FaultDetectionandDiagnosisusingQualitativeModellingandInterpretation

J. M. Vinson andL. H. Ungar

Departmentof Chemical Engineering,Universityof Pennsylvania,

Philadelphia,PA

Abstract. TheQualitativeModelling andInterpretation(QMi) systemtranslatesnoisysensordatainto aqualitativedescriptionof theunderlyingbehaviorof achemicalplantandusesthisinformationtogetherwith qualitativemodelsto identify faultsandoperatingregimes.Qualitativemodelsof normalandfaulty equipmentaresimulatedto describetherangeof possiblebehaviorsinachemicalplantwithout theneedforexactnumericmodelswhichareunavailablefor manyfaults.Sensordataarethenusedto selectbetweendifferentmodels.Simultaneouslyusing interpretationsfrom multiplesensorsreducessensitivityto sensornoise,increasingdiagnosisreliability. QMIhasbeenimplementedonasimulatedpropyleneglycol reactorwith goodresults.

~ Failuredetection,identification,leak detection,monitoring,qualitativesimulation.

INTRODUCTION

QualitativeModellingandInterpretation(QMI) isan on-line processmonitoring systemwhich combinesquantitativechangedetectionwith qualitativemodellingto diagnosefaults in chemicalplants. QMI translatessensorreadingsto aqualitativedescriptionwhereeachvariableischaracterizedby its relationto landmarkvalues (e.g.zero,boiling point,equilibrium molefraction)andthesignof its derivative.Thesesensorinterpretationsarecomparedto simulationsof multiplequalitativemodelsin orderto find themodelwhichmatchestheobservedbehavior.

Manyprocessmonitoringsystemshavebeendevelopedwhich detectanddiagnosepotentiallycostly ordangeroussituations.Two commonnumericalmethodsarechangedetection,typically usingalarm thresholds,andmodelselection. Becauseincomingdatafrom sensorsisgenerallynoisy.alarmthresholdsfor singlesensordetectionmethodsmustbe settobalancebetweenquickdetectionwith frequentfalsealarmsandinfrequentfalsealarmswith slowerdetection.Traditionally,alarmthresholdsaresetto eliminatefalsealarms.Moresophisticatedalarm thresholdtechniquesincludeShewhartand cumulativesum(CUSUM) control chartswhich arestatisticaltestsfor thedeterminationof achangefrom expectedbehavior(Bowker,1972;Box,1970; Shewhart,1931).

In contrast,modelselectionmethodsfit incomingdatafrom singleor multiplesensorsto detailedplant modelsvia techniquessuchasKalmanfiltering or non-linearprogramming(Frank,1990;Isermann,1984; Wiisky,1976). Themodelwhichbestfits thedatais consideredto bethecurrentmodelof the plant,andthus thediagnosis.Toachieveawide coverageof faults andoperatingconditions,quantitativemodelsmustbebuiltwhich describeall possiblesituations,includingseveralmagnitudesof thesametypeof faults,suchas 10%,40%and80% leaks. Unfortunately,quantitativemodelsareoftenunavailablefor changeswhichtaketheplantinto unknownor transientoperations,suchasduringstart-upandshutdownprocedures.

Qualitativemonitoringanddiagnosissystemsavoid theneedforquantitativemodelsby describingplantdatainqualitativeterms: valuesmay behigh, normal or low,andtrendsmaybeincreasing,steady,ordecreasing.Thisqualitativeinterpretationis usedto determinethecausesof changesin theplant. Rule-basedor expertsystemsmapthesesymptomsdirectly to causesvia rulesobtainedfrom processexperts(Ramesh,DavisandSchwenzer,1992; VenkatasubramanianandRich, 1988).Rule-basedsystemsdo notrequireaplantmodel,howevertheydorequireamultitudeof rulesto coverallpossiblefaultsin achemicalplantandhavedifficultieswith unexpectedoperationsor newequipment. Incontrast,model-baseddiagnosissystemsexamineaqualitativeplantmodelto determinewhatchanges(faults)in themodelcouldhavecausedtheobserved

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symptoms.Recently,severalinvestigatorshave startedcombiningnumericalandqualitativemethods,eitherbyusingquantitativeinformationto constrainqualitativemodels(D~oste,1990;DvorakandKuipers,1991;BerleantandKuipers,1990;Forbus,1987),or bymixing qualitativeandquantitativemodelsto getabetterdescriptionof thephysicalsystem(ForbusandFalkenhainer,1990;Oyeleye,FinchandKramer, 1990;Yu andLee,1991).

