Fuzzy cognitive maps A model for intelligent supervisory control systems

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

ComputersinIndustry39 1999.229–238

FuzzyCognitiveMaps:amodelforintelligentsupervisory

controlsystems

ChrysostomosD.Stylios),PeterP.Groumpos

Abstract

FuzzyCognitiveMaps FCMs.isanewapproachinmodellingthebehaviourandoperationofcomplexsystems.FCMsareproposedtobeusedinthemodellingofcontrolsystemsandparticularlyinthemodellingoftheupperpartorsupervisorofahierarchicalcontrolsystem.ThedescriptionandtheformulationofFCMareexamined,moreoveraprocesscontrolproblemispresentedanditsmodelandcontrolisinvestigatedusingFCMs.ThentheimplementationofFCMinthemodellingofthesupervisorofacontrolsystemisdiscussedanditbecomesapparenthowefficientFCMsareinexpressingqualitativeinformationandknowledgeabouttheprocessstructure.Finally,someinterestingpointsforfurtherresearcharepresentedanddiscussed.q1999ElsevierScienceB.V.Allrightsreserved.

Keywords:FuzzyCognitiveMap;Supervisorycontrol;Intelligentsystems

1.Introduction

Inthepastyears,conventionalmethodswereused,successfully,tomodelandcontrolsystemsbuttheircontributionislimitedintherepresentation,analysisandsolutionofcomplexsystems.Insuchsystems,theinspectionoftheiroperation,especiallyfromtheupperlevel,dependsonhumanleadership.Generally,thereisagreatdemandforthedevelop-mentofautonomouscomplexsystemsthatcanbeachievedtakingadvantageofhumanlikereasoninganddescriptionofsystems.Humanreasoningpro-cessforanyprocedureincludesuncertaindescrip-tionsandcanhavesubtlevariationsinrelationto

boratoryforAutomationandRobotics,DepartmentofElectricalandComputerEngineering,UniversityofPatras,26500Rion,Greece.Tel.:q30-61-997293;fax:q30-61-997309;e-mail:stylios@ee.upatras.gr

)

timeandspace;forsuchsituationsFuzzyCognitiveMaps FCMs.seemtobecapabletodealwith.

FCMisacombinationofFuzzyLogicandNeuralNetworks;itcombinestheheuristicandcommonsenserulesofFuzzyLogicwiththelearningheuris-ticsoftheNeuralNetworks.TheywereintroducedrecentlybyKoskow1,2x,whoenhancedcognitivemapswithfuzzyreasoning,thathadbeenpreviouslyusedinthefieldofsocio-economicandpoliticalsciencestoanalysesocialdecision-makingproblemsw3x.Koskoconsideredfuzzyvaluesinthevariablesofcognitivemapsandutilisedtheminordertorepresentcausalreasoning.TheuseofFCMsformanyapplicationsindifferentscientificfieldswasproposed.FCMhadbeenemployedtoanalyseex-tendgraphtheoreticbehaviourw4x,tomakedecisionanalysisandco-operatedistributedagentsw5,6x,wereusedasstructuresforautomatinghumanproblemsolvingskillsw7xandasbehaviouralmodelsofvir-tualworldsw8x.FCMswerealsousedtomodeland

0166-3615r99r$-seefrontmatterq1999ElsevierScienceB.V.Allrightsreserved.PII:S0166-3615 98.00139-0

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

230C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238

supportplantcontrolsystemsofawatersystemw9,10x.FCMswereproposedassystemmodelsforFailureModesandEffectsAnalysisinprocessindus-try i.e.,theoilrefinery.w11,12xandtheywereusedforstrategicplanningandanalysingthebusinessbehaviourofacarindustryw13x.AuthorsofthispaperproposedtheuseofFCMfromadifferentstandpoint,asamodeloftheSupervisorincomplexcontrolsystemsw14,15x;theinvestigationconcernshierarchicalintelligentsystemswhichincorporateknowledgeandarecapableoflearningrelationalstructuresandevidentialreasoning.

Theorganisationofthispaperisasfollows.Sec-tion2describesbrieflytheformulationanddevelop-mentofFCMsandinSection3thedifferentusesofFCMsincontrolaspectsaresummarised.Section4presentsagenericmodelthatcontroldirectlyapro-cess;thedevelopmentofacontrollerforaprocessproblemisdescribedindetailandthisFCMisusedtocontroltheprocess.Section5discussestheimple-mentationofFCMsinSupervisoryControlprob-lems.Finally,Section6concludesthepaperandgivessomepossiblefutureresearchdirections.

