A goal-based ...em-of-systems_FENG Yimin.pdf filename-=utf-8''A goal-based ...em-of-systems_FENG Yimin.pdf

A goal-based approach for modeling and simulation ofdifferent types of system-of-systemsFENGYimin1,ZHOUChenchu2,ZOUQiang1,*,LIUYusheng1,LYUJiyuan3,and WUXinfeng31.StateKeyLabofCAD&CG,ZhejiangUniversity,Hangzhou310027,China;2.XianAerospacePropulsionInstitute,Xian710100,China;3.ChinaAstronautResearchandTrainningCenter,Beijing100094,ChinaAbstract:A system of systems(SoS)composes a set of inde-pendent constituent systems(CSs),where the degree of autho-rity to control the independence of CSs varies,depending on dif-ferent SoS types.Key researchers describe four SoS types withdescending levels of central authority:directed,acknowledged,collaborative and virtual.Although the definitions have been re-cognized in SoS engineering,what is challenging is the difficultyof translating these definitions into models and simulation envi-ronments.Thus,we provide a goal-based method including amathematical baseline to translate these definitions into moreeffective agent-based modeling and simulations.First,we con-struct the theoretical models of CS and SoS.Based on the theo-retical models,we analyze the degree of authority influenced bySoS characteristics.Next,we propose a definition of SoS typesby quantitatively explaining the degree of authority.Finally,werecognize the differences between acknowledged SoS and col-laborative SoS using a migrating waterfowl flock by an agent-based model (ABM)simulation.This paper contributes to theSoS body of knowledge by increasing our understanding of thedegree of authority in an SoS,so we may identify suitable SoStypes to achieve SoS goals by modeling and simulation.Keywords:simulation,systems agent-based modeling,systems-of-systems(SoS),systems thinking.DOI:10.23919/JSEE.2023.0000841.IntroductionA system of systems(SoS)comprises a collection ofindependentsystemsthatinteroperatetogethertoachieveoverarchingcapabilities1,2.ApplicationsofSoScanbefoundindiversedomains,suchasmilitary1,aerospace3,health care 4,transportation 5,and energy 6,amongothers.Comparedtothetraditionalsysteminthefieldofsystemsengineering(SE),thedevelopmentofanSoSinthefieldofSoSengineering(SoSE)ischallengedbyincreasingcomplexityresultsfromtheindependenceofconstituentsystems(CSs)7,8.Thechallengepromptstheneedfortwoaspectsofefforts:analyzingtheindepen-denceofCSsandmodelingmethodsforSoS.Ontheonehand,aseachCShasmanagerialandoperationalinde-pendence9,10,anSoScanbedesignedbyconsideringfourtypes(archetype,category,classification,typology)based on the degree of authority(managerial control)11.UnderstandingSoStypesisnecessarytoprovideaframeworkforunderstandingSoS1214andsupportsthe development of SoS 1517.On the other hand,model-based systems engineering(MBSE),whichfocusestheSEprocessonwell-constructedmodelsthatcapturetheessenceofthesystem,canhelpaddressthecomplexityofSoS18,19.Therehasbeenconsiderableinterest in using model-based techniques for SoSE20,21.For effective model-based SoS engineering(MBSoSE),Nielsenetal.8identifieddifferentdimen-sions,oneofwhichisthecategoryofSoS,forposition-inganMBSoSEapproach.TheypointouttheneedforSoStypestoguidethedevelopmentofanSoSbecausethe degree of managerial control determines the adapt-abilityandcollaborationofeachCSintermsofrequire-ments,interfaces,dataformats,andtechnologies8.Inaword,theneedforunderstandingandmodelingSoStypestoenrichSoStheoryandSoSpracticeisapparent.How-ever,theproblemishowtoprovideawell-defineddefini-tionthatcanbetranslatedintomoreeffectivemodelsandsimulationsofSoSs.AbasicunderstandingoftheSoStypescanbeobtaineddirectlythroughthemostpopulardefinitionofSoStypesManuscriptreceivedMarch15,2022.