基于灰色Verhulst模型和时间序列预测的BP神经网络的一种新混合灰色神经网络(IJITCS-V5

I.J.InformationTechnologyandComputerScience,2013,10,114-120PublishedOnlineSeptember2013inMECS()DOI:10.5815/ijitcs.2013.10.12Copyright©2013MECSI.J.InformationTechnologyandComputerScience,2013,10,114-120ANewHybridGreyNeuralNetworkBasedonGreyVerhulstModelandBPNeuralNetworkforTimeSeriesForecastingDeqiangZhouSchoolofInformationandMathematics,YangtzeUniversity,Jingzhou,ChinaE-mail:[e-mail]—TheadvantagesanddisadvantagesofBPneuralnetworkandgreyVerhulstmodelfortimeseriespredictionareanalyzedrespectively,thisarticleproposesanewtimeseriesforecastingmodelforthetimeseriesgrowthinS-typeorgrowthbeingsaturated.Fromthedatafitting'sviewpoint,thenewmodelnamedgreyVerhulstneuralnetworkisestablishedbasedongreyVerhulstmodelandBPneuralnetwork.Firstly,theVerhulstmodelismappedtoaBPneuralnetwork,thecorrespondingrelationshipsbetweengreyVerhulstmodelparametersandBPnetworkweightsisestablished.Then,theBPneuralnetworkistrainedbymeansofBPalgorithm,whentheBPnetworkconvergences,theoptimizedweightscanbeextracted,andtheoptimizedgreyVerhulstneuralnetworkmodelcanbeobtained.Theexperimentresultsshowthatthenewmodeliseffectivewiththeadvantagesofhighprecision,lesssamplesrequiredandsimplecalculation,whichmakesfulluseofthesimilaritiesandcomplementaritiesbetweengreysystemmodelandBPneuralnetworktosettlethedisadvantageofapplyinggreymodelandneuralnetworkseparately.ItisconcludedthatgreyVerhulstneuralnetworkisafeasibleandeffectivemodelingmethodforthetimeseriesincreasinginthecurvewithS-type.IndexTerms—TimeSeriesPrediction,BPNeuralNetwork,GreyVerhulstModel,GreyNeuralNetwork,GreyVerhulstNeuralNetworkI.IntroductionTimeseriespredictionreferstotheprocessbywhichthefuturevaluesofasystemisforecastedbasedontheinformationobtainedfromthepastandcurrentdatapoints[1].Atpresent,therearealotofmethodsfortimeseriesprediction,fromtraditionalstatisticalmethodsuchasARMA(AutoRegressiveMovingAverage)modeltoartificialintelligencebasedapproaches,thecoreofthesemodelsistoestablishapredictionmodel[2].NeuralNetwork(NN)basedmodelsarewidelyusedasanartificialintelligence-basedapproach,backpropagation(BP)beingthemostwidelyusedtechniqueforupdatingtheparametersofthemodel.BPneuralnetworkisthemostusedneuralnetworkatpresent.Ithasuniqueapproximationabilityandsimplestructure,anditisaneuralnetworkwithgoodperformance.TheBPlearningprocessworksinsmalliterativesteps,andthenetworkproducessomeoutputbasedonthecurrentstateofit'ssynapticweights(initially,theoutputwillberandom).Thisoutputiscomparedtotheknown-goodoutput,andamean-squarederrorsignaliscalculated.Theerrorvalueisthenpropagatedbackwardsthroughthenetwork,andsmallchangesaremadetotheweightsineachlayer.Theweightchangesarecalculatedtoreducetheerrorsignalforthecaseinquestion.Thewholeprocessisrepeatedforeachoftheexamplecases,thenbacktothefirstcaseagain,andsoon.However,notonlyarethestatisticalmodelsnotasaccurateastheneuralnetwork-basedapproachesfornonlinearproblems,theymaybetoocomplextobeusedinpredictingfuturevaluesofatimeseries.OnemajorcriticismabouttheBPmodelisthatitdemandsagreatdealoftrainingdata[3]anditsapplicationwasinhibitedlargelybytheslowconvergencerateandover-prolongedtrainingtime,primarilytheresultsofinappropriatesamplepreprocessingforalargeinitialsampledomain.Ontheotherhand,itiswellknownthatselectingthenumberofneuronsinhiddenlayerisalsoanimportantandtoughproblembecauseitaffectstheoverallperformanceofneuralnetworks.However,thereisstillnodefinitetheorytosettleitout.Astheneuralnetwork,thelargeamountofdatathatcanbeusedtoprovideinformation,butalsoincreasethedifficultiesofdealingwiththesedata[3].Greysystemtheoryisaninterdisciplinaryscientificareathatwasfirstintroducedinearly1980sbyDeng[4].Inthefieldofinformationresearch,deeporlightcolorsrepresentinformationthatisclearorambiguous,respectively.Meanwhile,blackindicatesthattheresearchershaveabsolutelynoknowledgeofsystemstructure,parametersandcharacteristics,whilewhiterepresentsthattheinformationiscompletelyclear.Colorsbetweenblackandwhiteindicatesystemsthatarenotclear,suchassocial,economicorweathersystems.Thefieldscoveredbygreytheoryincludesystemsanalysis,dataprocessing,modeling,prediction,decisionmakingandcontrol.Thegreytheorymainlyworksonsystemsanalysiswithpoor,incompleteorANewHybridGreyNeuralNetworkBasedon115GreyVerhulstModelandBPNeuralNetworkforTimeSeriesForecastingCopyright©2013MECSI.J.InformationTechnologyandComputerScience,2013,10,114-120uncertainmessages.Becausethegreysystemmodelneedslittleorigindata,hassimplecalculateprocessandhigherforecastingaccuracy,ithasbeenwidelyusedinthetimeseriespredictionofalotofresearchfields.Inthesestudiesandtheothers,greysystemtheory-basedapproachescanachievegoodperformancecharacteristicswhenappliedtoreal-timesystems,sincegreypredictorsadapttheirparameterstonewconditionsasnewoutputsbecomeavailable.Becauseofthisreason,greypredictorsaremorerobustwithrespecttonoiseandlackofmodelinginformationwhencomparedtoconventionalmethods[1,4].Agreypredictionmodelisoneofthemostimportantpartsingreysystemtheory[5],andthat,thegreyVerhulstmodelis