基于双层线性神经网络学习的时变模态参数的快速识别算法(IJEM-V1-N6-7)

I.J.EngineeringandManufacturing,2011,6,44-51PublishedOnlineDecember2011inMECS()DOI:10.5815/ijem.2011.06.07Availableonlineat(NovelInformationCriterion)usingtwo-layerlinearneuralnetworklearningforsubspacetracking.Comparingwiththeoriginalalgorithm,thereisnoneedtosetakeycontrolparameterinadvance.Simulationexperimentsshowthatnewalgorithmhasafasterconvergenceintheinitialperiod.IndexTerms:Subspacetracking,time-varyingmodalparameter,identificationalgorithm,neuralnetworklearning©2011PublishedbyMECSPublisher.Selectionand/orpeerreviewunderresponsibilityoftheResearchAssociationofModernEducationandComputerScience.1.IntroductionLineartime-varying(LTV)structuresarewidelyexistedinthefieldofaerospace,mechanicsandtransportation,suchasexpendingofsolarpanelsandmechanicalarmsandhigh-speedtrain[1].Forlineartime-invariable(LTI)system,measuringandanalyzingtechniquesofmodalparametershavereachedamaturedevelopment.HowevertheconventionalconceptsofmodalparametersareoutofinvalidationforLTV.ByadoptingdefinitionofmodalparametersinLTIandusing“timefrozen”technique,theconceptof“pseudomodelparameters”[2,3]isproposed.Liu[4,5]extendedidentificationalgorithmsofmodalparametersbasedonsubspaceinLTV.Theprocedureofmodalparameteridentificationalgorithmbasedonsubspaceisthat:firstextractsignalsubspacebyapplyinginput/outputtime-serials,thenestimatesystemmatrix,finallyobtaintime-varyingmodalparametersbymodaltheory.Yu[6]solvedtime-varyingmodalparameteridentificationofmovingmass/simple-supportedbeambyusingmodalparameteridentificationalgorithmbasedonsubspaceofensembledata[2].Pang[7]gotanewversionofthealgorithmbasedonsubspaceofensembledatabyreplacinginputmatrix*Correspondingauthor.E-mailaddress:[e-mail],[e-mail]rithmofTime-varyingModalParameterBasedon45Two-layerLinearNeuralNetworkLearningwithgeneralizedobservabilitymatrixandapplyingorthogonalityofsingularmatrix,whosecomputeloadandnoiseimmunityarebothbetterthanthatoftheoriginalone.Buttheabove-mentionedmethodsareisnotsuitablefortrackingmodalparametersforlargecomputeloadandmemoryspace.Soidentificationalgorithmsbasedonrecursivesubspacederivedfrombatchsubspacemethod[8]takestheadvantageinon-linemodalparameteridentification.F.Taskeret.al[9,10]proposedon-lineidentificationalgorithmoftime-varyingmodalparametersusingTQR-SVD[11]fortrackingsignalsubspace.Wu[12]obtainedanewon-linealgorithmbyintroducingFAST(FastApproximateSubspaceTracking)andappliedintime-varyingmodalparameteridentificationofthree-linksystem.Panget.al[13,14]gotafastidentificationalgorithmoftime-varyingmodalparametersbyintroducingPAST[15](ProjectionApproximationSubspaceTracking)andappliedintwo-linksystemandmovingmass/simple-supportedbeamsystem.Thekeyofalgorithmsbasedonsubspacetrackingistofindanefficientandfastalgorithmforsubspacetracking.ThesignalsubspaceobtainedbyPASTconvergesasymptoticallytotheorthogonalsubspace,byintroducingorthogonalmethod1/2()TOPAST[16]isobtained.OtherwisebydeflationtechniqueofPCA(PrincipalComponentAnalysis),PASTd[15,17]isderived.Similarly,signalsubspaceobtainedbyPASTdhasastrongloseoforthogonality,byintroducingorthogonalmethodGram-SchmitforincorporatingcharacteristicofPASTd,amodifiedPASTd[18]isobtained.PASTcanbeviewedasaclassicalpoweriterationmethod.ComparingwithPAST,NPI[19](NaturalPowerIteration)hasafasterconvergencespeedandensuresorthogonalityofsubspacevectorswithoutcomputeloadincreasing.InbothPASTandNPI,1ppWWisusedintheprocessofalgorithmderivation,sotheyareonlysuitablefortrackingslowsubspace.DifferentfromPASTandNPI,API[20](ApproximatedPowerIteration)cantrackrapidsubspaceandapplyupdatingdatainbothinfiniteexponentialwindowandfinitemovingexponentialwindow.DifferentfromPASTincostfunction,NIC[21,22](NovelInformationCriterion)isproposed,adoptingintwo-layerlinearneuralnetworklearningforsubspacetracking.Byintroducingorthogonalmethod,amodifiedversionisobtainednamedFONIC[23].ThispaperpresentsamodifiedversionofNICadoptingintwo-layerlinearneuralnetworklearningforsubspacetracking.Comparingwiththeoriginalalgorithm,thereisnoneedtosetanimportantparameterinadvance.Simulationexperimentsshowthatithasafasterconvergenceintheinitialperiod.2.Recursiveformofupdatinginput/outputdataTotrackingsubspaceofupdatinginput/outputdates,itisunnecessarytoevaluateTpppYUYeverystep.Byadoptingrecursiveformofupdatinginput/outputdata,principlesubspacetrackingalgorithmcanbeappliedandthenfastidentificationoftime-varyingmodalparameterisachieved.UpdatingtheinputandoutputHankelmatrix,wehave:1111[],[]ppppppYYyUUu(1)Where1[(1)(2)()]TpyypypypM,1[(1)(2)()]TpuupupupM,46FastIdent