deviate frorn thei rexpected valu es. Som e key publicati ons for the model -based approach are [Willsky ( 1976) ], [Bassev ille( 1988 )], [Isermann (19 84)], [Isermann ( 1993)] and

260

IFrunk ( 1990)I· Oft en the terrn knowled ge-based diag-nosis is used when exp ert sys tem like methods arecornbined with the analyti cal models, e. g . [Isermann( 1993)] .

An advantage of rnodel-based d iagn osi s is the apriori know ledge about the fault, beeause it is inco rpo -ratcd into the math emat ical mod el. Hen ce there is noneed to acquirc add itiona l know ledge by example situ-ations. The fundame ntal probl em s of the model-basedapproac h are the need to model the proeess ana lyti-cal ly, the es tima tion of the invol ved var iables and thediscrepancy between the rea l process and the mod el(model error) . A process of e leva ted complexi ty is d if-ficult to rep rese nt ana lytica lly.

Alterna tive ly di agnosis can be ap proached bypa ttern recognitio n, see [Himrnelbl au ( 1978)] for <inea rly work in this direction . A reeent publica tion fromone of the most importa nt co nfe renees in the field offau!t det eetion and diagnosis, IFAC-SAFEPROCESS ise.g . [Poul ard-Labreche ( 1997)] .

Th e fundamental d ifference to model-based faultdetection lies in the way how the knowledge about thefaul ts is represented. Each process situation is consid-ered as a point in a high-dimen sional patt ern spacewhere eac h ax is represents a measured or'vestimated

variable of the processo Normal functioning and faultsfonn different classes which have to be clas sified bypauern recognition techniques .

Artificial neural networks are the preferred para-digm to model the know ledge about the faults, see e.g.[Sor sa et aI. (199 1)], [Sorsa-Koivo (1993)] or [Fuente-Represa (1997)] . Like in other application areas artifi-cial neura l nets are able to perforrn multivariate regres-sion and classificati on tasks without having the needfor a deep understanding of the statistical nature of thepattern generating processo

2. Model-Free Fault Detection andDiagnosis

In this section we give a brief introduction into thefield of pattern recognition and how it can be applied tomodel-free fault detection. Fir st we will view the pro-cess of a pattern generating source which produces ahigh-dimensional feature vector. The vector is assoei -ated to the actual situ ation of the process , the class .Classes represen t the normal behavior and the variou sfau lts. We will analyze the questi ons related to the situ-ation representation by a high-dimensionaI feature vec-tor. We have to filter out irrelevant and redund antinformation that is hidden in the feature values in orde rto achieve optimal result s. This can be done by featureselect ion and feature extraction. The processed fea-tures are then fed to the clas sifier, e.g. a neural net.Often, no preprocessing of the features is performed oris intrinsically perforrned within the classifier itself.We will point out that the most important quality cri te-rion of the classifier is a low error rate . Thi s criterion isnot always taken into consideration in the literature.

The visua lizat ion of high-dimensional featurevectors is most ly done by the fi rst two values of theprincipal components of the original feature vector. Wewill illustrate that more sophisticated methods forinstance the nonlin ear Sammon map is a viable altern a-tive to visualize the process state, especi ally when themutual feature correlation is nonlinear.

2.1 Process as Pattern SourceThe basic philosophy of the model-free pattern-recog-nition approach to fault dete ction and diagnosis is tocollect as many measurable information from the pro-cess as possible. For the sake of easier understandingwe will consider only continuous measurernents . A setof measurement s from the process using sensors is rep-resented as e pauernx = (x i' . .., xD / in the form ofaD-dimensional vector of continuous features, i.e.J E RD

. A situation in which the process is encoun-tered (normal, fault I, fault2, etc .) is a class (f)i from theset n = {(f)I ' . . . , (f)i' . . . , (f)el of c mutually exclu siveclas ses. If we allow a rejec tion opt ion, an additionalc1ass (f)o is introduced [Duda-Hart ( 1973)].

Patterns in the sense of cla ssification problems

are pairs (J, co) which associate the feature vector -!with its meaning , i.e. to which class (f)i it belongs. Fig .I depicts an example process, in this case a lathe. Sen-. sors collect different measurements which are assem-bled into the feature vector.

