粗神经网络故障诊断研究(IJIGSP-V3-N2-8)

I.J.Image,GraphicsandSignalProcessing,2011,2,51-58PublishedOnlineMarch2011inMECS()Copyright©2011MECSI.J.Image,GraphicsandSignalProcessing,2011,2,51-58RoughNeuronnetworkforFaultDiagnosisYuelingZHAOCollegeofElectricalEngineering,LiaoningUniversityofTechnology,Jinzhou,P.R.ChinaEmail:[e-mail],LihongWangandShuangWANGCollegeofElectricalEngineering,LiaoningUniversityofTechnology,Jinzhou,P.R.ChinaEmail:{jinhui5868,zdhwanglihong,shuang_lg}@126.comAbstract—ConsideringtrainingtimeoftraditionalBPneuralnetworkistoolonganditcannotsolvetheproblemsintheinputvectorwithmultiple-valued,anewmethodofBPneuralnetworkbasedonroughneuronispresented.Aroughneuroncanbeviewedasapairofneurons.Oneneuroncorrespondstotheupperboundaryandtheothercorrespondstothelowerboundary.Upperandlowerneuronexchangeinformationwitheachotherduringthecalculationoftheiroutputs.Firstly,thecontinuousattributesindiagnosticdecisionsystemarediscretizedwithparticleswarmoptimization.Then,thereductsarefoundbasedonattributedependenceofroughset,andtheoptimaldiagnosticdecisionisdetermined.Lastly,accordingtotheoptimaldecisionsystem,roughneuronnetworkisdesignedforfaultdiagnosis.Apracticalexampleisgiven,themethodisfeasibleandavailable.IndexTerms—roughSet,roughneuron,particleswarm,roughneuronBPneuralnetwork,faultdiagnosisI.INTRODUCTIONIntelligentfaultdiagnosisisanimportantdevelopingdirectionofdiagnostictechnique.Thetraditionalfaultdiagnosismethodisbasedonthemathematicalmodelofthesystem,mathematicalmodelisdependentonthediagnosissystemstructurein[1],butmanyfaultscancausechangesinthestructureofthesystem.Neuralnetworktechnologyhasself-learning,nonlinearpatternrecognition,associativememoryandpresumedability,goodfaulttoleranceandexpansibility,sofaultdiagnosisiswidelyusedin[2-4].Therearealsomanyscholarsimprovedneuralnetwork,forexample,reference[5]optimizedBPneuralnetworkwithL-Mmethod,therearemanyvirtuessuchasfastconvergenceandhardintothelocalminimumvaluesforthenetwork.self-learningabilityofBPneuralnetworkandinterpretingabilityofexpertsystemiscombinedin[6],reliabilityandaccuracyofsystemareincreased.Butwhentheinputinformationdimensionbecomeslarge,theabovetrainingtimeofneuralnetworkistoolong.RoughSetsTheorywasproposedin1982byPawlakinpaper[7],itisanewmathematicaltooltodealwithvaguenessanduncertainty.Inreference[8-10],ithasbeenappliedinmanyareassuchaspatternrecognition,dataminingandfaultdiagnosis.Itsreductionoperationcanremoveredundantattributesandredundancysamples,compressioninformationspacedimension,simplifytheknowledgesystem,realizeThepretreatmentofinformationsystem.Literature[11,12]usedRoughSetsTheoryforpretreatmentofinputdataofneuralnetwork,extractingkeyingredientsasinputofnetwork,althoughsimplifiedstructureoftheneuralnetworks,theoperationmechanismofneuralnetworkwasnotimproved.Thispaperproposesanewneuralnetworkbaseonroughneuron,roughneuronnetworkmodelbycombiningroughsettheorywithneuronconcepts,whichhasbroadmeaninginrealworld.Roughneuronnetworkcansolveinputvectorwithmultiple-valuedeffectively.AnewkindofRoughneuronnetworkisproposedandappliedinfaultdiagnosis..PRELIMINARIESANDNOTATIONSA.BasicconceptsofRoughSetDefinition1Letaninformationsystemisa4-tuple(,,,)SUAVf=,whereUisanobjectscollection(Domain);ACD=Uisanattributeset,subsetCiscalledconditionattributeandDiscalleddecisionattribute;Aisanattributeset;Visasetofattributes,aaAVV∈=U;:fUAV×→isaninformationfunction,whichdesignateseachobjectaA∈,xU∈,(,)afxaV∈.Theinformationsystemthatprovidedwithconditionattributeanddecisionattributeiscalleddecisiontable.Definition2Letaninformationsystemisa4-tuple(,,,)SUAVf=,definedtheset(){[]}RRXxUxX=∈⊆asX’slowerapproximationset,and(){[]}RRXxUxXϕ=∈≠IasX’supperapproximationset.Definition3Letaninformationsystemisa4-tuple(,,,)SUAVf=,definedtheset/{|[]}cxUDxUxX∈∈⊆UFootnotes:8-pointTimesNewRomanfont;ManuscriptreceivedJanuary1,2008;revisedJune1,2008;acceptedJuly1,2008.Copyrightcredit,projectnumber,correspondingauthor,etc.52RoughNeuronnetworkforFaultDiagnosisCopyright©2011MECSI.J.Image,GraphicsandSignalProcessing,2011,2,51-58aspositiveregionofsetDinsetC,marksas()(())INDCPOSINDDor()CPOSD.Definition4Letaninformationsystemisa4-tuple(,,,)SUAVf=,ACD=UandthedependabilitybetweenDandCisdefined:()()cckDPOSDUγ==.FortheattributeofcC∈,if()()ccDcDγγ=-,thenattributecisredundantattributewhichisrelativetodecision-makingattributeD.Oritisindispensableattribute.UndertheimportanceofCrelativetoD,attributecisdefined:(,,)()()CCSSGFcCDDcDγγ=--.IfanyattributeisindispensableinCrelativetoD,thenCandDareindependent.Definition5Letaninformationsystemisa4-tuple(,,,)SUAVf=,ACD=UandPC∈.IfPandDareindependent,and()()cpDDγγ=,thenPiscalledC’srelativereductionofD,andmarksas()REDC.B.RoughNeuronAroughneuroninreference[13]canberegardedasconsistoftwoordinaryneurons,oneofthemiscalledtheupperboundaryr,theotheriscalledthelowerboundaryr,asshowninfigure1.Figure.1Roughneuron.Theinputofaconventional,lower,orupperneuroniscalculatedusingtheweightedsumas:ijijinputoutputω=×∑(1)whereiandjareeithertheconventionalneuronsorupper/lowern