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39920059JOURNALOFXI'ANJIAOTONGUNIVERSITYVol.39№9Sep.20051,2,1,1,1(1.,710049,;2.,710049,):、,、.,,,,,.,,,.:;;;:TH17;TP18:A:0253!987X(2005)09!0928!05NovelHybridIntelligentForecastingModelandItsApplicationtoFaultDiagnosisHuQiao1,HeZhengjia2,ZiYanyang1,ZhangZhousuo1,LeiYaguo1(1.SchoolofMechanicalEngineering,Xi'anJiaotongUniversity,Xi'an710049,China;2.StateKeyLaboratoryforManufacturingSystemsEngineering,Xi'anJiaotongUniversity,Xi'an710049,China)Abstract:Duetothefluctuationandcomplexityofelectromechanicalequipmentoperationconditionaffect-edbyvariousfactors,itisdifficulttouseasingleforecastingmethodtoaccuratelydescribethemovingtendency.Soanovelhybridintelligentforecastingmodelbasedonempiricalmodedecomposition(EMD),supportvectormachines(SVMs)andadaptivelinearneuralnetwork(ALNN),isproposed,wheretheseintrinsicmodecomponents(IMCs)areadaptivelyextractedviaEMDfromanonstationarytimeseriesaccordingtotheintrinsiccharacteristictimescales.TendenciesoftheseIMCsareforecastedwithSVMsrespectively,inwhichthekernelfunctionsareappropriatelychosenwiththesedifferentfluctuationsofIMCs.TheseforecastingresultsofIMCsarecombinedwithALNNtooutputtheforecastingresultoftheoriginaltimeseries.Theproposedmodelisappliedtothetendencyforecastingofabenchmarkexampleandavibrationsignalfrommachinesets,andthesimulatedresultsshowthattheforecastingperformanceofthehybridmodeloutperformsSVMswiththesingle-stepaheadforecastingorthemulti-stepaheadforecasting.Keywords:empiricalmodedecomposition;supportvectormachine;adaptivelinearneuralnetwork;hy-bridintelligentforecasting,、,:2004!11!17.:(1977),,;(),,,.:(50335030);(50175087;50305012);(2005CB724106);(20040698026).[1],,、.[2],,.,,---.,[3,4],、,.11.11998NordenE.Huang[5]、---,.2:&,0;’,0,.,[5].,x(t)(t=1,2,…,N)nfi(t)rn(t),x(t)=Σni=1fi(t)+rn(t)(1)(1)nfi(t),f1(t),fn(t),rn(t).1.2(SVR)V.Vap-nik[6]1995,[7][8],.(xi,yi),xi∈Rd,yi∈R,i=1,…,n,f(x)=(w·xi)+b(2):w∈Rn;b∈R;(w·xi)wxi,,Q(w)=12(w·w)+CRemp(f)(3):C,;Remp(f),*’.(3),+i+*i,i=1,…,n,(3)min12(w·w)+CΣni=1(+i++*i)(4)yi-w·x-b≤e++iw·x-yi+b≤e++*==ie,(4)α*i、αib,Q(α,α*)=-eΣni=1(α*i+αi)+Σni=1yi(α*i-αi)-12Σni=1(α*i-αi)(α*j-αj)(xi·xj)(5)Σni=1(α*i-αi)=00≤α*i,αi≤C;i=1,2,…,==nαi、α*ib,K(xi,xj),f(x,αi,α*i)=Σni=1(αi-α*i)K(xi,x)+b(6)(6)K(xi,xj)Mercer,,,.、、[6].,(5),,(SMO)[9].1.31,,,Widrow-Hoff,[10].,,.22!!9299,:pi(i=1,2,…,R):;a:;w1,i(i=1,2,…,R):;b:1f1(t)～f3(t):;rn(t):;x(t+l):;^x(t+l):;e(t+l):2.(1)(1),(EMD)、x(t)(t=1,2,…,N)n,fi(t)(i=1,2,…,n)rn(t).(2)fi(t)(i=1,2,…,n)rn(t),SVR.:(f1(t));、(f2(t)、f3(t)),;(rn(t)).