*Correspondingauthor.ThisworkwassupportedbytheNationalKeyResearchandDevelop-mentProgramofChina(61873236),theNaturalScienceFoundationofZhejiang Province(LZ21F020003;LY18F030001),and the CivilAerospacePre-researchProject(D020101).Journal of Systems Engineering and ElectronicsVol.34,No.3,June 2023,pp.627 64010,11.Thedefinitionprovidesatext-basedinterpreta-tionofthedegreeofSoSauthority.However,becausethedefinitionlacksaquantitativejudgmentbasis,itcanbechallenging to determine the SoS type when facing apracticalexampleofanSoS22.Therefore,arigoroustheoretical foundation with unequivocal concepts isneededtoavoidvaguenessandsubjectivity22.AnotherkindofunderstandingoftheSoStypescanbeobtained indirectly through the well-defined theory ofSoScharacteristicsbecausetheSoStypeisthefurtherstandardizationbasedonSoScharacteristics22.ThereisabroadagreementonSoScharacteristicsthatcanhelprecognizeorrealizeanSoS23.Subsequently,onecanthenproposeamathematicalframeworktotranslatesomeconceptsofSoScharacteristicsintoanunambiguoustheo-reticalmodelbasedonsettheory,aimingtorigorouslydefine the SoS characteristics 2426.However,theexistingdefinitionsofSoStypesusuallyrelyheavilyonthetext-baseddescriptionwithouttakingfulladvantageofthetheoreticalmodelsofSoScharacteristics.Whatismissing is a further explanation of the relationshipbetweenSoScharacteristicsandSoStypes;thisconnotesthatmoresignificanteffortmayberequiredtoexploretheclose relations between SoS characteristics and SoStypes.As mentioned previously,the existing definition ofSoStypesisbasedonthedegreeofauthority10,11,andSoSdevelopmentrequirestheguidanceofSoStypes8.SoS development prioritizes achieving SoS goals andthensatisfiesCSgoalsasmuchaspossible27.Thus,wearguethattheultimatepurposeofSoSauthorityistoachieveSoSgoals,andthereisarelationshipbetweenthedegree of authority and both SoS goals and CS goals.Usinggoalsbringsseveraladvantagescomparedtousingcharacteristics.First,SoSgoalsaregenerallyexplicitandconvenienttodetectexceptinavirtualSoSwhereSoSgoals are implicit 13.In particular,when there is noexplicit central management authority,the degree ofauthority is sometimes implicit and difficult to detect,such as in the example of swarm robots 28.Second,goalscanbemeasuredquantitativelyandobjectivelybythewell-definedgoalstatement29,30.Next,goalsareessentialelementsinSoSmodeling,suchasrequirementmodeling 31 and mission-based approaches 32,33,whichmeansthatgoalscanserveasabridgebetweenSoS theory and SoS practice.Therefore,a goal-basedanalysisappearstofurtherfacilitatetheunderstandingofSoStypesandstrengthenthelinkbetweenSoScharacte-risticsandSoStypes.RegardingSoScharacteristics,thebelonging index comprising two parameters,CS goalsandSoSgoals,indicatesthecohesionofanSoS30.Thechallenge is that SoS characteristics can not be useddirectly to explain the degree of authority.These twoparametersstillleaveroomforinterpretinghowmuchaCSwillcomply.In this paper,a goal-based approach is proposed tomodelandsimulatedifferenttypesofSoS.First,thetheo-retical models of both CS and SoS are constructed byintroducinganewconceptcalledpotential.Second,goalstates influenced by SoS characteristics are described.Then,differenceamongfourSoStypesbasedonthetran-sitionsamongthecombinationsofgoalstatesisunam-biguouslydemonstrated.AccordingtotheanalysisofSoStypes,thedifferencebetweenacknowledgedSoSandcol-laborative SoS is recognized based on the agent-basedmodel(ABM).The goal-based approach is valuable inprovidingacontributiontoSoStheory-relatedaspectsbyincreasingourunderstandingofSoStypeandprovidingamathematicalbaselinetotranslatethetheoreticaldefini-tionintoamoreeffectiveABMsimulationofSoS,whichhelps identify the suitable SoS types to achieve SoSgoals.Weorganizetheremainderofthispaperasfollows.Section2reviewstherelatedwork.Section3introducesconceptsofvariousgoalsandconstructstheCSandtheSoS theoretical