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an author's

https://oatao.univ-toulouse.fr/26696

https://doi.org/10.23919/ACC45564.2020.9147333

Kassarian, Ervan and Rognant, Mathieu and Evain, Helene and Alazard, Daniel and Chauffaut, Corentin Convergent

EKF-based control allocation: general formulation and application to a Control Moment Gyro cluster. (2020) In:

American Control Conference 2020, 1 July 2020 - 3 July 2020 (Denver, United States).

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Modularization

of

smart

product

service:

A

framework

integrating

smart

product

service

blueprint

and

weighted

complex

network

Zhihua

Chen

a,b

,

Xinguo

Ming

a,∗

,

Elise

Vareilles

b

,

Olga

Battaia

c

aDepartmentofIndustrialEngineeringandManagement,SchoolofMechanicalEngineering,ShanghaiJiaoTongUniversity,Shanghai,200240,China bISAE-SUPAERO,UniversitédeToulouse,Toulouse,31400,France

cKedgeBusinessSchool,680coursdelaLiberation,33405,TalenceCEDEX,France

Keywords:

Smartproductservice Modularization Productserviceblueprint Rough-fuzzynumber Complexnetwork Girvan-Newman

a

b

s

t

r

a

c

t

Modularizationofsmartproductservice(SPS)emergesasaprioritystrategytoagilelysatisfythedynamic customizationrequirementandtoflexiblyresponsetotherapidmarketchange.Comparedwiththe tra-ditionalproductservice,theSPShavemorecomplicatedinteractionsbetweentheservicecomponents duetothenovelcharacteristicscausedbytheapplicationofsmarttechnologies.TheSPSmodularization presentsgreatdifferencesfromtheidentificationofservicecomponent,correlationevaluationand mod-ulepartitionwiththetraditionalproductservicemodularization.However,mosttheexistingresearch mainlyfocusesonthecontextoftraditionalproductservice,whilecontainingscantstudyofsmart prod-uctservice.Therefore,thisstudyproposesahybridframeworkforSPSmodularization.Intheframework, acyber-physicalproductserviceblueprintisfirstlyproposedtorepresenttheSPSoperationprocess andidentifytheSPScomponents.Then,arough-fuzzycorrelationmatrixispresentedtodeterminethe comprehensiveinterdependencebetweenallpairsofSPScomponentswithfullyconsideringthehybrid decisionuncertaintiesinvolvedintheevaluationprocess,i.e.,intrapersonallinguisticvaguenessand interpersonalpreferencediversity.Afterthat,thecomplexnetworktheoryisusedtoconstructtheSPS networkandamodifiedGirvan-NewmanalgorithmisadoptedfortheSPSmodulepartition.Finally,an illustrativemodularizationcaseofsmartgearboxmaintenanceserviceandsomecaparisonswithother methodsdemonstratethefeasibilityandvalidityoftheproposedapproach.

1. Introduction

Smartproductservicesystem(PSS)hasemergedasthe

main-streamstrategyemployedbythemanufacturerstoachievehigher

marketcompetiveness,customersatisfactionandenvironmental

sustainabilityintheeraofsmartplus(Zhengetal.,2019;Saunila

et al., 2019). Smart PSS comprises a smart connected product

(SCP)andvarioushigh-valuedsmartproductservice(SPS)which

are deliveredtomeet customers’ personalized requirementsas

anextension ofproduct (Zheng et al.,2019; Songetal., 2015).

TheseSPS solutions areprovided onthebasis ofapplication of

smarttechnologiesintheproductoperation,suchassmart

main-tenance service, smart updating service, smart sharing service

andsmartrecoveryservice(Chenetal.,2020a).The

revolution-∗ Correspondingauthorat:DongchuanRoadNo.800,MinhangDistrict,Shanghai, 200240,China.