2.FuzzyCognitiveMaps

ThegraphicalillustrationofFCMisasigneddirectedgraphwithfeedback,whichisconsistedofnodesandweightedarcs.Nodesofthegraphstandfortheconceptsthatareusedtodescribethebe-haviourofthesystemandtheyareconnectedbysignedandweightedinterconnectionsrepresentingthecausalrelationshipsthatexistbetweenthecon-cepts Fig.1..Itmustbementionedthatallthevaluesinthegrapharefuzzy,soconcepts

takes

Fig.1.GraphicaldrawingofaFuzzyCognitiveMapwithcon-ceptsandweightedinterconnections.

valuesintherangebetweenw0,1xandtheweightsoftheinterconnectionsbelongtotheintervalwy1,1x.Fromsimpleobservationofthegraphicalrepresenta-tionofFCM,itbecomesclear,whichconceptinflu-enceswhichotherconcepts,showingtheintercon-nectionsamongconceptsanditpermitsthoughtsandsuggestionsforthereconstructionofthegraph,astheaddingordeletingofaninterconnectionoraconcept.Inconclusion,FCMsarefuzzy-graphstruc-ture,whichallowsystematiccausalpropagation,inparticularforwardandbackwardchaining.

BehindthegraphicalrepresentationofanFCMthereisamathematicalformulationwhichdescribestheFCM.Valuesofconceptsarefuzzyandarisefromthetransformationoftherealvaluesofthecorrespondingvariablesforeachconcept;andtherearefuzzyvaluesfortheweightsoftheinterconnec-tionsamongconcepts.Then,FCMisfreetointeract,ateverystepofinteractioneveryconcepthasanewvaluethatiscalculatedaccordingtothefollowingequation:

n

Atisf

Ý

Atjy1Wji

js1j/i

1.

Namely,AtiisthevalueofconceptCconceptCiatstept,Atjy1isthevalueofweightoftheinterconnectionjatstept-1,andWisthefromconceptCjitoconceptCandfisathresholdfunctionthatjsquashestheresultiofthemultiplicationintheinter-valw0,1x.

BuildinganFCMmodelofaprocessorplantdependsonhumanexpertswhohaveknowledgeontheoperationofthesystemw14x.Oneexpertoroperatorofthesystemisaskedtodescribethebehaviourandmodelofthesystem.Accordingtohisexperience,hedevelopsanFCM,hedeterminestheconcepts,whichstandforthedifferentaspectsthatinfluencetheprocess,thepathsofsystem’smalfunc-tion;generallyconceptsstandforstates,variables,events,actions,goals,values,trendsofthesystem.Theexperthasobservedthegradewithwhicheachvariableofthesysteminfluencesothersandso,hedeterminesthenegative,positiveornilpotenteffectofoneconceptontheothers,withafuzzydegreeofcausation.

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238231

Thisapproachisdependentonthereliabilityandknowledgeofeachoneexpert.Itispossibletoexploittheknowledgeofagroupofexpertswhohaveexperienceontheoperationormodellingofthesystem.Firstly,alltheexpertsarepolledtogetherinordertodeterminetherelevantfactorsthatshouldbepresentinthemap.Then,expertsareindividuallyaskedtoexpresstherelationshipamongthesefac-tors.Inthisway,acollectionofindividualFCMsiscreatedwhichmustbecombinedintoacollectivemap.Ifitisconsideredthatthereareexpertsofvaryingcredibilitythentheircontributionismulti-pliedwithanonnegative‘credibility’weightbeforecombiningitwithotherexpert’sopinions.Andifthereisanexpertwhoisextremelyknowledgeableaboutcertainfactorsorpartsofthesystemandnotothers,itcanbeuseddifferentcredibilityweightsondifferentlinks.Ontheotherhand,itisstillanopenquestionifthecontributionofallexpertsshouldbeconsideredequallyorforsomeofthem,itisneces-sarytopenalisetheircontributionwithanegativecredibilityweight.

3.TheuseofFCMincontrol

AfterthepresentationofFCMs,theirillustrationandtheirmethodologywithwhichtheyarecon-structed;theirapplicationisexaminedincontrolaspects.Therearetwodistinctusesofaknowledge-ablebasedmodelliketheFCMintheupperlevelofaprocessw16x.One,whenFCMisusedfordirectcontrolandFCMinfluencesdirectlytheprocess,asitisdepictedinFig.2.

