基于BP神经网络优化建立GM(1-1)模型-(IJCNIS-V4-N1-3)

I.J.ComputerNetworkandInformationSecurity,2012,1,24-30PublishedOnlineFebruary2012inMECS()DOI:10.5815/ijcnis.2012.01.03OptimizationModelingforGM(1,1)ModelBasedonBPNeuralNetworkDeqiangZhouSchoolofInformationandMathematics,YangtzeUniversity,Jingzhou,ChinaEmail:[e-mail]—Ingreytheory,GM(1,1)modeliswidelydiscussedandstudied.ThepurposeofGM(1,1)modelistoworkonsystemforecastingwithpoor,incompleteoruncertainmessages.TheparametersestimationisanimportantfactorfortheGM(1,1)model,thusimprovingestimationmethodtoenhancethemodelforecastingaccuracybecomesahottopicofresearchers.ThisstudyproposesanoptimizationmethodforGM(1,1)modelbasedonBPneuralnetwork.TheGM(1,1)modelismappedtoaBPneuralnetwork,thecorrespondingrelationbetweenGM(1,1)modelparametersandBPnetworkweightsisestablished,theGM(1,1)modelparametersestimationproblemistransformedintoanoptimizationproblemfortheweightsofneuralnetwork.TheBPneuralnetworkistrainedbyuseofBPalgorithm,whentheBPnetworkconvergence,optimizationmodelparameterscanbeextracted,andtheoptimizationmodelingforGM(1,1)ModelbasedonBPalgorithmcanbealsorealized.Theexperimentresultsshowthatthemethodisfeasibleandeffective,theprecisionishigherthanthetraditionalmethodandotheroptimizationmodelingmethods.IndexTerms—Greysystem;GM(1,1)model;BPneuralnetwork;Datafitting;Optimizationmodeling1.IntroductionGreysystemtheoryisaninterdisciplinaryscientificareathatwasfirstintroducedinearly1980sbyDeng[1,2].Sincethen,thetheoryhasbecomequitepopularwithitsabilitytodealwiththesystemsthathavepartiallyunknownparameters[3-5].Inthefieldofinformationresearch,deeporlightcolorsrepresentinformationthatisclearorambiguous,respectively.Meanwhile,blackindicatesthattheresearchershaveabsolutelynoknowledgeofsystemstructure,parametersandcharacteristics,whilewhiterepresentsthattheinformationiscompletelyclear.Colorsbetweenblackandwhiteindicatesystemsthatarenotclear,suchassocial,economicorweathersystems.Thefieldscoveredbygreytheoryincludesystemsanalysis,dataprocessing,modeling,prediction,decisionmakingandcontrol.Thegreytheorymainlyworksonsystemsanalysiswithpoor,incompleteoruncertainmessages.Becausethegreysystemmodelneedslittleorigindata,hassimplecalculateprocessandhigherforecastingaccuracy,ithasbeenwidelyusedinthepredictionofalotofresearchfields.Agreypredictionmodelisoneofthemostimportantpartsingreysystemtheory,andthat,theGM(1,1)modelisthecoreofgreyprediction[6].ThepurposeofGM(1,1)modelistoworkonsystemforecastingwithpoor,incompleteoruncertainmessages.TheGM(1,1)hasmoreadvantageswithcontrasttothosetraditionalpredictionways,becauseitdoesnotneedtoknowwhetherthepredictionvariablesobeynormaldistributionornot,doesnotrequiretoomuchstatisticsample[1].However,manyscholarsfindthatCopyright©2012MECSI.J.ComputerNetworkandInformationSecurity,2012,1,24-30OptimizationModelingforGM(1,1)ModelBasedonBPNeuralNetwork25therearemanytheorydefectsintraditionalGM(1,1)model[7],anddoalotofresearchesforthis.TheseresearchesalmosttaketraditionalGM(1,1)modelingstepsandthoughts,thustherearesomefollowingdefects,first,theseimprovedmodelsneedtofacethereasonableselectionofbackgroundvalue.Ontheotherhand,theparametersestimationisanimportantfactorfortheGM(1,1)model,thusimprovingestimationmethodtoenhancethemodelforecastingaccuracybecomesahottopicofresearchers.Inaboveimprovedmodels,theparametersestimationtheoreticalbasisoftransformationfromdiscreteformtocontinuousformalsocannotavoidthejumpingerrorsfromthedifferenceequationtodifferentialequation.Generally,fromtheevaluationcriteriaofthemodelfitting,whensolvingGM(1,1)model,weshoulddirectlytakeminimizingtheerroroftheprimitivevalueandthepredictedvalueandtheactualvalueasthecriterion[9].Accordingtotheabovedescribing,weneedfindanewmethodtoimprovetheprecisionofGM(1,1)model.Fromthedatafitting'sviewpoint,thisstudyusesBPneuralnetworkmodeltoimprovetheprecisionofGM(1,1)model.Thegreysystem'sprimitivediscretedataisfittedbyacontinuousmodelwhichhasthesameformwithGM(1,1)model'stimeresponsetype,themodelparametersaretrainedandoptimisedbymeansofBPalgorithm,thenthedirectandoptimizationmodelingforGM(1,1)modelisrealized.Theremainderofthispaperisorganizedasfollows:inSection2,therelationshipsbetweenGM(1,1)modelparametersandBPnetworkweightsisestablished,whereBPnetworkalgorithmisusedtooptimiseGM(1,1)modelparameters.TheexperimentresultsanddiscussionsarepresentedinSection3.Conclusionandfutureworkaregiveninthefinalsection.2.GM(1,1)modelandBPneuralnetworkmappingrelationships2.1GM(1,1)modelGM(1,1)typeofgreymodelisthemostwidelyusedintheliterature,pronouncedas‘‘greymodelfirstorderonevariable’’.Thismodelisatimeseriesforecastingmodel.ThedifferentialequationsoftheGM(1,1)modelhavetime-varyingcoefficients.Inotherwords,themodelisrenewedasthenewdatabecomeavailabletothepredictionmodel.TheGM(1,1)modelconstructingprocessisdescribedbelow:Considerasingleinputandsingleoutputsystem.Assumethatthetimesequence(0)Xrepresentstheoutputsofthesystem:(0)(0)(0)(0)((1),(2),,()),Xxxxnn4=⋅⋅⋅≥(1)where(0)Xisanon-negativesequenceandnisthesamplesizeofthedata.Whenthis