Process monitoring and modeling using the self-org

ProcessMonitoringandModelingusingtheSelf-OrganizingMapEsaAlhoniemi,JaakkoHollmØn,OlliSimulaandJuhaVesantoHelsinkiUniversityofTechnologyLaboratoryofComputerandInformationScienceP.O.Box2200,FIN-02015HUT,FinlandAbstractTheSelf-OrganizingMap(SOM)isapowerfulneuralnetworkmethodforanalysisandvisualizationofhigh-dimensionaldata.Itmapsnonlinearstatisticaldependenciesbetweenhigh-dimensionalmeasurementdataintosimplegeometricrelationshipsonausuallytwo-dimensionalgrid.Themappingroughlypreservesthemostimportanttopologicalandmetricrelationshipsoftheoriginaldataelementsand,thus,inherentlyclustersthedata.Theneedforvisualizationandclusteringoccur,forinstance,intheanalysisofvariousengineeringproblems.Inthispaper,theSOMhasbeenappliedinmonitoringandmodelingofcom-plexindustrialprocesses.Casestudies,includingpulpprocess,steelproduction,andpaperindustryaredescribed.1IntroductionInmodelingandcontrolofindustrialprocesses,itisusuallyassumedthataglobal,analyticalsystemmodelcanbedened.Ifsuchamodelcannotbebuilt,ordierentkindofapproachisdesirable,ArticialNeuralNetworks(ANNs)canbeused.ANNmodelsarebuiltdirectlybasedonprocessmeasurements,andthusprovideameanstoanalyzeprocesseswithoutexplicitphysicalprocessmodel.ANNscanalsobeusedassoftsensorstoestimatesignalvaluesorprocessvariablesthatarediculttoobtainorcanonlybemeasuredo-line.TheuseoftheANNs,however,requiresthatalargeamountofgoodquality,stable,numericaldatadescribingtheprocessareavailable.TheSelf-OrganizingMap(SOM)(Kohonen,1995)isoneofthemostpopularneuralnetworkmodels.Thealgorithmisbasedonunsupervisedlearning,whichmeansthatthetrainingisentirelydata-driven.Unlikenetworksbasedonsupervisedlearning(likethemulti-layerpercep-tron)whichrequirethattargetvaluescorrespondingtoinputvectorsareknown,theSOMcanbeusedforclusteringdatawithoutknowingtheclassmembershipsoftheinputdata.Itcan,thus,beusedtodetectfeaturesinherenttotheproblem.TheSOMhasbeensuccessfullyappliedinvariousengineeringapplications(Kohonenetal.,1996b)covering,forinstance,areaslikepatternrecognition,imageanalysis,processmonitoringandcontrol,andfaultdiagnosis(Simulaetal.,1996;SimulaandKangas,1995;TrybaandGoser,1991).Intelecommunicationsystems,theSOMhasbeenusedinadaptiveresourceallocationandoptimization(TangandSimula,1996a;TangandSimula,1996b).Inspeechprocessing,theSOMhasbeenusedinphonemerecognition(Kohonen,1988)andinspeechsignalqualityanalysis(Leinonenetal.,1993).Ithasalsoproventobeavaluabletoolindataminingandknowledgediscoverywithapplicationsinfull-textandnancialdataanalysis(Kaski,1997;Kohonenetal.,1996b).Inthispaper,SOMbasedmethodsintheanalysisofcomplexsystemsarediscussed.Specialemphasisisonindustrialapplicationsinwhichalotofmeasuredinformationisavailablefromautomationsystems.2TheSelf-OrganizingMapTheSOMalgorithmperformsatopologypreservingmappingfromhigh-dimensionalspaceontomapunitssothatrelativedistancesbetweendatapointsarepreserved.Themapunits,orneurons,formusuallyatwo-dimensionalregularlattice.TheSOMcanthusserveasaclusteringtoolofhigh-dimensionaldata.Italsohascapabilitytogeneralize,i.e.thenetworkcaninterpolatebetweenpreviouslyencounteredinputs.EachneuronioftheSOMisrepresentedbyann-dimensionalweight,ormodelvector,mi=[mi1;:::;min]T(nisthedimensionoftheinputvectors).TheweightvectorsoftheSOMformacodebook.Theneuronsofthemapareconnectedtoadjacentneuronsbyaneighborhoodrelation,whichdictatesthetopology,orthestructure,ofthemap.Usuallyrectangularorhexagonaltopologyisused.Immediateneighbors(adjacentneurons)belongtoneighborhoodNioftheneuroni.InthebasicSOMalgorithm,thetopologicalrelationsandthenumberofneuronsarexedfromthebeginning.Thenumberofneuronsdeterminesthegranularityofthemapping,whichaectsaccuracyandgeneralizationcapabilityoftheSOM.AnexampleofapplyingtheSOMinindustrialprocessanalysisisshowninFigure1.ThedierentstagesintheFigurearediscussedmorecloselyinSections2.12.4.2.1DataprocessingTheSOM,likeotherneuralnetworkmodels,followsthegarbagein-garbageoutprinciple:iferroneousdataareused,theresultispoor.Forthatreason,theinputdatamustbeprocessedcarefully.Figure2illustratesdataacquisitionandmanipulationprocessbeforetrainingtheSOM.Dataacquisitionmeansmakingadatabasequery,measuringvariablesetc.Dataofthisformareoftencalledrawdata.Ifthedataarecodedinanon-metricscale,thecodingmustbetransformed.Measurementsmustbequantiable,becausetheEuclideandistanceisusuallyusedasameasureofsimilaritybytheSOM.Codingmustbeinharmonywiththesimilaritymeasureused.SymbolicdatacannotbeprocessedwiththeSOMassuch,butitcanbetransformedtoasuitableform(RitterandKohonen,1989).Datapreprocessingstageremovesorcorrectserroneousdata.Typicalpreprocessingoperationislteringusingxedoradaptiveconditions.Theltersaretypicallybuiltusingaprioriknowledgeoftheproblemdomain.Unfortunately,lteringsometimesleavesgapsofmissingvaluesintheinputvectors.However,eventhiskindofdatacanbeutilizedelegantlybytheSOM(SamadandHarp,1992).Segmentationdividestheinputdataintoseparatesubsetsaccordingtocriteria,whichareoftendeterminedusingaprioriknowledge.Featureextractiontransformsinputdatavectorsintosuchformtha