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Computer simulation



Introduction

Computersimulation,alsoknownascomputersimulation,referstoacomputerprogramusedtosimulateanabstractmodelofaspecificsystem.

History

Thedevelopmentofcomputersimulationisinseparablefromtherapiddevelopmentofthecomputeritself.Itsfirstlarge-scaledevelopmentwasanimportantpartofthefamousManhattanProject.IntheSecondWorldWar,inordertosimulatetheprocessofanuclearexplosion,peopleappliedtheMonteCarlomethodtosimulatewith12hard-ballmodels.Computersimulationwasoriginallyusedasasupplementtootheraspectsofresearch,butwhenpeoplediscovereditsimportance,itwaswidelyusedasaseparatesubject.

Types

Usuallydividedintothefollowingcategories:

  • Discretesimulation

  • Analogoussimulation

  • Simulationbasedonprobeelement

  • Simulationofrandomprocessordeterministicmode

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Advantagesanddisadvantagesofcomputersimulation

Intheapplicationofcomputersimulationforriskanalysis,itshouldbepointedoutattheendthatthismethodrequiresinvestmentexpenditure,unitsales,andproductprices.,Theprobabilitydistributionofmanyvariablessuchasthepriceofinputfactors,thelifeofassets,etc.,andaconsiderableamountofprogrammingcostsandcomputeroperatingcostsneedtobespent.Therefore,full-scalesimulationisgenerallynotapplicable(exceptforlarge-scaleandexpensiveplanssuchasexpansionoflargefactoriesorproductionofnewproducts).Intheseexceptionalcases,whencompaniesaredecidingwhethertoimplementalarge-scaleplanthatwillcostmillionsofdollars,computersimulationscanhelpin-depthevaluationoftheadvantagesanddisadvantagesofthevariousalternatives.

Developmentprocess

Whenpeopledesignandconstructcomplexsystems,orstudythelongevolutionaryprocessinnature,humansociety,andthingsthatarenoteasytorepeatexperiments,ifyouTocarryouttheexperiment,consideringthefactorsoftime,manpower,materialresources,etc.,itwillbeexpensive,orevenimpossible.Therefore,amodelneedstobemanufacturedtoperformvarioustests.

Inordertosimulatethesystem,wemustfirstdetermineorexpressthesystemtobestudied.Mathematicalmodelscanbeusedtodetermineasystemmoreconvenientlyandfullyreflecttheexistingknowledgeofthesystemorhypothesesthatneedtobeverified,butitlacksintuitionandisnotconvenientforexperimentation.Onthebasisofthemathematicalmodel,aphysicalmodelcanbefurthermade,whichreflectsthenatureoftherealsystemrequiredbypeople,butdoesnothavetobecompletelyconsistentwiththerealsystemintermsofformandscale.Itismoreintuitiveandcredibletotestwithaphysicalmodel,butitisstillnoteconomicalandconvenient.

Aftertheemergenceofprogrammabledigitalcomputers,becauseofitsstrongmathematicaloperationsanddataprocessingcapabilities,mathematicalmodelscanbecompiledintocomputerprogramstoprovidenewanduniversaltestmethods.Computerscanalsobeusedtosimulateactivitiesrelatedtooperationsresearch,forexample,tosimulatethestepstakenbythetwopartiesparticipatinginthecompetitionandthefinaloutcome.Itsapplicationfieldsquicklyexpandedtovarioustypesofsystems,fromlarge-scalesystemstosmall-scalesystems.Themathematicaldescriptionofthesesystemsisoftenverycomplicated,anditisverydifficulttogiveacompleteanalyticalsolutionoranaccuratenumericalsolution.Throughtrialanderror,computersimulationhelpspeopleunderstandtheperformanceofthesystem,testexpectedhypotheses,andperformsystemanalysis,design,predictionorevaluation.Itcanalsoprovideaveryrealisticenvironmenttotrainandtrainpersonnel.Computersimulationhasbecomeapowerfultoolinmanyfieldssuchasengineeringresearchanddevelopment,naturalscienceresearch,economicandsocialproblemresearch,teachingandtrainingactivities,militaryresearch,organizationandmanagement.