TheQualitativel~de1lingandInterpretation(QMI)systemcombinesbothdetectionanddiagnosisinto onepackagewhich bormwsfrom bothnumericalandqualitativemethods.Multiple sensorsareanalyzedandcomparedto knownqualitativemodelsof theplant, andthatmodelwhIch fits bestis takento be thecurrentmodel of theplant. TightertolerancescanbesetonindividualsensorsbecauseQMT filtersout aphysicalinterpretationswhich may be suggestedin singlesensormethodssuchasalarmthresholdsandcontrol charts,allowing earlierdiagnosisof processdisturbanceswithoutcausingmorefalsealarms. Useof qualitativemodelsalsopermitsdiagnosingarangeof faultsandbehaviorsfor whichexactequationsarenotknown.QMI hasbeentestedon asimulatedcontinuousstirredtankreactorandgivesrelativelyrapidandaccuratediagnoses,

QUALITATIVE MODELS

In qualitativemodelling,anentireclassof faultsisdescribedwith asinglemodel, ratherthanby severalquantitativemodelswith differentnumericvaluesofparameters.Thisapproachis usefulwhen themagnitudeof the fault isunknownandplant behavior mayvarywith thesizeofthe fault. For example,a “small” leakfrom atankmay becompensatedforby acontroller,butalargerleakmaycausethecontrollertosaturate.

Qualitativemodelsusequalitativeequationsto describehowvariableschangewith respecttooneanother(e.g. inlaminar flow, flow rateis proportionaltopressuredrop).Variablesaredescribedby thesignof their slopeandrelation to landmarks(e.g. mole fractionhasthelandmarksof zero,oneandperhapsequilibrium). Thedescriptionof all thevariablesin thesystemis calledthequalitativestateof the system(e.g. watertemperatureisincreasingandbetweenfreezingandboiling points,andtheamountofwateris steadyandpositive). QMI usestheQSIMqualitativesimulationpackage(Kuipers,1986) to “solve” thequalitativemodels,producinga“tree” of behaviorsfor the models, as shownin Fig. 1.Eachbehaviororpaththroughthe tree is a series ofqualitativestates.

For example,in Fig. 1, State1 is the steadystateoperationof alevelcontrolled,watercooledCSTRandstates2 and3 areinducedchangesto thesystemwith thesubsequentstatesbeingthereactionto thesechanges.State2 is theonsetof a tank leak,wheretemperatureandconcentrationarestill steady,buttank level andoutletflow havebegunto decreasein responseto the leak; andstate3isachangeintheinletflowrate.State4describesthequalitativestatewheretemperatureandconcentrationhavebeguntoreactto thechangeinreactorlevel,with temperaturedecreasingandreactantconcentrationincreasing. State7 is thequalitativestatewherethecontrollerhasbegunto reactto the levelchange,but the level andoutlet flow rates are stilldecreasing.Behaviorsbranchingfrom state7 includereturnto setpointor saturationof thecontroller.

Normal DisturbancesState

ResultingStates

S-4 S-7~

L~S-3 i S-5~

LS-6Fig. 1. Samplebehaviortree

Qualitativemodelling ofchemicalplantsis anareaofactiveresearch.For example,DalleMolle andcolleagues(1988,1989)havemodelledchemicalreactionsystemsandproportional-integrallevel controlusingQSIM. Vinson,GranthamandUngar(1992)havemodelledachemicalplantconsistingof heatexchangers,areactor,astripperandacondenserusingtheQualitativeProcessTheoryframework(Forbus,1984),andOyeleyeandcolleagues(1990)havemodelledajacketedCSTRfor applicationin MIDAS, a fault diagnosissystem.Whenbuilding modelsof morecomplexsystemsthenumberof solutionscangetquite large,thuscaremustbe takento limit thenumberof solutionswithouteliminatingrealbehaviors(KuipersandChiu,1987;Catino, 1991).