Inthiscase,FCMisreplacingcompletelytheconventionalcontrolelementanditperformseveryfunctionthataconventionalcontrollercouldimple-ment.Itissimilartotheclosedloopcontrol

ap-

Fig.2.StructureofFCMforDirect

Control.

Fig.3.StructureofaSupervisorControlusinganFCM.

proachbecauseFCMisdependeddirectlyontherealbehaviouroftheprocess.SuchanapplicationofFCMwillbepresentedinSection4whereaprocessproblemwillbeexaminedandanFCMwillbeconstructedinordertocontroltheprocess.

AnotherimportantuseofFCMisforsupervisorycontrolofaconventionalcontrolelement,thuscom-plementingratherthanreplacingaconventionalcon-troller.TheschemeofthisstructureisdepictedinFig.3.Inthiscase,theroleofFCMistoextendtherangeofapplicationofaconventionalcontrollerbyusingmoreabstractrepresentationofprocess,gen-eralcontrolknowledgeandadaptationheuristicsandenhancetheperformanceoftheoverallsystem.Thus,FCMmayreplicatesomeoftheknowledgeandskillsofthecontrolengineeranditisbuiltbyusingacombinationoftheknowledgerepresentationtech-niquesascausalmodels,productionrulesandobjecthierarchies.

Attheconventionalcontrollerlevelorattheprocessitselfmayexistmorethanonecontrollersfordifferentpartsoftheprocessandonlylocalinforma-tionisavailabletoeachcontrollerwhocommuni-cateswiththesupervisoratthehigherlevel.Theroleofthesupervisoristoelaborateinformationofthecontrollersandtoallocateactionstocontrollerstak-ingintoaccounttheireffectontheglobalsystem.Supervisorindicatesundesiredorunpermittedpro-cessstatesandtakesactionssuchasfailsafeorreconfigurationschemes.SupervisoryFCMisusedtoperformmoredemandingprocedureasfailuredetection,diagnoseabnormalities,decisionmaking,planningtasksandintervenewhenacertaintaskorstateisreachedandtakecontrolinabnormalorhazardoussituations.Ahumansupervisorofthecontrolledprocessusuallyperformsthesetasks.

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

232C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238

4.AnFCMsystemfordirectcontrolofaprocessThefirsttypeofapplicationofFCMisconsideredforthedirectcontrolofaprocessoracomplexplant.ThenthecontrolledsystemcanbedescribedindetailasthemultilevelmodelthatisillustratedonFig.4,whereintheupperlayerastorageoftheexistingknowledgeofthesystem’soperationislying.ThisknowledgeisrepresentedbyanFCM,whichmodelstheoperation,andbestdescribesthebehaviouroftheprocessinthelowerlevelandanexpert,asprevi-ouslypresented,constructsit.Ifthenatureoftheprocessundercontrolissuchthatappropriateana-lyticmodelsdonotexistorareinadequate,buthumanoperationattheprocesscanmanuallycontroltheprocesstoasatisfactorydegree,thentheneedtouseanabstractmethodologyasFCMsismotivated.Thefunctionofthewholemodelofthesystemcanbedescribedfromthelowerleveltotheupperone.Inthelowerlevelsensorsmeasuresomedefinedvariablesoftheprocessandthesemeasurementsmustpasstothehigherlevelwhereinformationoftheprocessisorganisedandcategorised.Afterthat,availableinformationonprocessisclusteringandgrouping,becausesomemeasuredvariablescouldcausechangesinthevalueofoneormoreconceptsoftheFCM,thentheorganisedinformationcaneasilytransformedinFCMmodewhichpasses

into

Fig.4.AgenericmodelofthecontrolledprocessusingFCMfordirectcontrol.

theFCMontheupperlevel.TheFCMontheupperlevelisaccompaniedbyabox,whichsymbolisestheknowledgeableexpertwhodevelopedtheFCM,andanotheronebox,whichrepresentsFCMtrainingprocedure.FCMshavebeendescribedasthecombi-nationofNeuralNetworksandFuzzyLogic.Thus,learningtechniquesandalgorithmscanbeborrowedfromNeuralNetworkstheoryandcanbeutilisedinordertotrainFCMandadjusttheweightsofitsinterconnections.