models based on set theory.Section 4analyzestheinfluenceofSoScharacteristicsongoalsbysome possible combinations of goal states.Section 5explainstheSoStypethroughthetransitionsofthecom-binations.Section6implementstheproposedapproachusingABMtosimulatethemigratingwaterfowl.Section7discussestheresults.Finally,Section8summarizestheconclusions.2.BackgroundandliteraturereviewRelated work to this study can be classified into threetopics,which are the explanations of SoS types,SoScharacteristicsandtheoreticalmodels,aswellasmodel-ingofSoStypes.2.1ExplanationsofSoStypesMaier9describedthreedifferentSoStypes“directed,collaborative,andvirtual.”DahmannandBaldwin11addedanintermediatetypecalledacknowledgedbetweendirectedandcollaborative.ThedegreeofSoSsauthorita-tivecontroloverCSsdecreasesfromdirectedSoStovir-tualSoS.ThesefourSoStypesmayhaveimplicationsfortherelevantengineeringprocessesbecausetheauthorityrelationshipsbetweenSoSsandCSsaffecthowSoSengi-neering(SoSE)canbeimplemented2.Toillustrate,adirectedSoSthathasthedesignatedSoSmanagerwithcompletecontroloverCSsneedstoconsiderthetechni-calfeaturesoftheCSstoachieveSoSgoals.Meanwhile,628JournalofSystemsEngineeringandElectronicsVol.34,No.3,June2023anacknowledgedSoSoracollaborativeSoSthatdoesnotdirectlyauthorizeCSsneedstoconsiderhowtheCSscanparticipateinSoSdecisionsthatimpactCSgoals2.Theprimaryissueisthattheaforementionedtext-basedinterpretation of the degree of authority has vaguenessandsubjectivity.Specifically,duetothelackofrigorousmodels8todescribethedegreeofauthority,determin-ing SoS types usually relies heavily on human experi-ence,whichmayresultinmisclassification10orevennoclassification12.Forexample,supposeacollabora-tiveSoSismisclassifiedasdirected.Inthatcase,theSoSoperators will have less control over the purpose thanthey think,resulting in collective operations acrossadministrativeboundariesthatwillnotreliablyoccurinpractice10.Asaresult,perhapsonlyexperiencedengi-neerscanrelyontheirownexperiencetounderstandanddeterminetheSoStype.Thus,therehavebeenvariousattemptstoexplainthesetypesbetter,suchasusingbi-directionalarrowsbetweentheSoSEteamandCSs34and multi-dimensional classification 16.However,ambiguityandsubjectivitystillexistduetothequalita-tivedescriptionwithoutanyrigoroustheoreticalmodel.2.2SoScharacteristicsandtheoreticalmodelsNielsen et al.8 discussed Maiers characteristics(acronym“OMGEE”)9andBoardmanandSauserscharacteristics(acronym “ABCDE”)23,35.MaierscharacteristicsdealwiththelackofasharedagreementontheSoSdefinition.BoardmanandSauserscharacter-isticsdistinguishSoSsinSoSEfromconventionalsys-tems in SE,using the following five aspects 25,36.Autonomy(A)istheabilityofaCStoachieveitsownCSgoalswithlimitswithoutthecontroloftheSoSorotherCSs.Belonging(B)istheabilityofaCStoreceivethe benefit of its own CS goals and contribute to SoSgoalsorgoalsofotherCSs.Connectivity(C)isthecapa-bilitytoformconnectionsasneededtobenefiteachother.Diversity(D)emphasizes the difference in CS goalsamongvariousCSs.Emergence(E)meansthecumula-tiveactionsandinteractionsbetweentheconstituentsofanSoSgiverisetobehaviorsattributedtotheSoSasawhole.Basedonthedefinitionsabove,SoStypesappeartocorrelatemostwithauthorityandbelongingduetothecorrelationbetweenCSgoalsandSoSgoals.Felder and Baldwin 29 calculated the belongingindex(gains/contributions)byamathematicalexpression.However,thereisnofurthersegmentationinthesetwogoaldimensions.Asaresult,itisdifficulttosupporttheclassification of multiple SoS types.For this reason,expandingthesetwoparametersisnecessarytoanalyzequantitatively.WeconstructtheSoStheoreticalmodelbyintroducinganewconceptcalled“potential”forfurthersegmentationofCSgoalsandSoSgoals.Weproposetheterm“goalstate”torepresentscalarsintwodimensionsofgoals,whichindicatesthatagoalisachievedbywhatkindsoffunctionandpotential.Asthescalesofthetwogoalsdimensionsincrease,thecombinationsofdifferentstatesarelikelytobesufficienttodistinguishSoStypes.2.3ModelingofdifferentSoStypesBaldwinandFelderquantifiedametricofSoSfeatureattribution