QMI ALGO~THM

TheQMI algorithmconductstwo operationson~line:1)It translatesnoisy sensordatainto aqualitativedescription, and2) it comparesthis interpretationto thebehaviorspredictedby thequalitativemodels.Qualitativesimulationof the modelsis donebeforehand,so the behavior tree is alwaysavailableto QMI, Thealgorithmis shownin Fig. 2.

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Qualitativeinterpretationof theincomingdatais doneby finding thebestfit linethroughthe incoming datawith linear leastsquares.Theestimateof the slopeisthengivenameasureofbelief(zero - one)that it ispositive,zeroor negativevia thead-hoc functions:1

p(inc)=

1+e t\ CUtOfI

aiop~

1 + e~+~t0t~

p(~d)=1~-p(inc)-.p(~)

whereais usedtoadjusttheslopeof the curvesandcutoff is theinflectionpoint.. Largevalues of a (> 10)yield on-offfunctionswhich trip atthecutoffvalue,andsmallvalues(-. 1) give flat curves. Weusea= ~ in oursimulations.Thecutoff is set from knowledgeof thenoisein thesignal sothatavalueof p(std),p(inc) orp(dec)greaterthan0.5 indicates that the currentinterpretationis probablycorrect.

In orderto speeddetectionandeliminatefalsealarms,thebeliefsin theinterpretationsof severalsensorsaremultiplied to yield anoverallbelief in theinterpretation

ofthe stateoftheplant. In the reactorexampleabove,oneof thequalitativestateshastemperatureincreasing,concentrationdecreasingand both level and outlet flowsteady. If theinterpretationofthesesignals isp(inc,temperature)= 0.8,p(dec,concentration)=0.7,p(std,level)= 0.75andp(std,flow) 0.65, thentheoverallbelief in thequalitativestateis 0.273. We takeabeliefgreaterthan0~5Ntobea significantbeliefin thequalitativestate,whereNis thenumberof sensors.Combiningthe sensorinterpretationsallows QM] tooverlooksensorswhichappearto bechanging(duetonoise)whiletheothersremainnormal. Similarly, QMIis less sensitive to sluggishsensorswhenthe othersensorsarechangingasexpectedfrom adisturbance.

Initially, QMI assumesthe systemis behavingnormallyandonly comparesthequalitativeinterpretationto thenormalstateandthefirst statesof thedisturbancesin thebehaviortree. As moredatacomesin from theplant thequalitativeinterpretationsof thesignalschangeduetonoiseandprocessdisturbances.If adisturbanceoccursinthe plant, the qualitativeinterpretationwill changetoproducea high confidencein the initial state of thedisturbance,With thenextsetof dataQM1 will look forinterpretationswhichmatchthisstateandthosefollowing it. Diagnosisis auainedwhenonedisturbancehasabeliefthat is muchhigherthantheothers.

EXAMPLE SYSTEMAND TESTCASES

1 Wehaveexaminedtheuseof statisticalanalysistechniquesin determiningtheconfidencein thesignof agivenslope,buthavefound themto be limited in thatthereis only onehypothesisto test;whethertheslopeiszero. In statistics,thereis no ability to testfor anumberbeinggreaterthanzerowithout specifyingthevaluewhich is “greaterthanzero.”