E-mailaddresses:zh03.chen@sjtu.edu.cn(Z.Chen),xgming@sjtu.edu.cn

(X.Ming),Elise.VAREILLES@isae-supaero.fr(E.Vareilles),

olga.battaia@kedgebs.com(O.Battaia).

arydevelopmentoftheadvancedsmarttechnologies(e.g.smart

sensing, Internet of Things (IoT), cyber-physical system (CPS),

digital-twin(DT),virtual-/augmented-reality(VR/AR),artificial

intelligence(AI))enablemostofthecomponentsinasmartPSS

tobeperceptible,communicable,diagnosable,interpretable,

pre-dictable,controllableandoptimizable (Chenetal., 2020a;Siow

etal.,2018;Rymaszewskaetal.,2017).Thesecriticalcharacteristics

empowerthesmartPSSpresenthigherpotentialtoagilelysatisfy

the dynamic requirements or needs of various multiple

stake-holders(Chowdhuryetal.,2018;Chenetal.,2020b)andflexibly

responsetotherapidchangesintheexternalenvironment(Saunila

et al.,2019).Although thepotentialof smart PSStomeet

per-sonalizedrequirementshasbeenwidelyacknowledged(Valencia

etal.,2015;LerchandGotsch,2015;Changetal.,2019),itdoesnot

implythatsmartPSSwouldinherentlyhavethis capability.The

development,implementation,andoperationofsmartPSSarestill

challenging(Zhengetal.,2019).

Modularizationofproductserviceisacknowledgedasa

promis-ingapproachtocopingwiththecurrentrequirementforefficient

servicecustomization,reduceddevelopmentcost,decreased

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times,easierportfoliosofservicemodulesandincreasedflexibility

toresponserapidmarketchange(Gengetal.,2019;Fargnolietal.,

2019;SongandSakao,2017;Sakaoetal.,2017).However,mostthe

existingresearchmainlyfocusesonthemodularizationofphysical

productservice,whilecontainingscantstudyofSPS

modulariza-tion.Inaddition,theemergingcharacteristicsofSPScomponents

withtheapplicationofsmarttechnologieshavealsobroughtabout

newchallengestotheSPSmodularization.Therefore,itisnecessary

totakeadeepexplorationofSPSmodularizationinthecontextof

smartPSS.

Accordingtotheliteraturereviewresults, theservice

modu-larizationprocessofPSScanbedividedintothreetypicalphases:

identification of service components, evaluation of correlation

betweenservicecomponentsandpartitionofservicemodule(Song

etal.,2015;Gengetal.,2019;Sakaoetal.,2017;Yuetal.,2008).

ComparedwiththeservicemodularizationfortraditionalPSS,SPS

modularizationforsmartPSSpresentssomedifferencesinthethree

phases.First,theidentificationofSPScomponentsismore

com-plicatedinpracticedue totheservice processintangibility and

thecomplexinteractiveinterrelationshipbetweenservice

compo-nents.Notonlythematerialflow,functioninterdependenceand

physicalactivityinteractionexistbetweentheservicecomponents

(Songetal.,2015;Sakaoetal.,2017),butalsoalargeamountof

data,knowledgeand wisdomfrequentlyflow acrosstheservice

componentsand thecyber-physicalservice space(Zhenget al.,

2018;Malekietal.,2018;Wiesneretal.,2017).Theidentification

ofservicecomponentsinthecontextofsmartPSSshouldthus

con-siderthespecificserviceoperationprocessandcomplexinteraction

betweenthephysicaloperationspaceandcyberoperationspace.

Theusedtoolsormethodsintherealmofpureproductdesignor

physicalproductservicedesignarenotsuitabletosolvethe

prob-lemofSPScomponentsidentification,sincetheydonotfullytake

thenewcharacteristicsofSPScomponentsintoaccount.Therefore,

itisnecessarytodevelopafeasibletooltoidentifySPScomponents

forsmartPSS.