TheprocedureoftheoperationofthegenericmodelofFig.4hasasfollows.Firstly,theFCMisinitialised,eachconcepttakesaninitialvaluethatbestrepresentsthecurrentstateaccordingtotheexpert’sopinionandtheweightsoftheFCMhavebeendeterminedduringthetrainingperiod.TheinputinformationfromtheprocesslevelcauseschangeinthevalueofoneormoreconceptsoftheFCM.Then,conceptsoftheFCMinteracteachotheruntilanequilibriumpointisreached,inthiscasethevalueofsomeconceptshavechangedandthisinfor-mationmustpasstothelowerlevelandinfluencetheprocesssothereverseprocedureisfollowed.Valuesofsomeconceptsaretransformedinphysicalmagni-tudesinasimilartothedefuzzificationprocedurethatisimplementedinfuzzycontrolsystems.TheinformationwhichdescendfromtheFCMrepresentrealvaluesforsomevariablesofthesystemsoitmustbeorganised,filteredinsomewayanditwillpostedtothePlanningrControlpart.TheControlpartwilldeterminethecontrolactionsthatmustbeappliedtotheprocessandsomevariablesoftheprocesswillbeinfluencedbythecontrolsignalsthatplanningandcontrolpartissending.

Theabovehasbrieflydescribedhowthisgenericmodelworks.Howeversometimes,ifFCMisnotappropriatedevelopedornotwelltrained,valuesoftheconceptsoftheFCMmayleadtheFCMintoalimitcyclewherevaluesofallconceptswillperiodi-callychange,andinthiscaseanexternalhumaninfluenceandinteractionareneeded.

ThiswasthedescriptionofagenericmodelfordirectcontrolusingFCM.Nowthemodellingofapracticalprocessproblemwillbeexamined.ThemostimportantcomponentindefininganFCMisthedeterminationoftheconceptsthatbestdescribethesystemandthedirectionandgradeofcausalitybetweenconcepts.Theseaspectswillberepresented

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238233

throughanexampletakenfromaprocesscontrolproblem.ThesystemconsistsoftwotanksdepictedinFig.5.Eachtankhasaninletvalveandanoutletvalve.Theoutletvalveofthefirsttankistheinletvalveofthesecond.

Theobjectiveofthecontrolsystemisfirsttokeeptheheightofliquid,inbothtanks,betweensomelimits,anupperHmaxandalowlimitHmin,andsecond,thetemperatureoftheliquidinbothtanksmustbekeptbetweenamaximumvalueTmaxandaminimumvalueTmin.Thetemperatureoftheliquidintank1isregulatedthroughaheatingelement.Thetemperatureoftheliquidinthetank2ismeasuredthroughathermometer;whenthetemperatureoftheliquid2decreases,valve2needsopening,sohotliquidcomesintotank2fromtank1.Thecontrolobjectiveistokeepvaluesofthesevariablesinthefollowingrangeofvalues:

11

FH1FHmaxHmin

22HminFH2FHmax11TminFT1FTmax22TminFT2FTmax

2.

ForthissystemanFCMistobeconstructed.Variablesandstatesofthesystem,suchastheheightoftheliquidineachtankorthetemperature,willbetheconceptsofanFCM,whichdescribesthesystem.Thenconceptsareassignedforthesystem’sele-mentsthataffectthevariablessuchasthestateofthevalves.Forthissimplesystem,teron,anyotherconceptcan

beadded,whichcouldhelptheoverallviewandcontrolofthesystem:

Concept1:Theheightoftheliquidintank1.Theheightofliquidisdependentonstateofvalve1andvalve2.

Concept2:Theheightoftheliquidintank2.Theheightofliquidisrelatedtovalve2andvalve3.Concept3:Thestateofthevalve1.Thevalveisopen,closedorpartiallyopen.

Concept4:Thestateofthevalve2.Thevalveisopen,closedorpartiallyopen.

Concept5:Thestateofthevalve3.Thevalveisopen,closedorpartiallyopen.

Concept6:Thetemperatureoftheliquidintank1.Concept7:Thetemperatureoftheliquidintank2.Concept8:Describestheoperationoftheheatingelement,whichhasdifferentlevelsofoperationandwhichincreasesthetemperatureoftheliquidintank1.

Theseconceptsmustbeconnectedwitheachother.Firstitmustbedecidedforeachconcepttowhichanotherconceptisconnected.Thenthesignoftheconnectionisdecided,andthentheweightofeachconnectionisdetermined.Forthisprocedurethehumanexperienceonthesystem’soperationisused.Theconnectionsbetweenconceptsare:

Event1:Connectsconcept1withconcept3.Itrelatestheamountoftheliquidintank1withtheoperationofthevalve1.Whentheheightoftheliquidinthetankislow,openingofvalve1increasestheamountofincomingliquid;

Event2:Relatesconcept1withconcept4;whentheheightoftheliquidintank1ishigh,

opening

Fig.5.Exampleofaprocesssystemtobecontrolled.