The QMI algorithmhasbeentestedwith a simulatedpropyleneglycol productionreactorpicturedin Fig.3,from Fogler(1986). Equalvolumes(46.62cfh each)ofpropyleneoxideandmethanolaremixed with water(233.1 cfh) containing0,1 wt % H2S04which catalyzesthereaction. The~-MeOH andwaterfeedstreamsareinitially at58°Fandmixing increasestheir temperature

QualitativeInterpretation

Fig. 2 QualitativeModellingand InterpretationAlgorithm

296

to 75°F. The reactionis exothermicandpropyleneoxide is relativelylow-boiling, so reactor must be cooledto keepthetemperaturebelow 125°Fto preventexcessivevaporization.A proportionalcontrolleradjuststheoutletflow rateto preventthe level from changingdrasticallyduetochangesin supply ordemand.Thenumericalsimulationwaswritten in FORTRANandusestheLSODEnumericalintegrationpackage,basedon theGearmethod.Possiblefaults in the simulatedreactorarechangedfeedflow, tankleak,changedacidcoroeniration,changedfeedtemperature,andchangedreactantfeedconcentration.

Qualitativesimulationof thesefaultswith thequalitativemodel for thereactorproducesabehaviortree,similar to Fig. 1, with nearly400 historiesand about2000qualitativestates.As in theexample behaviortreein theQualitativeModelssection,therearemanyhistoriesproducedby qualitativesimulation,ratherthanonefor eachfault. Thesehistoriesoftendiffer in therelative timeof occurrenceofof differentevents.Forexample,whentemperatureandconcentrationbothhaveinverseresponse,qualitativereasoningcannotdeterminewhich will peakfirst.

QMI wascomparedto aversionof QMI whichhasBooleanequationsforbeliefsin thesensorinterpretationsandtoabasicalarmdetectionmethodusingsingle-sensortiu’esholds. Twelve single-faultsimulationswereconducted,andthesethreemethodswere comparedfordiagnosistime,numberanddurationof falsealarms,andnumberanddurationof misseddiagnoses.Thediagnosistime indicateshow long ittakestoproperlyidentify the fault. Falsealarmsoccurwhenthebeliefsin incorrectqualitativestalesbecomehigherthanall theothersandis dueto noisein thesignal. Misseddiagnosesarisewhentheprobabilityofthenormalstatedropsbelow0,5N(numberof sensors),

PropyleneOxide

andnoneof theotherqualitativestatesmatchestheinterpretation. This is causedby a combination ofnoiseandslower signals, suchastemperaturechangein a largetank.

In all the testcases,QMI observesfour ser~as: tanktemperature,tankconcentration,tank level,and outletflow rate. Figures4 a, b, c, anddshow the timeplotsofeachof thesesensorsfora0.25%decreasein theinletreactantconcentrationat 1.00hour. In Fig. 4 a, the tankcompositionincreasesto anew steadystatevalue,butthe initial responseis adecreasein thetankcomposition,which is difficult to detectvisuallybut isanimportantcharacteristicof thischange.Temperaturedecreasesto a newsteadystateandthe tank level andoutletflow rate remain constant.

As thisdatacomesfrom the plant,QM[ calculatesbeliefs thateachmeasurementis increasing, steadyordecreasing;thesebeliefsare shown in Fig. 5. The topgraph showsthe interpretation of theconcentrationsignal: above zerois the beliefthatthe signal isincreasingandbelow, decreasing. Thisshowsaninitialbeliefthatthe concentrationis increasing,whichwouldcauseanalarmtobesoundedwith Booleanalarms,butcomparisonwith theothersignalsshowsthattemperatureandlevelareboth steadywhileoutlet flowmaybedecreasing(belief0.5). Thisdoesnot correlatewith anyqualitativestate,so thenormalstateis stillvalid, althoughit hasalow confidence.Alarms andBooleanQMI signalachangehere,althoughnodiagnosisisproposed.Thead-hocfunctionscapturetheinverseresponseof theconcentrationat 1.105hours,atwhich time diagnosisof the fault occurs.TheBooleanversionof QMI doesnot capturethe fault until the slopeof theconcentrationcrossesthe 0.5 belief line at 1.140hours.

