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ID:51508161
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页数:13页
时间:2020-03-26
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1、ONMODELLINGANDSIMULATIONUsingmathematicalmodellingandsimulationinsteadofpracticaltrial-and-errorexperimentsmaysavehumanlifes,health,property,timeetc.Modelsaredevelopedbasedoncommonandacceptedknowledgeonphysics,chemistry,computerscienceetc.Anoverallmo
2、delisoftenbuiltbycombiningsub-systemmodels.Manymodelsexplainthebehaviorofthesystemoveratimerangeusingeitheracontinuous-timetimevariableor(e.g.whenwearesatisfiedwithsamplevaluesoffunctions)adiscrete-timetimevariable.Thetimerangemayhaveafinitestarttime
3、butthisisnotnecessary.Thetimerangemayhaveafinitestoptimebutthisisnotnecessary.Inmanyapplicationsonemayatleastinprincipleconsiderfunctions(liketemperature,flowrate,pressure)whicharedistributedbothintimeandspace:forexample,aroomtemperatureisalsospatial
4、lydistributedsothatatatimeinstantwemayhaveadifferenttemperatureinthedifferentpointsofthe3D-space(3-dimensionalspace).SuchfunctionsaresometimesmodelledbyPDE(partialdifferentialequation)models.SomeassumptionsmayallowuseofPDEmodelswith2spatialcoordinate
5、sorjustwithasinglespatialcoordinate,seeÅMpp.238-239.However,mostoftenwetrytomanagecompletelywithoutusingspatialcoordinatestogete.g.ODE(OrdinaryDifferentialEquation)models.Thismaybecomepossiblebysuitableimplementationandmodellingconventions,e.g.averag
6、ingoverspace.Modelsaremostoftenatleastslightlyinaccurateduetolackofskills,impracticalassumptions,intentionalsimplifi-cationsetc.Onemustdevelopamodelwhichdescribestheessentialphenomenaaccuratelyenough,whichdoesnotdescribe/proposenon-existingphenomenaa
7、ndwhichdonotnecessarilydescribeveryweakphenomena.Oneshouldnotrelyonmodellingpracticeswhichmightrequireunnecessaryassumptionslikedifferentiabilityofcertainfunctionsetc.Firsttrialstodevelopsuchamodelmayfailandnewbettertrialsmaybeneeded…evenhereweneedfe
8、edbackcontrolormeasure&correct!OnTime-DelaymodelsInmanyapplicationswewillfacedelayphenomenawhereafunctionycanberegardedasadelayedversionofanotherfunctionu.Apossiblemodelstructureisy(t)=u(t-T),tÇtÇtstartendHereTiscalledaTimeDelay.Insomestudiesofthecou
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