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橋樑強震資料之工程應用─總計畫羅俊雄台灣大學土木工程學系郭鎧紋黃正耀中央氣象局地震測報中心12橋樑強震資料之工程應用─子計畫一：應用類神經網路之系統識別羅俊雄黃致傑台灣大學土木工程學系ABSTRACTAneural-network-basedmethodisproposedtothemodelingandidentificationofdiscrete-timenonlinearhystereticsystemduringstronggroundmotion.Thelearningormodelingcapabilityofmultilayerneuralnetworkisexplainedfromthemathematicalpointofview.Themainideaoftheproposedneuralapproachwillbeexplained,anditisshownthatmultilayerneuralnetworkisageneraltypeofNARMAXmodelandissuitablefortheextremenonlinearinput-outputmappingproblem.Numericalsimulationandrealstructurecasesareusedheretodemonstratetheproposedmethod.Theresultsillustratethattheneuralnetworkapproachisareliableandfeasiblemethod.INTRODUCTIONThemodelingandidentificationofstructuralsystemwithnonlinearhystereticbehaviorisawidelyencounteredprobleminthefieldofstructuralandearthquakeengineering.Manyeffortshavebeendevotedtoestablishthemodelsofnonlinearhystereticsystemandnumeroustechniquesaredevelopedbymanyresearcherstoidentifythemodelparameters.Thepurposeofthesesystemidentificationmethodsistousenumericalsimulationorfieldmeasurementstoimprovethedynamicmodelingcapabilityforamonitoringofstructuralsystemssuchasbuildings,bridgesanddams.Duetothecomplexnatureofcivilstructurestheavailableresponsemeasurementsareusuallyinsufficientandnoise-polluted,anditbecomesachallengingtasktomodelthecurrentconditionofstructuresviasystemidentificationapproach.Besides,on-linestructuralcontroloftenrequiresanaccurateestimationofstructural3responsetodeterminethepropercontrolforce,andthesuccessofhealth-monitoringsystemreliesonitsabilitytodetecttheminordamageofstructures.Allofthesecircumstancesillustratetheneedofareliable,feasible,andeasy-implementedmodelingapproach.Theuseofartificialneuralnetworksinsystemidentificationhasbeengainingmoreandmoreattentionsinrecentyears.AseriesofworksperformedbyChen,Billingsandtheirco-workershavedevelopedthefoundationofusingneuralnetworkasatoolfornonlinearsystemidentification(Chen1989andChen1990).Fromthemathematicalpointofview,theydemonstratedthatneuralnetworkisakindofNARMAXmodel(Billings1992).Theworksontheapplicationofneuralnetworksincivilengineeringfiledcanbecontributedtoseveralresearchers.Masriandhisco-workershaveappliedtheneuralnetworkstothemodelingoflinearandnonlinearstructuralsystems(Masri1993andChassiakos1996).Theyalsopresenteditsapplicationtothedamagedetectionofsimulatedandrealstructures(Masri1996andNakamura1998).Similarworksbyotherresearcherscanbefoundin(Wu1992,Elkordy1993,Worden1994andSzewczyk1994).Thepurposeofthispaperistoillustratethefeasibilityandpossibilityofusingneural-network-basedapproachtothemodelingandidentificationofsimulatedandrealstructuralsystems.Abriefdescriptionoftheinternaloperationofneuralnetworkanditstrainingalgorithmisdescribed.Theideaoftheproposedmethodfromsimplelinearmodeltocomplexinput-outputmappingandstructure-unknownproblemisexplained.Somediscussionsrelatetothisapproachandtheperformanceoftheproposedmethodwillbegivenbasedoncasestudy.Thestructuralsystemsunderconsiderationare:(1)asingledegree-of-freedomsystemwithnonlinearityandhysteresisloop,(2)realcase:apre-stressedbox-girderbridge(New-LianRiverBridgeII).NEURALNETWORKAccordingtodifferentnetworktopologyandtrainingrules,researchershavedevelopedmanykindsofnetworks.Theoneusedinthispaperisamultilayerneuralnetwork(MNN)whichisamassivelyparallel,interconnectednetworkofneurons.Theneuronsareorganizedintolayerswithnofeedbackorlateralconnections.4Eachlayerconsistsofsomeneuronswhichreceivesitsinputsfromotherneuronsinthepreviouslayer,andiftheweightedsumoftheinputsexceedsathresholdlevelwilltheneuronproduceanoutputanddistributeittotheneuronsinthenextlayer.Theequationthatdescribestheseoperationsis:=0,1,2,…,M-1)(1mmmmmbawfa+=−m(1)whereistheoutputofm-thlayer,istheweightconnectingthem-1-thlayertom-thlayer,isthebias,istheactivationfunction,andMisthenumberoflayersinthenetwork.Generally,theinput-outputrelationshipofnetworkcanbeexpressedas:mamwmbmf)))...))(((...((1211121MMMMbbbbpwffffa++++=−−(2)wherepistheinputvectorandaisthenetworkoutput;theactivationfunctionmaybechosenasthecontinuousanddifferentiablenonlinearsigmoidfunction.(.)fThetrainingalgorithmusedinthisstudyistheLevenberg-Marquardt(LM)algorithm.LMalgorithmisavariationofNewton’smethodthatwasdesignedforminimizingfunctionsthataresumsofsquaresofnonlinearfunctions.Thisisverywellsuitedtoneuralnetworktrainingwheretheperformanceindexisthemeansquarederror(Hagan1996).Theperformanceindexofneuralnetworkcanbedefinedas:∑===NiTixxxxF12)()()()(ννν(3)where)(kxνistheerrorvector.Then,Levenberg-Marquardtalgorithmcanbeexpressedas:)()(])()([11kkTkkkTkkxxJIxJxJxxνμ−+×+−=(4)whereisavectorofweightsandbias,andistheJacobianmatrixofkx)(kxJ5performanceindex.Askμisincreaseditapproachesthesteepestdescentalgorithmwithsmalllearningrate:kkkkkTkkxFxxxJxxμμν2)()()(1∇−=−≅+,forlargekμ(5)whileaskμisdecreasedtozerothealgorithmbecomesGauss-Newton.Detaileddescription,implementationandapplicationofLMalgorithmcanbefoundin(Scales1985,Hagan1994,andHagan1996).NEURALMODELINGANDIDENTIFICATIONMETHODOLOGYSystemmodel