基于结点优化的决策导向无环图支持向量机及其在故障诊断中的应用

363Vol.36,No.320103ACTAAUTOMATICASINICAMarch,20101111;2(Supportvectormachine,SVM),,.(Decisiondirectedacyclicgraph,DDAG),,,.,..,,,,DOI10.3724/SP.J.1004.2010.00427SupportVectorMachineBasedonNodesRe¯nedDecisionDirectedAcyclicGraphandItsApplicationtoFaultDiagnosisYIHui1SONGXiao-Feng1JIANGBin1WANGDing-Cheng1;2AbstractSupportvectormachine(SVM)isanintelligentmethodwhichcancreatediagnosticmodelsautomaticallybyusingo®/on-linedatasets,butitneedstobeextendedtoamulti-classclassi¯erformulti-faultdiagnosis.Decisiondirectedacyclicgraph(DDAG)isanextendingstrategywithoutstandingperformance.However,itsdecisionlargelydependsonthesequenceofnodeswhichisarbitrarilyselected.Thisa®ectstheaccuracyofdiagnosis.Inthispaper,weproposedamethodtore¯nethesequenceofnodesaccordingtothedistributionoffaultdatasets,soastoimprovetheaccuracyofSVM-baseddiagnosis.Multi-classSVMextendedbyourmethodhasbeenemployedasatransformerfaultdiagnosis,andsatisfactoryresultshavebeenobtained.KeywordsSupportvectormachine(SVM),faultdiagnosis,multi-class,decisiondirectedacyclicgraph(DDAG),node-re¯ned.:[1].,()[2],;()(),2008-11-112009-04-01ManuscriptreceivedNovember11,2008;acceptedApril1,2009(60874051),(20070411044),(BK2007195),(0701014B)SupportedbyNationalNaturalScienceFoundationofChina(60874051),ChinaPostdoctoralScienceFoundation(20070411044),NaturalScienceFoundationofJiangsuProvince(BK2007195),andJiangsuPlannedProjectsforPostdoctoralResearchFunds(0701014B)1.2100162.2100441.CollegeofAutomation,NanjingUniversityofAeronauticsandAstronautics,Nanjing2100162.InstituteofComputerandSoftware,NanjingUniversityofInformationScienceandTechnology,Nanjing210044,,,.,,,.,,.(Supportvectormachine,SVM)(Statisticallearningtheory,SLT).[3],,.1,,.,.(1-against-rest)[4]1-a-1(1-against-1)[5].,,,,;2002Takahashi[6],,,.,,(Evaluationpath),.1.1,(Decisiondirectedacyclicgraph,DDAG).(Directedacyclicgraph,DAG),Platt[7].k,k(k¡1)=2k,1,,22,,ii.,iji+1jj+1.DDAG41(Notii).1DDAGFig.1Proceduresforafour-typeDDAGdecision,,.SVM.,DDAG,DDAG,[8].,,.,DDAG.2DDAG1.kDDAG,1,ii().m.E=f1;¢¢¢;m;¢¢¢;k¡1g.,:1¸2¸¢¢¢¸a¡1¸max(a;a+1;¸k¡1);a=bp2(k¡1)+0:25¡0:5c(1).,E=f1;¢¢¢;m;¢¢¢;k¡1g,m2f1;2;¢¢¢;k¡1g,p=1¡(1¡m)(1¡m+1)£¢¢¢£(1¡k¡1)(2)9i2[1;m¡1];j2[m;k¡1],ij,:p=1¡(1¡m)(1¡m+1)£¢¢¢£(1¡j)£¢¢¢£(1¡k¡1)(3)p0=1¡(1¡m)(1¡m+1)£¢¢¢£(1¡i)£¢¢¢£(1¡k¡1)(4)p0p(5)p;p:min(Ei)¸max(Ej);Ei=f1;2;¢¢¢;m¡1gEj=fm;m+1;¢¢¢;k¡1