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

234C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238

ofvalve2 concept4.reducestheamountofliquidintank1;

Event3:Connectsconcept2withconcept4;whentheheightoftheliquidintank2islow,openingofvalve2 concept4.increasestheamountofliquidintank2;

Event4:Relatesconcept2withconcept5;whentheheightoftheliquidintank2ishigh,openingofvalve3 concept5.reducestheheightofliquidintank2;

Event5:Connectsconcept3 valve1.withcon-cept1 tank1.;anychangeinvalve1influencestheamountofliquidintank1;

Event6:Thevalueofconcept4 valve2.causesthedecreaseornotofthevalueofconcept1 tank1.;

Event7:Thevalueofconcept4 valve2.causestheincreaseornotoftheamountofliquidintank2 concept2.;

Event8:Relatesconcept5 valve3.withconcept2 tank2.,thevalueofconcept5causesthedecreaseornotoftheamountoftheliquidintank2;

Event9:Connectsconcept6 temperatureintank1.withtheconcept8 theoperationoftheheatingelement..Whenthetemperatureintank1islow,itcausestheopeningoftheheatingelement;

Event10:Connectsconcept8withconcept6;thevalueofconcept8 operationoftheheatingele-ment.increasesthevalueofconcept6 tempera-tureintank1.;Event11:Connectsconcept6withconcept3 valve1.;whenthetemperatureintank1reachesanupperlimit,openingofvalve1emptiesliquidoflowtemperatureintank1;

Event12:Relatesconcept7 temperatureintank2.withconcept4 valve2.;whenthetemperatureintank2isbelowalimit,openingofvalve2causeshotliquidtopassfromtank1totank2;

Event13:Showstheeffectofconcept4 valve2.onconcept7 thetemperatureintank2.;whenthevalve2 concept4.isopenthenhotliquidcomesintotank2andthetemperatureintank2 concept7.isincreased.

Interconnectionsamongconceptscaneasilybechangedandsomenewcanbeaddedorotherscanberemovedifthehumanoperatordecidesso,inordertohaveabettermodelofthesystem.More-over,aconceptcanbeaddedorremovedifthisimprovesthesystem’sdescription.Forexample,an-otherconcept,thatcouldbeaddedlater,isaconcept,whichwillincludethedesirableoutputofthevalve3.EachconceptoftheFCMtakesavaluewhichrangesintheintervalw0,1xanditisobtainedafterthresholdingtherealmeasurementofthevariableorstatewhicheachconceptrepresent.Asanexample,only20%ofthetankcontainsliquid,ingasimilarmethodol-ogyotherconceptstakevalues.Thevaluesoftheevents interconnectionsbetweenconcepts.arede-terminedmorearbitrary.Eachconnectionis

charac-

Fig.6.TheinitialFCM,withthefirstvaluesfortheconcepts.

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238

235

Table1

ThevaluesofconceptsateachstepofFCMinteractionStepsTankTankValveValveValveHeatThermTherm

12123element_tank1_tank210.200.010.550.580.000.050.200.1020.490.610.530.530.500.530.510.5130.500.550.580.680.590.570.580.5140.470.570.580.670.580.580.580.5250.480.570.580.680.590.580.590.526

0.48

0.57

0.58

0.68

0.59

0.58

0.59

0.52

terisedbyaweightthatrangesbetweenwy1,1x,whichisdecidedbythehumanexpertwhodevel-opedtheFCManddeterminedthepositiveornega-tivecausality,betweentwoconceptsanditsdegree.Sohedeterminedthatthestateofthevalve1 concept3.influencespositivelywithadegree0.76 Event5.theamountofliquidintank1 concept1..TheseweightsamongconceptswereadjustedandchangedduringthetrainingperiodoftheFCM.Generally,itshouldbementionedthatthetransfor-mationfromtherealvaluesofthephysicalmeasure-mentstothevaluesoftheconcepts,needsmoreinvestigationanditmusttakeintoconsiderationtheactualmechanismwithwhichrealvaluesaretrans-formedinFCMmodeandviceversa.