Second,afterthevariousSPScomponents areidentified,the

subsequent task is to evaluate the correlation among them,

whichprovidescriticalbasistoorganizeservicecomponentsinto

appropriateservicemodules (Songet al.,2015).Thecorrelation

evaluationtogreatextendsaffectstheformationwayofthe

ser-vicecomponentscombinedintomodules.Therefore,itisnecessary

toaccurately and objectively calculatethe correlationbetween

eachpairofservicecomponents.Theevaluation isusually

con-ducted byinviting a groupof expertstofill thequestionnaires

(Gengetal.,2019;Sakaoetal.,2017).Inthisprocess,twotypesof

uncertaintyareinvolved(WuandMendel,2010),namely,

intrap-ersonaluncertaintycausedbytheindividuallinguisticvagueness

andinterpersonaluncertaintyresultedfromthegrouppreference

subjectivity,bothwhichmayleadtoinaccurateevaluationresults

(Chenetal.,2020c).However,mosttheexistingresearchonPSS

modularizationcontainsscantstudyofthesimultaneous

manipu-lationoftheseuncertainties.

Third,fortheSPSmodulepartitionbasedontheobtained

cor-relationevaluationresults,theefficiencyofthepreviouspartition

methods,suchasfuzzyclusteringalgorithm(Sunetal.,2017),

map-pingmatrix(Lietal.,2012),fuzzygraph(Songetal.,2015;Song

andSakao, 2017), transitiveclosuremethod(Gengetal., 2019;

Shengetal.,2017)andmorphologicalmatrix(Lietal.,2018),would

markedly decreaseand easilysuffered inlocal optima(Sayama

etal.,2013).Mostofthesemethodscannotbecapabletoacquire

optimalSPS modulepartitionschemes interms ofa larger

cal-culationscaleandworkload,and toprovideavisualizationway

todirectlyunderstandthepartitionprocess.Moreover,mostthe

existingmethodsrarelyoffermeasurementforevaluatingthe

qual-ityof partitionschemes, sothat theoptimalschemecannotbe

accuratelyselected.

Basedonthedescriptionabove,threeresearchissuesare

iden-tifiedasfollows:(1)ResearchissueI:Howtoaccuratelyidentify

theSPScomponentsinthecontextofsmartPSSwhich involves

morecomplicatedinteractionbetweenservicecomponentsover

traditional PSS? (2) Research issue II: How to precisely

evalu-atecorrelationbetweenSPScomponentsunderintrapersonaland

interpersonaluncertainenvironments?(3)ResearchissueIII:How

tovisualizeandmeasuretheSPSmodulepartitionprocesswith

largecalculationworkload?

Therefore, to solve the issues discussed above, the current

studyproposesahybridframeworkforSPSmodularization,which

includes three parts: SPS components identification using the

CPS-based SPS blueprint, SPS correlation evaluation with the

rough-fuzzy number, and SPS module partition based on the

weighted complex network and the modified Girvan-Newman

(GN)algorithm.TheproposedCPS-basedSPSblueprintcanprovide

aholisticdescriptionofthecyberandphysicalserviceoperation

process and a visual representation of thecomplex interaction

betweeneachpairofSPScomponents.Withthistool,the

embed-dedservicecomponentscanbeclearlyandaccuratelyidentified

by the service designers. In addition, the proposedcorrelation

evaluation method combines thestrength of fuzzy setin

han-dlingintrapersonallinguisticvaguenessandthemeritofroughset

inmanipulatinginterpersonalpreferencediversity.Moreover,the

applicationofcomplexnetworktheoryandGNalgorithmprovides

a visualizedrepresentation of thecorrelationbetweenall pairs

ofSPScomponentsthroughthetransformationofthecorrelation

matrixintoaweightedcomplexnetworkandoptimalSPS

mod-ulepartitionscheme.Finally,theproposedframeworkisapplied

inacase ofsmartgearboxmaintenance servicetoillustratethe

practicalimplementationprocess.Thefeasibilityandvalidityare

demonstratedthroughcomparisonwithotherapproaches.