Fig. 3 PropyleneGlycol Reactor

Water (0.1 wt% H2S04)

~ ~

CL. .k~ ~

H._1. •~

Pro~leneGlycol

F

297

~-,LEft

OutletFlow (cth)

Th1.00 2.00 3.00

Time (hr)Fig. 4 a,b, c, d Concentration, Temperature, Level

andOutletFlowBelief

1.00

0.00

-1.01.000.00

-1.01,000.00

-1.01.00

0.00

-1,0

(‘nh~t~i~n

Level

E

F*~

~

0.50 1.00 2,00Time(hr)

Fig. 5 Beliefs for EachSensor

3.00

Theaveragestatisticsfor thetestrunsarepresentedinTable1. Thethresholdsin theseexampleswereintentionallysettightly to force falsealarmsin thedetectionanddiagnosissystems.For theBooleanQMItests,therearetwo caseswherediagnosisis never

achievedbecausethemagnitudesof sensornoiseandthechange are nearly the same,sothosestatisticsarefor tenexamples.QMI is abletoreachadiagnosisin thesecasesthroughits useofthe belieffunctions. Diagnosistime is reportedin minuteswith standarddeviationinbrackets.Alarms,of course,do not givediagnoses.Forfalsealarmsandmisseddiagnoses,Table 1 reportstheaveragenumberoffalsealarmsandtheiraverageduration. The differencebetweendiagnosistime for QMIandBooleanQMI isnegligible,butdiagnosistime forthealarm thresholdtestsis fasterthanbothbecauseit isdetectiontimeandonly one sensorhasto changefromthenormal stateto detecta change.

TABLE 1 Statisticsfor All Examoles

BooleanQMI QMI

AlarmThresholds

CorrectDiagnosis 12 10 NA

DiagnosisTimeaminutes

8.1(4,5)

9.4(5.2)

4.2(3.8)

FalseAlarmsDurationb

0.50.8

1.43.9

2.221.

MissedDiagnosesDuration~’

0.44.3

1.830.

NA

Diagnosistimefor alarm thresholdsis changedetectiontime.b Duration is measuredin samplingintervals.

QMI outperformsBooleanQMI by far in numberoffalsealarmsandmisseddiagnoses.With theexcessivelytight thresholdsusedherefor illustrative purposes,QMIhasone falsealarmor misseddiagnosisfor everytwoexamples,whereastherearethreetimesasmanywithBooleanQMI. Hardthresholdsalsoaveragetwo falsealarmsper test. Thedurationof thesefalsealarmsisalsomuchgreaterfor BooleanQMI andhard thresholds.With looserthresholdsthenumberof falsealarmswoulddecreaseat the costof diagnosisspeed.Weexpectthatreasonablethresholdsin QMJ wouldstill beunsatisfactoryforBooleanQMI or alarm thresholds.

RelatedWork andCurrentResearch

QMI is similar to two otherqualitativemonitoringanddiagnosissystems:DATh4I (DeCoste,1990)andMIMIC (DvorakandKuipers,1991). Like them,QMIattemptsto usequalitativemodelsto determinetheunderlyingbehaviorofa systembasedon informationprovidedby its sensors.DATMI andMIMIC arein

Temperature(R)

0.086

0.085

0.084

0.083

565

564

563

562

4.20

4.00

3.20

0.00

298

severalwaysmoresophisticatedthanQMI: boththosesystemsarebetterthanQMI atusingthatfact thatinstantaneousstatesareoftennotobserved.

Ratherthanpredefiningall possiblefault modelsas inQMI, MIMIC hypothesizeschangesto themodel whenit canno longertrackobservations.MIMIC allows onlysingle-changehypotheses,but subsequentdiscrepanciesbetweenreadingsandpredictionsmaycauseMIMIC tohypothesizemorechanges.Currently, thesemodelchangesareonlychangeslandmarks ofoperatingparameterswith newquantitativeranges(i.e. changeinlet flow from “normal” at9 to 10 gallonsper minuteto “low” at 5 to 6 gpm). Eachhypothesisgeneratedinthismanneris simulated and comparedto thecurrentobservations,andthosehypothesesthat match becomethe setof candidate modelswhich aretracked by MIMIC.The algorithm forMIMIC is shownin Figure6.