Fig.6showstheFCMthatwasconstructedtomodelandcontroltheprocess,withtheinitialvalueofeachconceptandtheweightedinterconnectionsbetweenconcepts.Thevaluesofconceptscorre-spondtotherealmeasurementsofthephysicalpro-cess.Thevaluesoftheevents weights.havebeendeterminedafterobservationofthechangesintherealexperimentalsystemandaftertrainingtheFCMusingtheDifferentialHebbianlearningmethodw2x.ArunningstepoftheFCMisdefinedtobethetimeunitduringwhichthevaluesoftheconceptsarecalculatedandchangeaccordingtoEq. 1..AteachrunningstepoftheFCM,thevaluesofeachconceptisdefinedbytheresultoftakingallthecausaleventweightspointingintothisconceptandmultiplyingeachweightbythevalueoftheconceptthatcausestheevent.Thenthesigmoidfunctionisappliedtotheresultofthecalculationsanditistransformedtotheintervalbetween0.00and1.00.

Theweightsoftheinterconnectionsareconsid-eredfixedafterthetrainingperiodandFCMinter-

actsfortheinitialvalues.Itcanbeseenthatafteronlyfiverunningsteps,FCMreachesastablestate.InTable1,thevaluesofconceptsforsixstepsaredepicted.Afterthisequilibriumpoint,ifadistur-banceoccursintherealsystem,whichwillcausechangeinthevalueofoneormoreconcepts,FCMwillinteractforalimitednumberofcycles,perhapsanotherfiveorsixcyclesanditwillreachagainanotherequilibriumpoint Fig.7..

Inthisapproachtotheprocesscontrolproblem,itwasassumedthatvaluesofconceptschangesimulta-neously,inthesametimeunitforeveryconcept,whichisreferredtoasarunningstep.But,inarealisticsystem,effectstakeplaceindifferentunittimes.Forexample,inFig.6achangeinconcept6 thetemperatureoftheliquidintank1.willleadalmostimmediatelytoachangetothestateoftheheatelement concept8..Howeverachangeinthestateofthevalve1willtakesometimetohavefulleffectintheamountofliquidinthetank1.Thus,timelagswouldbeintroducedcorrespondingtotimeduration

ofeacheffect,buttherecouldbeadiffi-cultyinestimatingtimelagsforeacheffect.Theycouldbeestimatedfollowingthemethodologypro-posedinRef.w17x.

Inthissection,theusageofFCMfordirectcontrolofaprocesswaspresented.Thismethodol-ogycouldbeenhancedinthefutureifitisconsid-eredananalogoustotheRamadge–Wohnamw18xapproachwheretheprocessismodelledasstatetransitionstructure,inwhichsometransitionsarelabelledascontrollable thosethatcanbedisabledbyexternalintervention.anduncontrollable those

Fig.7.TheFCMafterfiverunningcycles.

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

236C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238

cannotbepreventedfromoccurring..Similarly,someconceptsoftheFCMcanbeconsideredascontrol-lablewhenthechangeoftheirvaluescaninfluencetherealprocess,controlitanddriveavaluetoadesiredpoint.SomeconceptsofFCMcanbecharac-terisedasuncontrollablewhentheyrepresentstatesoftheprocessinwhichitisimpossibletointerfereandchangetheirrealvalue.Inthisprocessexamplethetemperatureoftank2isuncontrollable,asthereisnodirectcontrolactionwhichcaninfluencethismagnitude;butthestateofanyvalveiscontrollable.

5.FCMassupervisorofcontrolsystem

SupervisoryControlsystemshavebeendescribedassystemsthatcanperformsomeofthetasksthathumanoperatorsuccessfullyperformsinsupervisingsystems.Humanoperatorsdonotoperateaprocessbyresolvingmathematicalequationsbuttheyinte-gratealltheprocessinformation,eithercompleteorincomplete,withtheknowledgeabouttheprocesstoinfersolutionsforengineeringproblemsw19x.Suchanapproachshouldbeableasupervisorysystemtohandleandexpressthequalitativeinformationandhaveknowledgeabouttheprocessstructure.Supervi-sorycontroliscomposedofvarioustypesofreason-ingrelatedtodifferentaspectsofknowledgeaboutaprocess.Anappropriatemodelforsupervisionhastobebuiltindependently,ratherthanaimingatspecificcontroltasks,sothatitcaninvolveallthenecessaryknowledgeandfurthermorethismodelshouldrepre-sentbothqualitativeandquantitativeinformation.Supervisorycontrolishighlydependentontheexperienceoftheprocessoperators,somethingthatisreflectedinthemethodologywithwhichFCMisconstructed.FCMisamodelforrepresentinganddecodingtheexpert’sknowledgeandexperience.Thisapproachisbasedonthefactthattheremaybemanyphysicalpropertiesoftheprocessthatarenotpartoftheanalyticalmodelwhichisusedinconven-tionalapproachtodesignthecontroller;theymayresultfromthecomplexityoftheprocessorfromlackofunderstandingofthephysicsinvolved.Ontheotherhand,experiencedprocessoperatorsmayhavedevelopedanumberofheuristiccontrolrules,whichallowthemtocontrolsuchaprocessinasatisfactorymanner.TheproposedtechniqueofFCM