Theremainder of this paper isarranged like this:Section 2

reviewssomeliteraturesconcerningsmartPSSandtheprocessand

methodsforproductservicemodularization.Section3describes

theproposedintegratedframeworkforSPSmodularization.Section

4presentsacasestudyofapplicationoftheproposedframework.

Section5showscomparisonsofproposedapproacheswithsome

relatedmethods.Finally,theimplications,conclusionsand

limita-tionsaresummarizedinSection6.

2. Literaturereview

2.1. SmartPSS

Kuhlenkötter,etal.(Kuhlenkötteretal.,2017)indicatedthat

smartPSSisansocio-technicalPSSintegratingsmartconnected

products (SCPs) and smart service systems for the purpose of

providingnewfunctionalities.Zheng,etal.(Zhengetal.,2018)

pre-sentedaCPSstructureofsmartPSSinwhichSCPsareconsidered

asaninteractiveinterfacetoconnectthephysicalproduct/service

operationspaceandthecyberproduct/servicespace.Liu,etal.(Liu

etal.,2019a)exhibitedanevolutionoffuturestructureofsmart

PSSwhichaddressmainattentionsontheachievementof

excel-lentexperienceandhighpersonalizationincustomerscenarios.In

thecontext ofsmartPSS,smartproductsareconnectedtoeach

otherviathetechnologicalinfrastructurewithformingnetworked

physicalplatforms(Lietal.,2017;PorterandHeppelmann,2014).

AlargeamountofdatageneratedfromtheoperationofSCPsis

convertedtosmartdata(knowledgeorwisdom)usingbigdata

ana-lytictoolandartificialintelligence(Rymaszewskaetal.,2017;Ding

etal.,2019).Thesesmartdatacanprovideinsightfuldescription,

diagnosis,predictionanddecision-makingtooptimizethephysical

productserviceoperationperformance(Siowetal.,2018).Inthis

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physicalserviceactivitiesbutalsotheinteractionofsmartness(i.e.

data,information,wisdom)acrossthephysical-cybersystem(Chen

etal.,2020a).AwholeSPSoperationprocesscanbedescribedas

aprocessinwhichtheserviceresourcessupporttheserviceflow

undertheguidanceofsmartnesstoachieveexpectedservice

func-tion(Zhengetal.,2019).Suchaprocessconsistsofvariousworking

servicecomponentsthataredefinedasabasicelementtoconstitute

aproductservice(Songetal.,2015).Theserviceoperationprocess

andtherelationshipsbetweentheservicecomponentshave

sig-nificantlychangedwiththedeepapplicationofsmarttechnologies

(Chenetal.,2020c).Theinteractionbetweenthephysicalservice

domainandthecyberservicedomainaddsmorecomplexityand

multidimensionalitytotheservicerepresentationanddescription.

Notonlythevisiblematerialflow,activityflowandresourceflow,

butalsotheinvisibledataflow,informationflowandknowledge

flowareinvolvedintheserviceoperationprocess(Malekietal.,

2018;Wiesneretal.,2017).Thesecomplexinteractionsbringwith

newchallengestowardstheSPSmodularization,soitisurgently

necessarytotakemoreexplorationondevelopingadaptive and

feasiblemodularizationmethodforsmartPSS.

2.2. Productservicemodularizationprocess

Thenotionofproductservicemodularizationisfirstproposed

byAurich,etal.(Aurichetal.,2006a)wholeveragetheproduct

modularizationthinking(Bonvoisinetal.,2016)asabasicenabler

tobuildsystematicdesignframeworkforPSS.Alifecycle-oriented

design process for technicalPSS is then proposedwith

consid-eringtheproductmodularizationandservicemodularizationas

twoindependentengineeringactivitieswithinanintegratedPSS

developmentproject(Aurich etal.,2006b).Yu, etal. (Yu etal.,

2008)describedaservicemodularizationprocessforPSSincluding

fourphases:serviceprocessmodeling,standardizationofservice

process,generationofservicemodulerepositoryandservice

mod-ulesselectionandcombination.Wang,etal.(Wangetal.,2011)

