电气工程及其自动化毕业设计英语翻译.docx

电气工程及其自动化毕业设计英语翻译.docx

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电气工程及其自动化毕业设计英语翻译

郑州航空工业管理学院

英文翻译

2011届电气工程及其自动化专业0706073班级

题目遗传算法在非线性模型中的应用

姓名学号070607313

指导教师黄文力职称副教授

二О一一年三月三十日

英语原文：

ApplicationofGeneticProgrammingtoNonlinearModeling

Introduction

Identificationofnonlinearmodelswhicharebasedinpartatleastontheunderlyingphysicsoftherealsystempresentsmanyproblemssinceboththestructureandparametersofthemodelmayneedtobedetermined.Manymethodsexistfortheestimationofparametersfrommeasuresresponsedatabutstructuralidentificationismoredifficult.Oftenatrialanderrorapproachinvolvingacombinationofexpertknowledgeandexperimentalinvestigationisadoptedtochoosebetweenanumberofcandidatemodels.Possiblestructuresarededucedfromengineeringknowledgeofthesystemandtheparametersofthesemodelsareestimatedfromavailableexperimentaldata.Thisprocedureistimeconsumingandsub-optimal.Automationofthisprocesswouldmeanthatamuchlargerrangeofpotentialmodelstructurecouldbeinvestigatedmorequickly.

Geneticprogramming（GP）isanoptimizationmethodwhichcanbeusedtooptimizethenonlinearstructureofadynamicsystembyautomaticallyselectingmodelstructureelementsfromadatabaseandcombiningthemoptimallytoformacompletemathematicalmodel.Geneticprogrammingworksbyemulatingnaturalevolutiontogenerateamodelstructurethatmaximizes（orminimizes）someobjectivefunctioninvolvinganappropriatemeasureofthelevelofagreementbetweenthemodelandsystemresponse.Apopulationofmodelstructuresevolvesthroughmanygenerationstowardsasolutionusingcertainevolutionaryoperatorsanda“survival-of-the-fittest”selectionscheme.Theparametersofthesemodelsmaybeestimatedinaseparateandmoreconventionalphaseofthecompleteidentificationprocess.

Application

Geneticprogrammingisanestablishedtechniquewhichhasbeenappliedtoseveralnonlinearmodelingtasksincludingthedevelopmentofsignalprocessingalgorithmsandtheidentificationofchemicalprocesses.Intheidentificationofcontinuoustimesystemmodels,theapplicationofablockdiagramorientedsimulationapproachtoGPoptimizationisdiscussedbyMarenbach,BettenhausenandGray,andtheissuesinvolvedintheapplicationofGPtononlinearsystemidentificationarediscussedinGray’sanotherpaper.Inthispaper,Geneticprogrammingisappliedtotheidentificationofmodelstructuresfromexperimentaldata.Thesystemsunderinvestigationaretoberepresentedasnonlineartimedomaincontinuousdynamicmodels.

ThemodelstructureevolvesastheGPalgorithmminimizessomeobjectivefunctioninvolvinganappropriatemeasureofthelevelofagreementbetweenthemodelandsystemresponses.Oneexamplesis

（1）

Where

istheerrorbetweenmodeloutputandexperimentaldataforeachofNdatapoints.TheGPalgorithmconstructsandreconstructsmodelstructuresfromthefunctionlibrary.SimplexandsimulatedannealingmethodandthefitnessofthatmodelisevaluatedusingafitnessfunctionsuchasthatinEq.

（1）.ThegeneralfitnessofthepopulationimprovesuntiltheGPeventuallyconvergestoamodeldescriptionofthesystem.

TheGeneticprogrammingalgorithm

Forthisresearch,asteady-stateGenetic-programmingalgorithmwasused.Ateachgeneration,twoparentsareselectedfromthepopulationandtheoffspringresultingfromtheircrossoveroperationreplaceanexistingmemberofthesamepopulation.Thenumberofcrossoveroperationsisequaltothesizeofthepopulationi.e.thecrossoverrateis100℅.Thecrossoveralgorithmusedwasasubtreecrossoverwithalimitonthedepthoftheresultingtree.

Geneticprogrammingparameterssuchasmutationrateandpopulationsizevariedaccordingtotheapplication.Moredifficultproblemswheretheexpectedmodelstructureiscomplexorwherethedataarenoisygenerallyrequirelargerpopulationsizes.Mutationratedidnotappeartohaveasignificanteffectforthesystemsinvestigatedduringthisresearch.Typically,avalueofabout2℅waschosen.

Thefunctionlibraryvariedaccordingtoapplicationrateandwhattypeofnonlinearitymightbeexpectedinthesystembeingidentified.Acoreoflinearblockswasalwaysavailable.Itwasfoundthatspecificnonlinearitysuchaslook-uptableswhichrepresentedaphysicalphenomenonwouldonlybeselectedbytheGeneticProgrammingalgorithmifthatnonlinearityactuallyexistedinthedynamicsystem.

Thisallowsthesystemtobetestedforspecificnonlinearities.