QMI simulatestheentirebehaviortree,butMIMICsimulatesbehaviorson-line in a step-by-stepfashion.Thisallows theabovefault generationmethodto be usedaswell asprovidinganefficientway to incorporatequantitativeinformationinto thequalitativemodelsforusewith semi-quantitativesimulation(KuipersandBerleant,1988). Semi-quantitativesimulationusesrangesaroundthevariablesandenvelopesaroundproportionalconstraints,providingapredictionof thepossiblequantitativerangeof valuesfor variablesaswellasthe usualpredictionof qualitativedirectionprovidedby QSIM. Thisallows MIMIC to bettercompare

predictionsto observations,providingfasterdetectionofchangesin the behaviorof theplant.

QMI andMIMIC bothuseamembershipfunction tocalculatethedegreeof beliefthatastatematchesthereadings. In QMI only the slopeof thereadingisexamined,whereasMIMIC looksat both thereadingandits slope. The currentimplementation ofMIMIC isunableto handlenoisebecausethereadingsareassumedto beperfectmeasurementsof the plant.

The keyfeatureofQMI which is lacking in DATMI andMIMIC is the explicit recognitionthatprocessesandsensorshave noise andthatthis noise obeysstatisticallawswhich allow one to ascribeprobabilitiesto beliefsin interpretationsofboth individualsensorreadingsandcompletequalitativestares.The QMT work describedaboveusesanadhocinterpretationinspiredby fuzzylogic and thenotion of a “soft threshold”dividingdifferentqualitativeregions. We arenowmovingtowardthe useof more rigorousstatisticsto handlenoise. Thiswill beparticularlyimportantaswe increasinglyusesemi-quantitativesimulation to aid fault detection indynamicsystems.

Thiscomparisonhasled usto form QMIMIC, ahybridof QMI and MIMIC. Thenewsystemis calledQMIMIC and isbeingbuilt to handlecomplexphysicalsystemssuchas theCSTRexampleof this paper.QMTMTC retainsthe incrementalsimulationof MIMIC

Fig.6 Architectureof Mimic. Therectangularboxesrepresentprocessingelementsand the labeledlinesshowinformationflow

299

for semi-quantitativepredictionandfaultgenerationpurposes.FromQMI it borrowsandenhancestheability to deal with uncertaintyin theobservations,Readingsarenowcomparedto semi-quantitativepredictionsby statistical tests,ratherthanad-hocmeasuresof certainty. Also, QMIMIC doesnot lockprematurelyinto adiagnosescausedby sensornoise,asdoesMIMIC andtheBooleanversionsof QMI.

CONCLUSIONS

QualitativeModellingandInterpretationprovidesaninteresting additionto thefield of faultdetectionanddiagnosis.Sensorsignalsareindividually translatedintoa qualitativedescriptionwith associatedbeliefswhich arethen combinedforanoverallbelief in thequalitativestateofthe plant. Combiningmultiple sensorsallowsQMI to settighterthresholdsonsinglesensorsbecausechangesin sensorsmustcorrelatewith eachothertoproduceadiagnosisof faultsorprocesschanges.QMIperformsbetterthaneithera singlesensoralarmdetectionmethodor aversionofQMI with Booleanbelief functionsin diagnosistime, falsealarmsandmisseddiagnoses.We are currentlyaugmentingQMI touseprobabilitiesof differentfailures.

A major goalof this w~thasbeento integratethequalitative information availablein the real world ofchemicalplantsandrobotswith qualitativemodelsofthat world. In particular, we think that it is important toexplicitly modelthenoisethatcomesfrom disturbancesto thesesystems,aswell asthenoiseandinaccuracythatcomefrom the sensorsusedtomeasurevariablessuchasflow, temperature,concentrationandpressureandtousestatisticalcharacterizationsof that noisein the diagnosisprocess.

ACKNOWLEDG~NTS

Thisresearchhasbeenpartially supportedby NSFPresidentialYoungInvestigatorawardCBT86-57899.Thisworkoriginally appearedin a modifiedform in theProceedingsof theIFAC Symposium“On Line FaultDetectionin theChemicalProcessIndustries.”

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