Basicmethod

Computersimulationgenerallyrequiresmanystepsfromformingaproblemtoconfirmingthefinalmodel.①Formproblemsandclarifythepurposeandrequirementsofthesimulation.②Collectandprocesssystem-relateddataasmuchaspossible.③Formamathematicalmodel,findoutthevariouscomponentsthatmakeupthesystem,anddescribetherelevantvariables(generallyincludinginputvariables,statevariables,andoutputvariables)orparametersoftheirstateateachmoment;determinetherulesofinteractionandinfluencebetweenthecomponents,Thatis,thefunctionalrelationshipbetweenthesedescriptionvariables.Whenselectingparametersandvariables,itisalsonecessarytoconsiderwhethertheycanbeidentifiedorsolved,andwhetherthemodelissuitablefortestingbasedonthedataoftherealsystem.④Determineorestimatetheparametersinthemodelbasedonthecollecteddata,andselecttheinitialstateofthemodel.⑤Designtheflowchartoflogicorinformationuntilthecomputerprogramiscompiled.⑥Programverification,checkingtheconsistencybetweentheprogramandthemathematicalmodel,andthereasonablenessoftheinput.⑦Carryoutsimulationtest,executetheprogramonthecomputerforthegiveninput.⑧Analyzetheresultdata,collectandsortoutthetestresultsandmakeexplanations.Ifnecessary,theinputamountorpartofthemodelstructurecanbechanged,andtheexperimentcanbeperformedagain.⑨Modelconfirmation,tochecktheconsistencybetweentheresultsobtainedbythemodelandtheperformancedataoftherealsystem.Thisisakeyissuerelatedtotheeffectivenessofcomputersimulation.Itdependsontheleveloftestingtherealsystemitself,whethersufficientobservationdatacanbeobtained,andthecriteriaforjudgingconsistency.Theeffectivelevelofthemodelcanbedividedinto:effectivereproduction,thatis,themodelcanreproducetheperformanceoftherealsystem;effectiveprediction,thatis,themodelcaneffectivelypredictthefutureperformanceoftherealsystem;effective,thatis,themodelcanreflecttheinterioroftherealsystemStructure.Sincethesystemitselfchangeswithtimeorisrandom,thecomparisonbetweenrealsystemdataandmodeltestresultsoftenrequirestimeseriesanalysismethodsorstatisticalanalysismethods.

Simulationofthediscrete-timemodel

Thetimeinthediscrete-timemodelisexpressedasanintegersequence(representinganintegermultipleofacertaintimeunit),andonlythestatechangesofthesystematthesemomentsareconsidered.Atypicalsimulationprocedureofthismodelincludesthefollowingsteps:①SettheinitialvalueofthesimulationtimeTtot0.②Settheinitialvalueofthestatevariable.③Aftergivingthevalueoftheinputvariableatthecurrentsimulationtime,accordingtothestatetransitionfunctioninthemodel,determinethenexttimeT=t+hThevalueofthestatevariable.Thendeterminethevalueoftheoutputvariableatthatmomentaccordingtotheoutputfunctioninthemodel.④AdvancethesimulationtimeTbyoneunittimeh.⑤CheckwhetherthesimulationtimeThasreachedthepredeterminedendtime.Ifithasreached,stop;otherwise,gotostep③.

Simulationofthediscreteeventmodel

Inthediscreteeventmodel,thestatechangesofthesystemonlyappearatdiscretemoments,whicharecalleddiscreteevents.Takingthequeuingsystemasanexample,thebasicstepsandmethodsforestablishingthissimulationmodelare:①Determinealltherelevant"entities"andtheirattributesincludedinthesystem,all"events"thatchangethestateofthesystemandtheircausesandconsequences.Entitiesarethecomponentpartsofthesystem,andtheattributesofeachentityarerepresentedbynumericalvalues​​representingitsproperties,whichconstitutethestateofthesystem.Themostbasicentitiesinthequeuingsystemareacertainnumberof"servicestations"and"customers"whorequireservices.Theirattributesarethe"servicerate"ofthe"servicestation"andtheservicepriorityofthe"customer",andreachtheservicesystem.Themomenttowait.Basic"events"include:newentitiesenterthesystemorexistingentitiesleavethesystem,entityattributeschange,andscheduledschedulechanges.②Determinethemethodofsimulatingthepassageoftime.Ifthetimeisdividedintoequalintervalsandthesystemisexaminedinorderwhetheraneventoccursatthesemoments,itiscalledthefixedtimeintervalmethod;ifthelengthofeachtimelapseisbasedonthemomentwhenthenexteventoccurs,itiscalledthevariabletimeintervalmethodor"NextEvent"method.③Sincetheoccurrenceofeventsinthesystemisoftenrandomandobeysacertainprobabilitydistribution,itisnecessarytogeneraterandomnumbersofthesedistributionsonthecomputer.④Inordertorecordthestateofthesystemflexiblyandeffectively,scheduleevents,accumulaterelevantperformancedataandformreports,saveandautomaticallymanagefutureeventfiles,itisveryappropriatetousedatabasetechnologyinprogramdesign.

Continuoussystemsimulation

Asystemwhosestatechangescontinuouslyovertimeiscalledacontinuoussystem,andtherateofstatechangesatisfiesacertaindifferentialequation.Theestablishmentofthecorrespondingsimulationmodelonthecomputerdependsontheeffectivenumericalmethodofsolvingthedifferentialequation,anditiscompiledintoastandardsubroutinesothatvariousequationorders,coefficients,initialvalueconditionsorboundaryvalueconditionscanbeused.Thesimulationofsystemsinvolvingfeedbackandcontrolisatypicalexampleofthistype.