In a probabilistic framework we are interested inprobabilities and probability densities which can beused to model the probabilistic distribution of the pat-tem generating process and draw conclusions about theclass membership of a certain object.

The pattern classification of the process is basedon a lear.i ing-from-example approach. This means thatthe problem is described by a finite set of II examplepairs { (JI" (f)1'));:= I , each pair consisting of the fea-ture vector and the class label.

These examples are the only available informa-tion about the process in a model-free case. We musttherefor rely on them to build our pattern c1assifier, i.e .define the structure of the classifier. Furthermore, if weuse a parametric statistical or neural model we mustadapt the free parameters of the pattern classifier. AIsofor this task the data samples can be used. A good elas-sifier generalizes the data well. This means that futureunknown samples are c1assified conforming to the truedistribution of the data. It means also that the classifieris not overfitted to the noise in the samples, i.e. wemust find a good compromise between the degrees offr eedorn and the flexibility of our class ifier models.

The knowledge about the actual process situationclass roi has to be inserted into the example data baseby a human operator. A problem related to the learn-ing-from-example approach is that often some classesare underrepresented, for instance it is difficult to pro-vide training data for a certain fault class.

o Sensor [ ] Sensorialg XI pattern

- x2 = J =-!(l)

(f) = normal

Fig. 1 Process as pattern source

Generally speaking the patterns are time variant.Thi s means that the process state is described by amultidimensional feature vector -! = J(t) that variesover time , describing a path. in a high-dimensional fea-ture space. For instance in a controlled process thatapproaches and finally reaches a steady state at timeI = I", of ali the controlled variables, the path -!( l ) willreach a constant attractor after I." where -!(t) = -!(t )for I t" . For pattern recognition temporally stable pat-terns are desirable. Nevertheless spatio-temporal elas -sification shou ld be considered, especially in transientstates.

261

2.2 Information FilteringHuge amounts of da tu is acquircd during lhe learni ngphase and during lhe superv is ion 01" lhe proc es s todetect the faults. There are fe atures that are highl y cor-rel ated to ot he r feat urcs, there are irrcl evant fea turcsfor the c lass ification problem and thcre is noise cachedwit hi n lhe fea tures . The task of fea tur e se lec tion andfea ture ex traction is lo reta in lhe most usefu l informa-tio n for c lassification. As it was mentioned before weshould c1early bear in m ind lhe qua lity cri terion of lhefault detect io n and d iagn osis sys tern, nam ely a highaccuracy. Gen erall y it is indi spen sablc lo process lheraw feature vec tor .1 lo ob ta in ano ther Iea ture vectorthat ach ieves ex ac tly th at g lobal goal.

O ften Prin ci pal Compo ne nl A na lysi s (PCAl [Jo l-liffe ( 1986)] is employed for feature ex trac tion. Thefirst two princ ipal components ca n be used for vis ual-ization of the orig ina lly high -dimension al pauernspace. [Z hang et aI. (1996)] have used PCA for vis ual -izati on and the princi pal co rnpone nts for c lassifi cation.S ince in most cases there is a highly linear correlationamong the fea tures, the PCA ernpirica lly shows thatmo st in formation about lhe proccs s statc is co ntainedin the firs t few principal compo nents . 11' this linearinterdependence wcre not prescnt , i.c . lhe co rre lationamong the fea tures were highl y nonli near, then a non -linear mappin g frorn the high -dimen sional sp ace lolower d im ens ion s for visualizat ion would be better. Auseful techniques that kee ps the rel at ive mutual di s-tance among the features proportiona l is lhe Sammonmap [S ammon ( 1969)] thus prov id ing a better pic tureabout the pattern dis tri bution lo the obse rver than lin-ea r mapping techniques.

