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1、Title:ImprovementofGM(1J)ModelanditsApplicationMajor:AppliedMathematicsPostgraduate:YangYuedongMentor:DingWeiABSTRACTThroughdevelopmentofmorethan30years,thegreysystemtheoryhasbeenacceptedandrecognizedastheacademiccirclesathomeandabroad,hashadaprofoundimpactonthedevelopmentofsystemsscience.Ithasthea
2、dvantagesinmanyaspects,suchasthesmallrequiredsamplesize,simpleoperation,highpredictionaccuracyofshorttermandsoon.Ithasbeenwidelyusedinmanyfieldsofindustry,agriculture,transportationandaerospace,manypracticallydifficultproblemscanbesolved,showingtheextremelybroadprospectofapplication.However,asanewa
3、nduniquetheoreticalsystem,itneedstobefurtherimproved.Throughfurtherimprovementandoptimizationofthegreypredictionmodeltoimprovethepredictionaccuracyandexpanditsscopeofapplication,sothatitcanfurtherplaytheexcellentcharacteristicsandapplicationpotential.Thishasfar-reachingsignificance.Thispaperimprove
4、s,basedonanalysisofthesefactorsthatinfluencetheprecisionofGM(1，1),intheoriginaldatasequenceprocessing,Selectionofthebackgroundvalue,theinitialvalue,residualsequencetreatmentoftheGM(1,1),Themaincontentsareasfollows:1.FortheequalintervalGM(1,1),inthispaper,thethreemainfactors：thesmoothness,theclassra
5、tiodeviation,theconcaveconvexpropertyofthedatasequencearetakenintoaccount,discussingtheiradvantagesanddisadvantagesofthepower,exponential,logarithmicfunctionandtheircompoundfunctioninimprovingthepredictionaccuracyofmodel.Dosomeinnovationinthefollowingaspects(1)Maximumpointsofconcavesubsequenceisint
6、roducedtothestudyoftheconcaveconvexpropertyofdatasequence,expandthescopeoftheconcaveconvexpropertyapplicationofdatasequencefortheequalintervalGM(1,1),soithasbettermaneuverability.(2)Severalfactors,associatedwiththemodelaccuracy,areconsideredcomprehensively,thesmoothness,theclassratiodeviation,theco
7、ncaveconvexpropertyofdatasequenceovercometheinstabilityofthesolutionbroughtbyillthemoststudiesonlyconsideringafewfactors,improvethestabilityofthemodel.Theprocessingstepsandapplicationexamplesaregiven.Thefor