Simulationlanguage

Assemblylanguageandgeneralprogramminglanguages​​(suchasFORTRAN,ALGOL,etc.)canbeusedwhencompilingsimulationprograms.Varioussimulationlanguages​​canalsobeused.Computersimulationlanguageisahigh-levelprogramminglanguagethatdescribesthesystemmodel.Itprovidesmodulesthatrepresentmanybasicunits,components,andschedulingoperationsinthesystemmodel.Theusercanuseittodeterminethebasicstructureofthemodelmoreconveniently,andonlyneedtoaddsomeauxiliaryprogramstocompileasimulationprogram.

Thesimulationlanguageisgenerallyestablishedonthebasisofothergeneral-purposeprogramminglanguages.Itneedsitsowncompilertopre-compile,convertthesimulationlanguageprogramintoageneral-purposeprogramminglanguageprogram,andthenundergoanothercompilationandconversion.Intoacomputerexecutableprogram.Thesimulationlanguagecanreducetheuser'sprogramwork,butitalsoinevitablybringssomerestrictionsandconsumesmorememoryandcomputingtime.

Simulationlanguages​​canbedividedintodiscreteeventsimulationlanguages​​(suchasGPSSanditsvariousmodifications,SIMCRIPT,GASD,CSL,SIMULA,etc.)andcontinuoussystemsimulationlanguages​​(suchasDARE,ACSL,CSS,CSSL,etc.))Twotypes.Therearealsodedicatedsimulationlanguages​​forvariousapplicationfields.

Computersimulationiscloselyrelatedtothedevelopmentofcomputerhardwareandsoftwaretechnology.Inordertofacilitatetheestablishmentofthemodelandtheeffectivenessofthemodel,peopletrytomakethesimulationmodelhaveacertaindegreeofsimilaritywiththerealsystemintimeandspace.Inthesimulationprocess,Ihopetobeabletoeasilychangetheparametersandevenchangethestructureofthemodel,andtooutputdataandchartsatanytimethroughkeyboardcommands.Therefore,computersimulationrequiresthecomputertohavestrongparallelprocessingcapabilities,highcomputingspeed,human-computerinteractioncapabilitiesandeasy-to-usesimulationlanguages.

Application

Thescaleofcomputersimulationcanbeeithermacroscopicormicroscopic.Onthemacroscale,theexperimentaldatabasecanbeusedtopredicttheprocessflow,operatingconditionsandsystemproperties,calculatethemechanicsandprocessingpropertiesofmaterials,andisgenerallyusedinchemicalprocesssimulation,mechanicalmanufacturingandotherfields.Onthemicroscopicscale,thestructureandpropertiesofmicroscopicparticlesplayanimportantrole,andaregenerallyusedforreactionmechanismresearchandmacroscopicpropertysimulation.

Example

Inordertoillustratethismethod,letusstudytheconstructionofatextilefactory.Theconstructioncostoftheplanthasnotbeenaccuratelycalculated,anditisestimatedtobeabout150millionU.S.dollars.Iftherearenodifficultiesintheconstructionprocess,thecostmaybeaslowas125millionU.S.dollars.Butitisalsopossiblethatduetovariousunforeseenevents-strikes,unexpectedpriceincreasesofrawmaterials,technicalproblems,etc.-theinvestmentexpenditurescanreachashighas$225million.

Thenewfactorywillbeabletooperateformanyyears,anditsproductsalesincomedependsonthepopulationandincomegrowthoftheregion,thedegreeofcompetitioninthesameindustry,theresearchanddevelopmentofsyntheticfibers,andtheimportquotaofforeigntextiles.Theoperatingcostwilldependontherisingandfallingtrendsofproductionefficiency,rawmaterialsandwagelevels,andsoon.Sincebothsalesrevenueandoperatingcostsareuncertainfactors,theannualprofitisalsouncertain.

Iftheprobabilitydistributioncanbecalculatedforeachmajorcostfactorandrevenuefactor,acomputerprogramcanbeestablishedtosimulatepossibleevents.Thecomputeractuallytakesanyvaluefromeachrelevantdistributionandcombinesitwithothervalues​​selectedfromotherdistributionstoprovideanestimatedprofitandthenetpresentvalueoftheinvestment,thatis,theprofitrate.Thisspecificamountofprofitandrateofprofitareonlysuitableforthecombinationofspecificvalues​​selectedinthisexperiment.Thecomputercontinuestoselectthevalues​​oftheothergroups,anditispossibletocalculateotherprofitamountsandprofitratesforhundredsoftrials.Countandsavethenumberoftimesdifferentprofitratesarecalculated.Afterthecomputerisrunning,itcanbedrawnintoafrequencydistributionaccordingtothenumberoftimesthedifferentprofitratesappear.

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