2.3 Classification of Process Patterns intoFault Classes

CaIling the even tua lly new fea ture vcctor X aga in ·1,the ac t of fault detection and d iagnosis co nsis ts 01'using decision func tio ns çjC!;) , one diC!;l for cachc1ass roi' tha t m ap lhe teature vec tor -I into the classspace. Innumerou s c lass ifie r arc hi tec tures have beenproposed , for instance Nearest Neighbor/Proto type,Parzen Windows , den sity mo de l-based (e .g. Qu adrati cGaussian) , L inear Machines , Mul til ayer Perceptrons ,Rad ial Basis Funct ion networks, Learn ing Vect orQu antization or Po lynomial c lass ifiers. Re levant text-books are for instan ce [Duda-Hart (1973)] , [Devijver-Ki ttl er ( 1982)], [H aykin ( 1994)] and [Bishop ( 1996)] .

One importanl aspect of us ing a certai n c1ass ifierarchitecture is its sui tabili ty for fault detection anddiagn osi s . Model s lhal de live r an accurate estimate oI'the a posterior i probabili ty P( roJ-Il lhat pa ne rn ""belongs to c1ass ro are a good choice whe n decis io nris ks and reject ion options are co ns ide red. Mul tilayerPercep tron s, used for fault detecti on e.g . in [Sorsa e t a I.( 199 I )] must be cons idered with ca re. The net gives

a lways a response, even if the process feat ure vector iss itua ted in pa tte rn space far away fr orn pl au sible va l-ucs, Better cho ices are pro totype -based mod els, forins tance Learning Vect or Quantization [Kohonen( 1990) ] becau se the c lassifica tio n is based on a di s-lance function be tween representa tives o f a lreadyknown process s itua tio ns and the un known si tua tio n. Asit uat ion tha t is toa far away from known pro totypes(o utl ier) must then be treated in a spec ia l manner.

3. Example ProcessAs our object 01' study we choose a proces s s im ula tio nthat has been use d extensively in control and faultdctection and di agnosis [Oyeleye-Kramer (1988 )] ,[Sorsa e t aI. ( 199 1)], [Sorsa-Ko ivo ( 1993)], [Zhan g-Morr is ( 1994 )], [Zhang et aI. (1996)] . The co ntinu-ously stirred tank reacto r is a process that shows typi-ca l qu alities of an industrial processo Det a ils can befou nd in lhe annex .

4. Experimental ResultsWe will now co nduc t experime nts that employ so phis-ticated partem rec ognit ion techn iques used in the con-text 01" model-tree fault de tec tio n and diagn osis . Theaim is to crnp ir ica lly prov e the use fuln es s of ge ne ra lpurpose pa tte rn recognit ion app lied lo the monito rin g01' indus tria l processes .

4.1 Steady-State Patterns, PrincipalComponent Analysis for Visualizationand Polynomial Classification

Fi rst we will co ns ider pa tte rns that were acquired fromlhe pro cess wh en the involv ed variables were a lmosts tabilized after lhe occ urrcnce of a fault. What we canexpecl are c lusters in the 13 -dirnensiona l pattern spacetha l charac lerize a part icular fault si tua tio n. In the firs texper iment two different faults o/ere incurred . S tart ingat 5000 .\' = Sk s the inpu t pipe was partiall y blocked,i.e . Fo was red uced frorn 2 .5kg / s to 2 .0k g/s. T hefault was e lim inated again at 9ks . From 7ks to 10k slhe input concentra tio n of A was se t high fro rn120011l o /lm ' to 1500I1l o l/m'. The plot Fi g. 2 showsthe evo lutio n o f the fea tures in ihe co ns ide red tim einter val. It sho uld be noted that there are mult ipIefaults , i.e . from 7k s to 9ks two di fferen t faults oc curs imul tan eou sly.

Dat a wa s acquired from 1ks to Sks, from 6k s to7ks and 8ks to 9ks , each samp le ac quired each 50s ,resu lting in 120 sa,mples . T he features were un ivari-ate ly scaled to uni ty re lat ive to the default va lues .Whit e Gaussian noi se wi th a standard deviation oI'a = 0.05 was then appli ed to the features to achieve astochast ic beh avior in the pure steady -s tate case.