canbeusedtomodeltheheuristiccontrollawsandperformmoredemandingtasks.FCMemploysasymbolicqualitativemodelwhichallowsoneexperttoexplicitlyrepresentandreasonwiththeavailableheuristicknowledgewhichsupportshighlevelrea-soningandcreatesmoreflexiblecontrolsystems.ThestructureoftheSupervisoryControlSystemhasbeendescribedinSection3andithasbeenillustratedinFig.3.Inthismodel,aconventionalcontrollerisusedtoperformtheusualcontroltasksandregulatetheprocess.Ontheupperlevelofthehierarchy,thereisanFCM,whichstandsforthesupervisorofthesystem.ThisFCMisactivatedifanabnormalbehaviouroccursduringtheprocessandtriestobringthebehaviourbackintotheacceptableoperationregionorsomeemergencymeasurese-quencescouldbeperformed.TheSupervisorFCMcanbeusedtomodeldevicefailuremodes,effectsandcausesanalysisw11x,decisionanalysisandstrate-gicplanningw13x.Whentheprocessisregardedasabnormal,operatorswillidentifythepossiblereasonsanddecidehowtocorrecttheabnormalbehaviourthroughanalysingtheinteractionsbetweenprocesscomponents.Similarly,anFCMcouldbeusedforsupervisorcontrol,whichcanbeconsistedofcon-ceptsthatstandfortheirregularoperationofsomeelementsofthesystem,forfailuremodevariables,forfailureeffectsvariables,forfailurecausevari-ables,severityoftheeffectanddesignvariables.TheconstructionofFCMcanbebasedontheoperator’sheuristicknowledgeaboutalarms,faults,whatistheircause,andwhentheyhappen.Moreover,thisFCMwillincludeconceptsfordescriptionanddeter-minationofaspecificoperationofthesystemorotherqualitativepreferencesfortheplanningandschedulingoftheprocess.

InSection4,theusageofanFCMhasbeenpresentedforthedirectcontrolofaprocess.ItcanbeconsideredthatabovethisFCMthereisanotherlevelwiththesupervisorofthewholesystemmod-elledasanFCM.Thisco-operationoftwo-levelFCMsseemstobechallenginganditcouldlenditselftomoresophisticatedsystems.ThetwoFCMswillinteractwitheachotherandtherewouldbeanamountofinformationthatmustpassfromtheoneFCMtotheother.Thustwointerfacesareneeded,onewillpassinformationfromtheFCMinthelowerleveltotheFCMintheupperlevelandanotherone

Fuzzy Cognitive Maps FCMs is a new approach in modelling the behaviour and operation of complex systems. FCMs are proposed to be used in the modelling of control systems and particularly in the modelling of the upper part or supervisor of a hierarchical co

C.D.Stylios,P.P.GroumposrComputersinIndustry39(1999)229–238237

interfaceintheoppositedirection.Thetwointerfacesarenecessarybecausechangesontwoormorecon-ceptsintheFCMonthelowerlevelcouldmeanchangeinoneconceptintheupperlevelandthecorrespondingprocedure,wheninformationdescendsfromtheFCMontheupperleveltowardsthelowerlevel.

SymbolicrepresentationandprocessingofthesupervisorofahierarchicalsystemusingFCMoranyothersimilarapproachwillundoubtedlyplayanimportantroleintheconstructionofIntelligentCon-trolSystems.Theobjectiveisthedevelopmentofahierarchicalintelligentsystem,whichwillcombinethefeaturesofprimarycontrollerssuchasstability,controllabilityandfeaturesofhumanoperatorssuchasflexibilityandlearningcapabilities.TheproposedmodellingwithFCM,basedonthehumanknowl-edgeandexperienceofthesystem,andinspiredbytheparallelism,thathumansusetostoreknowledgeandmakedecisions,seemstobeasophisticatedcontrolstrategywhichwilllendtoahigherdegreeofautonomoussystems.6.Summary

Forlargeandcomplexsystemsthatarecommonintheprocessindustry,itisextremelydifficulttodescribetheentiresystembyaprecisemathematicalmodel.Thus,itismoreattractiveandusefultorepresentit,inagraphicalabstractwayshowingthecausalrelationshipsbetweenstates-concepts.Thissymbolicmethodofmodellingandcontrolofasystemiseasilyadaptableandreliesonexpertexpe-rienceandfollowsthegeneralruleof‘‘decreasingprecisionandincreasingintelligence’’w20x.

