基于分布滞后的结构鉴定系统(IJISA-V5-N11-1)

I.J.IntelligentSystemsandApplications,2013,11,1-10PublishedOnlineOctober2013inMECS()DOI:10.5815/ijisa.2013.11.01Copyright©2013MECSI.J.IntelligentSystemsandApplications,2013,11,1-10StructuralIdentificationofSystemswithDistributedLagNikolayKarabutov,Dr.,Prof.Dept.ofProblemsControl,MoscowStateEngineeringUniversityofRadioEngineering,ElectronicsandAutomation,Dept.ofMathematics,FinancialUniversityundertheGovernmentoftheRussianFederation,Moscow,RussiaE-mail:[e-mail];[e-mail]—Theproblemofstructuralidentificationofsystemswiththedistributedlagintheconditionsofuncertaintyisconsidered.Knownstatisticalapproachesarelaboriousandnotalwaysallowmakingthedecisiononlagstructure.Thereforeinworkfortheproblemdecisionthespecialclassofstaticstructures(SS)(virtualportraits)exploredsystemisintroduced.Processofthedecisionofaproblemconsistsoftwosteps.Atthefirststepsetofsecantsforinitialsystemisunderconstruction.Completenessofsetofsecantsisasignoflinearityofsystem.Nonfulfilmentofconditionsofcompletenessisasignofnonlinearityofsystem.Estimationofnonlinearityofsystemexecuteonanindicatoroflevelofnonlinearityofthesystem,offeredinwork.AtthesecondstepthespecialstructuralspaceisintroducedandisdefinedSSforanonlinearpartofsystem.TheestimationofnonlinearpropertiesofsystemisexecutedonthebasisofidentificationofparametersofsetofsecantsSS.Criteriaandalgorithmsofdecision-makingonstructureofalagonthebasisoftheanalysisofvirtualportraitsareoffered.TheanalogueofcriterionofDurbin-Watsonisoffered.Thereceivedresultsaregeneralizedonacaseofthedistributedlagininputandoutputvariablesofsystem.Itisshownthattostructuralidentificationofsystemswiththedistributedlagwewillnotapplytheanalysisofsectorsets.Theapproachtoparametricalidentificationofsystemwiththedistributedlagintheconditionsofuncertaintyisoffered.IndexTerms—StructuralIdentification,DistributedLag,VirtualPortrait,Decision-Making,ParametricalIdentificationI.IntroductionModelswiththedistributedlagsarewidelyappliedinaneconometricsandeconomy[1-4],theengineering[5-7]andmedicine[8-10].Delaycanhavebothindepend-ent,anddependentvariables.Theaccountofthedis-tributedlagactivatesautocorrelationbetweenvariables[1,2,4]andcomplicatesprocessofidentificationpa-rametersobject.Toidentificationofparameterssystemapplyvariousmodelsofapproximationparametersatthedistributedlags.Suchapproachallowsreducingnumberofestimatedparametersofsystem.TheKoyckscheme[2,12],basedonachangeoffactorsofmodelonadecreasinggeometricalprogressionismostwidelyapplied.TheFishermodel[1,11]isbasedonachangeoffactorsmodelonthesetdecreasingarithmeticalpro-gression.Fisherschemeareappliedinthatcasewhenobjectparametersdecreasefromthefirstmembersofaprogression.S.Almon[13]modifiedFishermodel,hav-ingappliedthepolynomiallawofchangefactors.Otherapproachestothedefinitionoflawschangeparametersatthedistributedlagsaredescribedin[4,11,14,15].Theaccountingofaprioriinformationondependencebetweenthedistributedlagsintheformofsomeration-alpolynomisstatedin[16].Theconsideredmodelsoffactorsminimizenumberofunknownparameters.Toanestimationofparametersapplyamethodleast-squaresmethod[1-4].Intheseworksthemodelstructureispostulatedaprioriandtheproblemofparametricalidentificationisconsidered.In[17]theinteractivealgorithmofanestimationparame-tersstaticplantwiththedistributedlagsisoffered.Thelengthofalagissetanddoesnotbecomeanyassump-tionsofinterdependencebetweensystemparameters.Thecaseofapiecewisemonotonicchangeofparame-tersplantisconsidered.Inanumberofworksmethodsofachoicemaximumlengthalagareoffered.Theyarefoundedonapplicationthestatistics,therestsbasedontheanalysis[1,15,18].In[19,20]variousmethodsofanestimationparametersmodelwiththedistributedlaginacaseofapriorisetstructureofmodelareconsid-ered.In[21]influenceofaprioriinformation,receivedfromtheanalysisoftheempiricaldata,onachoiceofstructuremodelwiththedistributedlagonanoutputvariableisresearched.Polynomialschemesforestima-tionparametersareoffered.Inwork[22]aredescribedalgorithmofanestimationparametersmodelwiththedistributedlag.OnthebasisofresultsmodellingthestructureofmodelwhichexplainsamismatchofmodelappliednowintheAmericaninterestrateonfederalfundsisselected.In[23]processofinflationwiththehelpautoregressivemodelsisresearched.Thechoiceoflengthalagiscarriedoutonthebasisofconsecutivemagnificationdelaysandanestimationofadequacythereceivedmodel.Thechoiceoflengthalagisbasedonstep-by-stepincreaseindelaysandanestimationofadequacythereceivedmodel.ThentheAkaikecriterion2StructuralIdentificationofSystemswithDistributedLagCopyright©2013MECSI.J.IntelligentSystemsandApplications,2013,11,1-10andBayesianinformationcriteriaareappliedandthesolutionismadeonmodelstructure.Thecaseofaprioriuncertaintyconcerningstructureandplantparameterswasnotstudy.Inwork[24]thereviewofexistingapproachestoconstructionofmodelsofaneconometricsisexecuted.Theanalysisisbasedonmethodologygeneral-to-specific.Itisbasedonsimplificationofthegeneralthe-oreticalmodelforthepurposeofitsconformitytoex-perimentaldata.Themethodologyisbas