A principal 'component an alysis was pe rforme dwi th the acquired data seI. The first two compo ne nts,

262

Firsr two Principa l Compon cnrs1.9 _"""'T---.----.r----.---..---r--,....-_.,

0.019 .*0.018

0.017.;;;"" 0.016"cJ)tii"O 0.015"'" 0.014

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Linear discriminam analys is104 Features are full quadratic ser of original 13 features

Fig. 4 Linear Oiscriminant Analysis of the fullquadratic set of lhe features. Two principal

-Icomponenls of SIVSB .

0.012 ......_---'__......._--1.__"'-_-'-__.....

-0.502 -0.5 -0.498 -0.496 -0.494 -0.492 -0.49ISI Eigenaxis

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of a General Linear Discriminant Function [Duda-Hart(1973)] . The expansion to a full quadratic set results ina total of 104 features. Then a linear discriminant anal -ysis was performed, in two non-negativeeigenvalues of the mat rix SB' where Sw is thewithin-scatter matrix and SB the between-scattermatrix of the 3 classes [Duda-Hart (1973)]. The plot ofthe linear discriminant analysis is shown in Fig . 4. Itcan be observed that the separation of the classes ismuch neater than in the case of lhe first two principalcomponents of Fig. 3. We can expect that a processmonitor based on this more elaborated feature modelwill commit less c1assification errors and is thereformore reliabl e than a c1assifier based on the original fea-ture set or its principal components .

S 9 10<}--l> t [IOOOsecl

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Fig. 2 Multiple faults: blocking of input pipe and inputconcentration of agent A high.

responsible for about 82.9% of lhe variance were usedto visua!ize lhe si tuation of lhe pracess situation in theoriginal 13-dimensional pattern space. Fig.3 showsthe situation of the fault s and of the normal behavior inthe 2-0 spac e of the first two components. The threeclasses can be c1early distinguished fram each other.Note that one c1ass represents a doubl e fault. Consider-ing the well behaved c1uster structure of the classes , ac1assifier that uses the first two principal componentscan be expec ted to linearly separate the classes.

Normal o

11/1'11/ I'il'e pnnial!» l>Iocket!InpUI p ip i! pnnialt, bl urketl + input con ccntration A !tigll o

Fig. 3 Process situation in lhe 2-0 space of lhe fi rst twoprincipal cornponents of the 13-0 originalpattern space. Steady-state, normalized and noiseadded.

We have to recall that the primary quality cr ite-rion of any c1assi fier should be a low error rate. Theprincip al compo nents do not always achieve that goa l.Since it is a linear transformation of the orig inal fea-tures it does not permit to search for nonlin ear combi-nations of the features which eventually lower the erra rrate . We performed an experiment where new fe atureswere generated for a polynomial c1assifier up to thesecond degree (i.e. a quadrat ic classifier), in the sense

1.2

J.I . ,

J.I 1.2 U 1.4 I.'i 1.6 1."7J s i Eigenaxis

4.2 Transient-state AnalysisWe will now analyze the behavior of the features in thecase where faults occurs whilst the variables are adapt-ing thems elves to the new situation. Thi s stabilizationof the 13 variables is equivalent to a movement of apoint or vector in the 13-dimensional pattem spacealong a path towards a constant, i.e. an attractor pointin the pattern space. For this experiment no noise wasadded to the feature values in order to enhance the pathalong which the pattem point is moving. Two differentfault s were incurred, this time single faultsat differenttimes. From 0.5ks to 1ks a malfunctioning of thepump was simulated, i.e. the pump parameter Ap wasincreased from -4200Pa s/ kg to -2000Pa s/ kg. Thetemperature contra I valve was stuck high from 3ks to3.5ks, see Fig. 5.

Data was acquired from 0.2ks to O.3ks , fram0.5ks to 0 .6ks and 3ks to 3.1ks , each sample acquiredeach 2s, resul ting in 200 samples. The features wereunivariately scaled to unity relative to the default val-ues. Fig. 6 shows again the first two principal compo-

263

Feat11re

Fina two Principal Componcrus

Fig. 5 Two faults: pump defect and tcmperature coutrolvalve stuck high

Our general impression about the presented .pro-cess is that a linear feature extraction meihod is suffi-cienl lo model the essential information hidden in alimeasured data. Hence nonlinear feature extraction andclassification approaches can show only a minimumgain with respecl to visualization and c1assification.