Programmingmodelstructureidentification

EachmemberoftheGeneticProgrammingpopulationrepresentsacandidatemodelforthesystem.Itisnecessarytoevaluateeachmodelandassigntoitsomefitnessvalue.Eachcandidateisintegratedusinganumericalintegrationroutinetoproduceatimeresponse.Thissimulationtimeresponseiscomparedwithexperimentaldatatogiveafitnessvalueforthatmodel.Asumofsquarederrorfunction（Eq.

（1））isusedinalltheworkdescribedinthispaper,althoughmanyotherfitnessfunctionscouldbeused.

Thesimulationroutinemustberobust.Inevitably,someofthecandidatemodelswillbeunstableandtherefore,thesimulationprogrammustprotectagainstoverflowerror.Also,allsystemmustreturnafitnessvalueiftheGPalgorithmistoworkproperlyevenifthosesystemsareunstable.

Parameterestimation

ManyofthenodesoftheGPtreescontainnumericalparameters.Thesecouldbethecoefficientsofthetransferfunctions,againvalueorinthecaseofatimedelay,thedelayitself.Itisnecessarytoidentifythenumericalparametersofeachnonlinearmodelbeforeevaluatingitsfitness.Themodelsarerandomlygeneratedandcanthereforecontainlinearlydependentparametersandparameterswhichhavenoeffectontheoutput.Becauseofthis,gradientbasedmethodscannotbeused.GeneticProgrammingcanbeusedtoidentifynumericalparametersbutitislessefficientthanothermethods.TheapproachchoseninvolvesacombinationoftheNelder-Simplexandsimulatedannealingmethods.Simulatedannealingoptimizesbyamethodwhichisanalogoustothecoolingprocessofametal.Asametalcools,theatomsorganizethemselvesintoanorderedminimumenergystructure.Theamountofvibrationormovementintheatomsisdependentontemperature.Asthetemperaturedecreases,themovement,thoughstillrandom,becomesmallerinamplitudeandaslongasthetemperaturedecreasesslowlyenough,theatomsorderthemselvesslowlyenough,theatomsorderthemselvesintotheminimumenergystructure.Insimulatedannealing,theparametersstartoffatsomerandomvalueandtheyareallowedtochangetheirvalueswithinthesearchspacebyanamountrelatedtoaquantitydefinedassystem‘temperature’.Ifaparameterchangeimprovesoverallfitness,itisaccepted,ifitreducesfitnessitisacceptedwithacertainprobability.Thetemperaturedecreasesaccordingtosomepredetermined‘cooling’scheduleandtheparametervaluesshouldconvergetosomesolutionasthetemperaturedrops.Simulatedannealinghasprovedparticularlyeffectivewhencombineswithothernumericaloptimizationtechniques.

OnesuchcombinationissimulatedannealingwithNelder-simplexisan（n+1）dimensionalshapewherenisthenumberofparameters.Thissimplesexploresthesearchspaceslowlybychangingitsshapearoundtheoptimumsolution.Thesimulatedannealingaddsarandomcomponentandthetemperatureschedulingtothesimplexalgorithmthusimprovingtherobustnessofthemethod.

Thishasbeenfoundtobearobustandreasonablyefficientnumericaloptimizationalgorithm.Theparameterestimationphasecanalsobeusedtoidentifyothernumericalparametersinpartofthemodelwherethestructureisknownbutwherethereareuncertaintiesaboutparametervalues.

RepresentationofaGPcandidatemodel

Nonlineartimedomaincontinuousdynamicmodelscantakeanumberofdifferentforms.Twocommonrepresentationsinvolvesetsofdifferentialequationsorblockdiagrams.Boththeseformsofmodelarewellknownandrelativelyeasytosimulate.Eachhasadvantagesanddisadvantagesforsimulation,visualizationandimplementationinaGeneticProgrammingalgorithm.Blockdiagramandequationbasedrepresentationsareconsideredinthispaperalongwithathirdhybridrepresentationincorporatingintegralanddifferentialoperatorsintoanequationbasedrepresentation.

Choiceofexperimentaldataset——experimentaldesign

Theidentificationofnonlinearsystemspresentsparticularproblemsregardingexperimentaldesign.Thesystemmustbeexcitedacrossthefrequencyrangeofinterestaswithalinearsystem,butitmustalsocovertherangeofanynonlinearitiesinthesystem.Thiscouldmeanensuringthattheinputshapeissufficientlyvariedtoexcitedifferentmodesofthesystemandthatthedatacoverstheoperationalrangeofthesystemstatespace.

Alargetrainingdatasetwillberequiredtoidentifyanaccuratemodel.Howeverthesimulationtimewillbeproportionaltothenumberofdatapoints,sooptimizationtimemustbebalancedagainstquantityofdata.ArecommendationonhowtoselectefficientstepandPRBSsignalstocovertheentirefrequencyrageofinterestmaybefoundinGodfreyandLjung’stexts.

Modelvalidation

Animportantpartofanymodelingprocedureismodelvalidation.Thenewmodelstructuremustbevalidatedwithadifferentdatasetfromthatusedfortheoptimization.Therearemanytechniquesforvalidationofnonlinearmodels,thesimplestofwhichisanaloguematchingwherethetimeresponseofthemodeliscomparedwithavailableresponsedatafromtherealsystem.ThemodelvalidationresultscanbeusedtorefinetheGeneticProgrammi