一种基于KPCA的非线性故障诊断方法

:20050215:863(:2004AA412050):(1981),,..Email:[e-mail]:16723961(2005)03010304KPCA邓晓刚,田学民((),257061):介绍了一种非线性故障检测方法核主元分析法(KPCA),通过核函数来完成非线性变换,将变量由非线性的输入空间转换到线性的特征空间.在特征空间中使用PCA计算主元,构造T2和SPE统计量检测过程故障的发生.提出了一种KPCA贡献图计算方法,根据测量变量和非线性主元的相关性,计算测量变量的贡献量绘制贡献图,用于故障变量的分离.仿真结果表明,KPCA方法可以比PCA方法更加迅速的检测到故障的发生,利用KPCA贡献图可以较好的辨识出故障变量.:核主元分析法;贡献图;非线性过程;故障检测;故障诊断:TP277:ANonlinearprocessfaultdiagnosismethodusingkernelprincipalcomponentanalysisDENGXiaogang,TIANXuemin(CollegeofInformationandControlEngineering,UniversityofPetroleum(EastChina),Dongying257061,China)Abstract:Anonlinearfaultdetectionmethodbasedonkernelprincipalcomponentanalysis(KPCA)isintroduced.KPCAperformsnonlineartransformationbykernelfunctiontomapthenonlinearinputspaceintolinearfeaturespace.BasedonT2andSPEchartsinfeaturespace,principalcomponentanalysis(PCA)canbeusedtodetectfaults.KPCAcontributionplotsareproposedtoisolatefaultyvariables.Accordingtocorrelationbetweenmeasuredvariablesandnonlinearprincipalcomponents,thecontributionofeachvariableiscalculatedtogivecontributionplots.ThesimulationresultsindicatethatKPCAissuperiortoPCAandthatcontributionplotscanisolatethefaultyvariableswell.Keywords:kernelprincipalcomponentanalysis;contributionplots;nonlinearprocess;faultdetection;faultdiagnosis0引言20,,,(PCA),(PLS)1!.,,.,2!,353Vol.35No.3()JOURNALOFSHANDONGUNIVERSITY(ENGINEERINGSCIENCE)20056Jun.2005,,.(KPCA)3!,.,KPCA,.,CSTR.1基于KPCA的故障检测1.1KPCA,X,X,C=1N-1∀Nj=1xjxTj.X(.),(X),CF=1N-1∀Nj=1(xj)(xj)T,,KPCACF,vk=CFvk(1),vkKPCAk.,(.),,KPCA.k(x,y)=#(x),(y)∃,,X,[K]ij=kij=#(xi),(xj)∃.3!,KPCAvk=∀Ni=1ki(xi)(2)(N-1)k=Kk(3)xk()tk=#vk,(x)∃=∀Ni=1ki#(xi),(x)∃(4),:k(x,y)=exp(-%x-y%2c),c.,,(5)(6)5!,K%=K-1NK-K1N+1NK1N(5)K%scl=K%trace(K%)(N-1)(6),1N1NN&N,trace.1.2KPCA,T2SPE4,5!,SPEQ.KPCA,KPCA,:T2=[t1,∋,tp]!-1[t1,∋,tp]T(7)T2F,T2p,N,~p(N-1)N-pFp,N-p,(8)N,p.SPE=%(x)-^p(x)%2=∀Ni=1t2j-∀pi=1t2j(9)SPE(10),SPE~g∀2h(10)g,hSPE.2基于KPCA贡献图的故障变量辨识,,,.PCA,,.KPCA,,,PCAKPCA.,,,.KPCA,,,.,(11).jT2CONTj=∀pi=1|conti,j|,conti,j=tTixji(11)pKPCA,tixjij104104()35,xj.,.3仿真结果CSTR,A,B,,,.CSTR1.CSTR,10(1).1CSTRFig.1CSTRsystem1Tab.1FaultpatternlistsF1F2F3F4,F5F6F7F8F9F10,,PCAKPCA.F2,200,2.2,PCAT2306,KPCAT2271.SPE,KPCA272,PCA.,KPCAPCA.2PCAKPCAFig.2ThecomparisonofmonitoringchartsbetweenPCAandKPCA,,(3).31053,:KPCA105,9,;36,.,3.,,,3.,.,,.3Fig.3Contributionplotsofvariables4结论CSTR,KPCAPCA,,,,.KPCA,,KPCA,,,.:[1]MILETICI,QUINNS,DUDZICM,etal.Anindustrialperspectiveonimplementingonlineapplicationsofmultivariatestatistics[J].JournalofProcessControl,2004,14(8):821836.[2]DONGD,MCAVOYTJ.Nonlinearprincipalcomponentanalysisbasedonprincipalcurvesandneuralnetworks[J].ComputersandChemicalEngineering,1996,20(1):6578.[3]SCHOLKOPFB,SMOLAA,M(ULLERKR.Nonlinearcomponentanalysisasakerneleigenvalueproblem[J].NeuralComputation,1998,10(5):12991319.[4]LEEJM,YOOCK,CHOISW,etal.Nonlinearprocessmonitoringusingkernelprincipalcomponentanalysis[J].ChemicalEngineeringScience,2004,59(1):223234.[5]LEEJM,YOOCK,LEEIB.Faultdetectionofbatchprocessesusingmultiwaykernelprincipalcomponentanalysis[J].ComputersandChemicalEngineering,2004,28(9):18371840.(编辑:陈斌)(上接第71页)CHULinbo,MAYulin.Theapplicationofconfigurationspaceapproachinassemblyplanning[J].JournalofHarbinInstituteofTechnology,1999,31(4):8087.[5]WANGYF,CHIRIKJIANGS.Anewpotentialfieldmethodforrobotpathplanning[A].ProceedingsoftheIEEEInternationalConferenceonRobotics&Automation[C].SanFrancisco:IEEEInc,2000.[6],,,.[J].,2004,(8):8689.FANChanghong,LUYouzhang,LIUHong,etal.Pathplanningformobilerobotbasedonneuralnetworks[J].ComputerEngineeringandApplication,2004,(8):8689.[7]WATANABEK,IZUMIK.Asurveyofroboticcontrolsystemsconstructedbyusingevolutionarycomputations[A].ProcIEEEIntConfonSystems,ManandCybernetics[C].Tokyo:IEEEInc,1999.[8]NELSONHC,YEYC.Anintelligentmobilevehiclenavigatorbasedonfuzzylogicandreinforcementlearning[A].IEEETransonSystems,ManandCybernetics[C],Tokyo:IEEEInc,1999.[9],.[M].:,1995.WANGDongsheng,CAOLei.Chaos,furcationandtheapplication[M].Hefei:UniversityofScienceandTechnologyofChinaPress,1995.(编辑:陈斌)106106()35