We have shown that fault detection and diagnosis isviable by a rnodel-free pairem recognition based onsupervised learning. Process situations are character-ized hy ali available sensorial data from the process oAstate 01' lhe process corresponds to a point in a high-dimensional pattern space, both in steady-state and intransient state. The c1assification is mainly studied inlhe steady state case. Classifiers for transient statecases are much more challenging. Spatio-ternporal pat-tem recognition must be applied to solve that problern.Future research could be directed to that case,

The simulated process, although possessing first-ordcr nonlinear dynamic equations seems to be intrin-sically linear. This is experienced when the 'principalcomponents are extracted, They eliminate the linearcorrelations among lhe features, leaving mostly onlyone ar two non-zero components . A future researchactivity could also be the simulation of more complexprocesses which exhibit the advantages of nonlinearvisualization and classification.

5. Conclusions and Future Work

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nents of ali features. Arrows are auached to thepatterns in order to show the temporal evolution of lhepath. It can be observed ihat lhe patterns approximatethe attractor which corresponds lo lhe steady state ofeach class. In comparison lo lhe plot of the principalcomponents, Fig. 7 shows the 2-D Sammon plot of lhesame transient evolution 01' lhe features. 11 seems thatthe nonlinear properties of lhe partem path are bettercaptured by this nonlincar mapping tcchnique, espe-cially in the case of lhe class "Purnp malfunctioning".

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AnnexWe adopted the specificarion 01' the continuouslystirred tank reactor 01' [Sorsa et al , (1991)], see Fig. 8.A chemical agent A is poured into a tank reactor whereun exothermic reaction A -7 B takes place. A enterswith a flow rate Fo, temperature TIl' and an input con-centration of CIIO. The processed product is transportedout of the tank by a pump with flow rate F. Products Aat concentration c11' B at cB ' both with flow rate F pare leaving the processo

Fig. 7 Sammon plot 01' the transient state

Fig. 6 First two principal cornponents 01' lhe transient state

-004 -0.3 -0.2 -0.1 O 0.1 0.2 0.3 04Mappcd dirn cnsion # I

Fig. 8The continuously'stirred tank reactor

In order to keep the ternperature in the tank con-stant a part 01' the liquid is conducted back into the tankat temperature TR through a heat exchanger whereenergy is transferred into a cooling circuit. The coolingfluid enters with flow rate FIV at ternperature T i ll and

Tcmperuturc control vulve-"IIe{ ,., '\. aa f

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a ..........

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264

leaves at temperature T" "I 'Three vari abl es are co ntrollcd , the levei o f the

tank LM at se t point Ls by controll er CL' the recycl eflow ra te FR at Fs by CR and the temperature of thereactor TM at Ts by Cr .

Th e 13 features that are used for fault det ecti onand di agnosis are the 11 enc ircle d varia bles plu s the 3manipulated variables of the three co ntro llers, a I ' (/2and F IV' Vari able F IV has been already includedbefore, and is the refor counted only once.

We made slight changes to [Sorsa et al, ( 199 1)] inorder to complete ar modify proc ess values and equa-tions supposedly not appropriate for the simulation:TR = 36"C T = 57.9"C , (/1 = 35.5, a-, = 0 .15,, 0111 _

Ali/a.r = 0.001 , brackeiing (RTMJ always,F = Fp+FR , LM = (1 / (p AMJ)(Fo-Fp-FletlkJ ,

using F IV directly as the controll ed variable o f control-ler Cr and substituting the PI-controllers by a PID-controller for Cr with TD = 200.1' . Th e othe r parame-ters for the controllers are (us ing the terminolo gy of[Ise rmann ( 1989 )]) : K = -I for ali co ntrolle rs ,TI = 10.1' for CL and T, = 15.1' fo r Cr and CR •

The simulator was coded in C . the so lutio n of theordinary d iffere ntial equations was done by a Iourth-orde r Runge-Kutta method and the nonlinear equationsfor the flow parameters Fp ano FI? were so lved byhisecti on [Press et al. ( 19S8 )J.

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