g(6),m.DDAG,k¡1.m(m+1)=2,:m(m+1)2·(k¡1))m·p2(k¡1)+0:25¡0:5(7)m=2,(6):1¸max(2;3;¢¢¢;k¡1)(8)m=3,:min(1;2)¸max(3;4;¢¢¢;k¡1)(9)(8),:1¸2¸max(3;4;¢¢¢;k¡1)(10),p,:1¸2¸¢¢¢¸a¡1¸max(a;a+1;¢¢¢;k¡1);a=bp2(k¡1)+0:25¡0:5c¤[9]:X~°2R+,X£f¡1;1gD,,R,`Sms(f)¸°errD(f)1¡±:errD(f)·(`;~;±;°)=2`µ64R2°2lne`°4Rln128`R2°2+ln4±¶;`2;64R2°2`(11):,°,p.SVM,d=2°.,:d1·d2¢¢¢·da¡1·min(da;da+1;¢¢¢;dk¡1);a=bp2(k¡1)+0:25¡0:5c(12),DDAG,,.(12),,a.DDAGSVM(Node-re¯nedDDAG-SVM,nrDDAG-SVM).S=fS1;S2;¢¢¢;Skg,Sii,nrDDAG-SVM,Matlab:1.k,k(k¡1)=2SVM.SVMi;jSiSj.2.SVMi;j,SiSjdi;j.3.(Sa;Sb):argmini;jdi;j;i;j2(1;2;¢¢¢;k);Sa;Sb.(Sa;Sb)=)(M1;Mk)(M=fM1;M2;¢¢¢;Mkg).4.Sa,Sb:Sc:argminida;i(i=1;2;¢¢¢;k;i6=a;b),Sc=)M2;Sd:argminidb;i(i=1;2;¢¢¢;k;i6=a;b;c),Sd=)Mk¡1.5.L=bk2c;4L,:S=fS1;S2;¢¢¢;Skg=)M=fM1;M2;¢¢¢;Mkg.6.1,MDDAG,X,Mj.7.MMj,5S()M,XSi.DDAG,,.,,,.nrDDAG-SVM,,,.3nrDDAG-SVM,nrDDAG-SVM.PC(2.8G,512M)Matlab7.1.3.1[10].¯nedmethod2nrDDAG-SVMTable2Classi¯cationresultsusingnrDDAG-SVM05100%4100%125100%13100%25100%6100%315100%2100%,DDAG,,3.3DDAGFig.3Correctclassi¯cationratiosforallpossibleDDAGstructuresDDAG,.,5=24.nrDDAG,DDAG.3.31-a-r1-a-1nrDDAG.,,.4,1-a-1,,1-a-1..(a)(a)Ratiosofcorrectclassi¯cation(b)(b)Ratiosofincorrectclassi¯cation4Fig.4Testingforthecapabilityofdiagnosis3.4.,.,1-a-r1-a-1nrDDAG,.Matlab,4,5.5,nrDDAG.,,,,.nrDDAG,.,nrDDAG,.(a)(a)Timefortraining(b)(b)Timefortesting5Fig.5Testingforthespeedofcomputing,nrDDAG,,.4,,..DDAG.DDAG,a(a=bp2(k¡1)+0:25¡0:5c).,DDAG(nrDDAG-SVM).,,.References1ZhouDong-Hua,YeYin-Zhong.ModernFaultDiagnosisandFault-TolerantControl.Beijing:TsinghuaUniversityPress,2000(,..:,2000)2JiangB,StaroswieckiM,CocquempotV.Faultaccommo-dationfornonlineardynamicsystems.IEEETransactionsonAutomaticControl,2006,51(9):1578¡15833ZhangXue-Gong.Introductiontostatisticallearningtheoryandsupportvectormachines.ActaAutomaticaSinica,2000,26(1):32¡42(..,2000,26(1):32¡42)4VapnikVN.StatisticalLearningTheory.NewYork:Wiley,1998:astepwiseprocedureforbuildingandtraininganeuralnetwork.Neurocomputing:Algorithm,ArchitecturesandApplications.NewYork:Springer-Verlag,19906TakahashiF,AbeS.Decision-tree-basedmulticlasssupportvectormachines.In:Proceedingsofthe9thInternationalConferenceonNeuralInformation.WashingtonD.C.,USA:IEEE,2002.1418¡14227PlattJC,CristianiniN,Shawe-TaylorJ.LargemarginDAG0sformulticlassclassi¯cation.In:ProceedingsofNeu-ralInformationProcessingSystems.Massachusetts