On Modeling and Diagnosis of Discrete Event Dynami

LinkopingStudiesinScienceandTechnologyThesisNo.648OnModelingandDiagnosisofDiscreteEventDynamicSystemsMagnusLarssonREGLERTEKNIKAUTOMATICCONTROLLINKÖPINGDivisionofAutomaticControlDepartmentofElectricalEngineeringLinkopingUniversity,S{58183Linkoping,Sweden://@isy.liu.seLinkoping1997OnModelingandDiagnosisofDiscreteEventDynamicSystemsc1997MagnusLarssonDepartmentofElectricalEngineering,LinkopingUniversity,S{58183Linkoping,Sweden.ISBN91-7219-094-9ISSN0280-7971LiU-TEK-LIC-1997:49PrintedbyUniTryckLinkoping1997AbstractThebasicmotivationforthisthesisisthefactthatthingsgowrong.Withthegrow-ingcomplexityoftodaysengineeringsystems,theneedhasarisenforsystematicapproachestofailurediagnosis.Inthisthesisanapproachformodelinganddiag-nosisofsystemsthatfallintheareaofdiscreteeventdynamicsystemsisproposed.Theapproachisapplicabletoallsystemsthatatsomelevelofabstractionhaveaninterestingdiscreteeventdynamicsthatcandisplayfaultybehavior.Thesystemssuitableforthisapproachtypicallyconsistofseveralinteractingcomponentswhereabrupt,butnon-catastrophic,faultscanoccurinthecomponents.Weusearelationalframeworkfordiscreteeventdynamicsystemsfocusingonaconceptuallysimplerepresentationoftherelationshipsbetweeninputs,outputsandstatesofadiscreteeventsystem.Themodelingphilosophypromotedhereistomodelfaultslocally,usingspecialfaultinputsorfaultstatesonlyforthatpurpose.Thediagnosisproblemthenbasicallyistoinferthepossiblevaluesoftheunobservablefaultinputsandstatesusingthesystemmodelandobservationsoftherealsystem.Afaultissaidtobedetectableifthereexistsatransitioninthesystemmodelthatleadstoadetectioninanitenumberofsteps.Thetransitionnecessaryfordetectioncanautomaticallybecomputedfromthesystemmodelundercertainconditions.Wealsoshowhowtocomputethenestpossiblefaultpartition.iAcknowledgmentsFirstofallIwouldliketothankmysupervisorProf.LennartLjungforgivingmetheopportunitytojointheAutomaticControlgroupandforcreatingthetrulyinspiringandfriendlyatmospherethatsurroundsthegroup.IwouldalsoliketothankLennartandmyco-supervisorsIngerKleinandJohanGunnarssonfortheencouragement,guidanceandmanyinsightfuldiscussions.IngerKlein,JohanGunnarsson,UrbanForsell1andChristoerKleinhascare-fullyreadthewholeorpartsofthemanuscriptandtheircommentshassignicantlyimprovedthenalresult.ForthisIamverygrateful.Anythingstillwrongorun-clearismyfaultalone.IwouldliketothankPeterLindskogandMatsJirstrandforhelpwithLATEX,AndersStenmanforhelpwithXEmacsandMattiasOlofssonandMagnus‘masun’Sundstedtforkeepingthecomputershappy.IwasalsoveryfortunatethatNiclasBergmannishedhisthesisatthesametimeasme,whichmadethelastminutestressandthenecessarypracticalitiesaloteasier.TheControlgroupinLinkopingisagreatplacetobe,andallmembersofthegrouparehearbygratefullyacknowledgedforbeingsuchaniceandhelpfulbunch.SomeonewhodeservessomeextraattentionisoursecretaryUllaSalaneck,withoutwhomthegroupwouldcometoagrindinghaltbeforeanyonecouldsaywhoknowsthat?.Myfriendsandrelativesdeservesmanydeeplyfeltthanksfordistractingmeandhelpingmegetmymindofwork.MysisterAsa,herUrbanandlittledaughterRebeckahaveprovidedmewithanearbyrefugewithawarmatmosphereandwhereyouneverneedtogounoccupied.Finally,Iwouldliketothankmyparents,UllaandLennart,foralltheloveandsupporttheyhavegivenmealways.Linkoping,September1997MagnusLarsson1Bydemand,[17]iiContents1Introduction11.1Overviewofdiagnosisapproaches....................21.1.1Traditionalandotherapproaches................21.1.2Modelbasedapproaches.....................41.2Theapproachinthisthesis.......................61.3Contributionsofthethesis........................71.4Outlineofthethesis...........................82TherelationalapproachtoDEDS92.1Relationsandsets............................92.2RelationalOperations..........................122.3Modeling.................................172.4RelationalModel.............................182.5Deterministic/NondeterministicDEDS.................202.6Unobservableevents...........................222.7CompositionofModels..........................222.8InterconnectingModels.........................222.9RestrictingModels............................262.10Analysis..................................272.10.1StaticAnalysis..........................272.10.2DynamicAnalysis........................283Modelingfordiagnosis353.1Introduction................................353.2Faultmodels...............................363.2.1Outputfaults...........................363.2.2Faultsontheinput........................373.2.3Faultstates............................373.3Sensors..................................404Amodelingexample414.1Introduction................................414.2Thevalve.................................42iiiivCONTENTS4.2.1Thevalvemodeledwithfaultinputs..............424.2.2Thevalvemodeledwithfaultstates..............434.2.3Thepropertyofow.......................464.3Thepump.................................464.4Thecontroller...............................464.5Thesensor.................................474.6Tyingitalltogether....