(3),^x(t+l),x(t+l)^x(t+l)e(t+l).33.1,ERMS(=1nΣnt=1(x(t)-^x(t)))21/2、EMA=1nΣnt=1|x(t)-^x(t)|EMAP=1nΣnt=1x(t)-^x(t)x(t).3.2、Mackey-Glass,dx(t)/dt=0.2x(t-,)/[1+x10(t-,)-0.1x(t)](7)[11].,x(0)=1.2,,=17,1024,1,512,512,.3,,5.SVM512,,SVM,1.x(t):;f1～f5:;r5:3EMD039391ERMSEMAEMAP/%ERMSEMAEMAP/%SVM0.0007520.0006300.07210.0007580.0006320.07200.0007120.0005810.06750.0007310.0005970.069050SVM0.0000980.0000980.01140.1831960.14703116.76450.0005820.0004420.05150.1016190.0972948.92634,SVM,.50,SVM,.1,50,3SVM,EMAPSVR16.76%8.92%,.a:SVM;b:4501,50,SVM,SVM,SVM,、.3.3、、.,,1h,.,120(5d),4.SVM5d(5).,120EMD61.a:SVM;b:55,SVM,,SVM,2.62,SVM,,,,.51ERMS、EMAEMAP,SVM.,,EMD、.1399,:2ERMS/$mEMA/$mEMAP/%ERMS/$mEMA/$mEMAP/%SVM0.0099560.0099140.01941.5937021.2718932.48670.4034260.2566380.50400.8302270.6292921.231824SVM0.0009960.0009920.00192.0392627.7297373.41320.1554120.1196470.23531.4958261.1951932.3944a:SVM;b:624,.4!!.,,.、,SVM.,、,.:[1]MitaniY,TsutsumotoK,KagawaN.Timeseriespredictionofacousticsignalsusingneuralnetworkmodelandwaveletshrinkage[A].ProceedingsoftheTenthInternationalCongressonSoundandVibration[C].Stockholm,Sweden:IIAV,2003.4189!4196.[2]SharkeyAJC,ChandrothGO,SharkeyNE,Amulti-netsystemforthefaultdiagnosisofadieselen-gine[J].NeuralComputing&Application,2000(9):152!160.[3]MurtaghF,StarckJL,RenaudO.Onneuro-waveletmodeling[J].JournalofDecisionSupportSystems:SpecialIssueDataMiningforFinancialDecisionMak-ing,2004(37):475!484.[4]SatishB,SwarupKS,SrinivasS,etal.Effectoftemperatureonshorttermloadforecastingusinganin-tegratedANN[J].ElectricPowerSystemsResearch,2004,72(1):95!101.[5]HuangNE,ShenZ,LongSR,etal.TheempiricalmodedecompositionandtheHilbertspectrumfornon-linearandnon-stationarytimeseriesanalysis[J].ProcRSocLond(A),1998,454(1):903!995.[6]VapnikVN.Thenatureofstatisticallearningtheory[M].NewYork:Springer-Verlag,1995.181!217.[7]VanajakshiL,RilettLR.Acomparisonoftheper-formanceofartificialneuralnetworkandsupportvec-tormachinesforthepredictionoftrafficspeed[A].2004IEEEIntelligentVehiclesSymposium[C].Par-ma,Italy:IEEE,2004.194!199.[8]MohandesMA,HalawaniTO,RehmanS,etal.Supportvectormachinesforwindspeedprediction[J].RenewableEnergy,2004,29(6):939!947.[9]PlattJC.Fasttrainingofsupportvectormachinesu-singsequentialminimaloptimization[A].SchölkopfB.AdvancesinKernelMethods:SupportVectorLearn-ing[C].Cambridge:MITPress,1998.185!208.[10]HaganMT,DemuthHB,BealeMH.[M].,.:,2002.168!182.[11]WangW,GolnaraghiF,IsmailF.Prognosisofma-chinehealthconditionusingneuro-fuzzysystems[J].MechanicalSystemsandSignalProcessing,2004(18):813!831.()23939