TheimplementationofanFCMcontrollerforaprocesscontrolproblemhasbeenpresented.Throughthisexample,ithasbeenshownhowFCMsdescribeinasimplewaythesystem’sbehaviourandcontroltheprocess.Theprospecttoexpandthecontrolcapabilitiesofthesystem,byaddingasecondFCMonahigherlevelwhichwillperformsupervisiontaskssuchasfailureanalysis,decisionanalysisandplanning,hasthenbeendiscussed.FuzzyCognitiveMapseemstobeausefulmodellingmethod,whichcanbeusedtocontrolcomplexsystems.Thismethodisappropriateforsystemsnotfullymathematicallydescribed,howeverthesesystemsareworkingwell

underhumansupervisionandintervention.Thereareplentyofsuchsystemsinthechemicalprocessin-dustries,thecementindustryandtheoilindustry.FutureresearchmayexaminethedescriptionandconstructionofFCMinthesupervisorylevel,appro-priatelearningalgorithmsforFCMs,andcontrolrelatedaspectssuchasthestabilityandcontrollabil-ityofFCMs.FCMappeartobeanappealingtoolinthedescriptionofthesupervisorofcomplexcontrolsystems.Itscombinationwithothermethodsmayleadtothenextgenerationofcontrolindustrialsystems.References

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ChrysostomosStyliosreceivedhisdiplomainElectricalEngineeringfromtheAristotleUniversityofThessalonikiin1992.HeiscurrentlystudyingforaPhDdegreeintheDepartmentofElec-tricalandComputerEngineeringattheUniversityofPatrasonthesubjectoftheHybridControlofHierarchicalSys-tems.Hisinterestsincludeintelligentcontrol,supervisorycontrol,fuzzylogicandneuralnetworks.HeisamemberoftheIEEEandtheNationalTechnicalChamberof

Greece

PeterP.GroumposreceivedhisPhDdegreeinElectricalEngineeringfromtheStateUniversityofNewYorkatBuffaloin1978.HeiscurrentlyaPro-fessorintheDepartmentofElectricalandComputerEngineeringattheUni-versityofPatras.Heisalsothechair-manoftheDivisionofSystemsandControlanddirectoroftheLaboratoryforAutomationandRobotics.HewasformerlyonthefacultyofClevelandStateUniversity,USA,in1979–1989.

HeservedasdirectoroftheCommunicationResearchLab.in1981–1986andwasamemberoftheTechnicalCommitteeoftheAdvancedManufacturingCenterin1985–1987.HeparticipatedonaTechnologyTransferProgramwiththeMinistryofHigherEducationofEgyptfrom1981to1984.HewasanAssociateEditorforBookReviewsforIEEEControlSystemsMagazine,1980–1985.Fortheacademicyear1987–1988,hewasaFul-brightvisitingscholarattheUniversityofPatras.HewastheGreekNationalRepresentativetotheHigh-LevelGroupforEU-REKAandforESPRIT1991–1994,andwasaconsultanttoanumberofcompaniesintheUSAandGreece.ProfessorGroumposistheGreekNMOrepresentativetoIFACandheisthevice-presi-dentoftheIFAC‘LargeScaleSystem’.HeisanassociateEditorfortheinternationaljournalsComputersandElectricalEngineer-ingandStudiesinInformaticsandControl.Prof.GroumposisamemberoftheHonorarySocietiesEtaKappaNuandTauBetaPi.HeistheCoordinatoroftheESPRITNetworkofExcellenceinIntelligentControlsandIntegratedManufacturingSystems ICIMS-NOE..Hehaspublishedover70journalsandconferencepapers,bookchaptersandtechnicalreports.HismainresearchinterestsareintelligentmanufacturingsystemsandCIM,processcontrol,simulationmethods,hierarchicallarge-scalesystemscon-trolandadaptivecontrol.

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