for a collaborative SoS migrating waterfowlflock29andadirectedSoSairdefensescenario30.Theycontendedthattheessentialdifferencebetweencol-laborativeSoSanddirectedSoSisagovernanceschemein which a central authority determines individual sys-temslevelandtypeofparticipation30.However,thedistinctionbetweenthesetwoSoStypesisonlydirectlyreflected in the concept introduction but not directlyreflected during the modeling and simulation process.TheSoStypeisonlyusedasafundamentalconceptwith-outpracticalguidanceformodelingandsimulationduetotheinsufficiencyofqualitativedescription.Soyezetal.37proposedamultilevelagent-basedmethodtomodeladirectedSoSoracknowledgedSoS,usingthecaseofintelligentautonomousvehicles(IAVs)andformalizingthefivecharacteristics.TheirworkmainlydealswithadirectedoracknowledgedSoS,whichmaybeappliedtoother types of SoSs if further studying the degree ofauthority.DarabiandMansouri28usedmulti-attributeutilitytheory(MAUT)torepresenttheutilityfunctionsofCSs and SoS.The swarm robot used in the case con-sumesresourcestofindtargets,buttheresearchersdidnotspecifywhichtypethisSoSis,makingitverydiffi-culttoextendtheirfindingstoallfourSoStypes.TheswarmrobotsweredesignedtoachieveSoSgoalsfirstandthenCSgoals.However,theystatedthattherobotsachievedCSgoalsandSoSgoalswithoutpriorityintheirfollow-updiscussion.Thus,therelationshipbetweenSoSgoalsandCSgoalsisambiguous.Seoetal.38ana-lyzedallfourSoStypesandusedaprobabilisticvariabletomodelthreeofthemexceptvirtualSoS.However,howtodefinethevalueoftheprobabilisticvariablestillleavesmuchroomforinterpretation.Therearetwomainstreamideasformodelingandsimu-lationofSoS.Baldwinetal.39comparedABMandevent-basedmodeling(EBM)andsuggestedthatABMismoresuitablefordescribingfourofthefiveSoScharac-teristicsautonomy,belonging,connectivity,anddiversity.Forexample,differentexamplesofSoSuseABM,suchas collaborative SoS birds flock 29,directed SoS airdefense scenario 30,directed or acknowledged SoSintelligentautonomousvehicles37.ABMdealswiththecomplexityofinteractionsbetweenCSsandrepresentsanFENGYiminetal.:Agoal-basedapproachformodelingandsimulationofdifferenttypesofsystem-of-systems629SoSthroughafewrules40.Thispaperanalyzesallpos-siblesituationsoftheinteractionsbetweenCSsthroughthegoal-baseddescription.Thus,thegoal-baseddescrip-tioncanguidethedevelopmentofeachagentsrules.3.TheoreticalmodelsTheSoStheoreticalmodelisbasedontheCStheoreticalmodel.The existing theoretical model 24 can onlydescribealimitednumberofgoalstatesofCSandSoS,whichisnotsufficienttospecifytheSoStypes.Wecon-structtheCStheoreticalmodel,onwhichtheSoStheo-retical model is constructed,to support the subsequentdescriptionofthegoalstate.3.1CStheoreticalmodelSiGiSiXifi(x)GiYipi(x)Weunifytheterminologyusedinthepaperas“CS”forasysteminSoSEand“system”forasysteminSE.DuetothedifferencebetweenSoSandsystems,thetraditionalsystemprinciples41stillhavesomeroomforinterpre-tationwhendescribingCSinSoS.BaldwinandSauser26describedtheCStheoreticalmodelandSoScharac-teristics based on set theory and first-order predicatelogic.However,itisnotsufficienttoexplainanddescribeSoStypesdirectly.Axelsson22proposedasetoftermsto describe the different states of CSs in an SoS.Forexample,“PassiveCS”meanstheCShasparticipatedinanSoS,and“Preparedsystem”meanstheCShasnotpar-ticipatedinanSoS.ThesetermscanhelpunderstandthedifferencebetweenaCSandasystemandbetterdeveloptheoreticalmodels.Thispaperintroducesanewconcepttothemostbasicformofthetraditionalsystemcalled“potential”fordescribingCS.Morespecifically,basedontheoriginalfunctionofCSasasysteminSE,wepro-posethepoten