exhibitedaW-typemodulardevelopmentframeworkofPSSwhich

contains three parts: service modularization, functional

modu-larizationandproduct modularization.Inthis work,descriptive

implementationstepsareprovidedintheframework,whilethe

operableandmathematictoolsormethodsarenotincluded.Li,

etal.(Lietal., 2012)establishedaninteractivemodulardesign

processforintegratedproductservicebasedontheanalysisofthe

interrelationshipbetweenphysicalmoduleandproductmodule.

Thisframeworkconsistsofservicemodulepartitionprocess,

prod-uctmodulepartitionprocessandmodulepartitionmethod.These

studiesindeedbringvaluableknowledgeonPSSmodularization,

butmostof themarecarried outfromtheconceptual

perspec-tivewhilecontainingscantquantitativemethods.amathematic

approachtoproduct-extensionservice modularizationwas

pro-posedbySong,etal.(Songetal.,2015),itconsistsofthreephases:

servicecomponentsidentification,correlationevaluationfor

ser-vicecomponentsandservicemodulepartition.Then,Sakao,etal.

(Sakaoetal.,2017)presentedageneralprocessforservice

modu-larizationincludingfivesteps,namely,describecustomers’needs,

determinelevelofgranularity,gatherservicecomponents,assign

interactionsandcreateservicemodules.Sheng,etal.(Shengetal.,

2017)introducedthreeparts,i.e.servicemoduledivision,

product-serviceintegration and configurationof product-service system

toconstituteaholisticframework forPSSmodulepartitionand

configuration. Larsen, et al. (Larsen et al., 2018)summarized a

descriptiveframeworkforPSSmodularizationwithoutproviding

quantitativemethodsthroughliteraturereview.Li,etal.(Lietal.,

2018)presentedamethodologicalframeworkincludingfoursteps:

serviceneedsacquisition,principalsolutionseeking,principal

solu-tioncombinationandmodularsolutionevaluation.Althoughthis

methodologyprovidesalogical,operableandmathematical

proce-dureforthePSSmodularization,itlacksofconsideringthespecific

operationprocessofproductservice.Liu,etal.(Liuetal.,2019b)

introduced anapproach toconcurrent product design and

ser-vicemoduleplanningusingasimulation-basedevaluationmethod.

Fargnoli,et al.(Fargnolietal.,2019)providesavaluable

frame-work thatcovers PSS componentsdefinition, services’modules

definitionand PSSoptimization.However,theapproach isonly

adaptive tothephysicalPSS while notrevealing the

character-isticsofsmarttechnology-enabledPSS.Inaddition,becausethis

approachismoreconceptualwithoutofferingspecificmathematic

proceduretoillustratetheimplementationprocess,itcannotbe

easilyusedandverified.

Accordingtothese studies,a generalservicemodularization

processcanbedividedintofourtypicalphases,i.e.service

compo-nentsidentification,correlationevaluationforservicecomponents,

servicemodulepartition,andpartitionmoduleevaluation.

There-fore,inthecurrentstudy,theproposedSPSmodularizationprocess

isorganizedbasedonthisgeneralprocess.

2.3. Productservicemodularizationmethods

Although the research on modularization process has been

widely exploredin the existing literature,the supportingtools

ormathematicalmethodstoimplementthemodularizationhave

beenoftenomitted.Somestudieshaveexploredtherelated

meth-ods to practically realize the PSS modularization. For instance,

Li,et al. (Li etal., 2012)suggestedto usetheQualityFunction

Deployment(QFD)toidentifyPSScomponentsandapplying

map-pingmatrixformodulepartition.Song,etal.(Songetal.,2015)

developedaproduct-extensionserviceblueprint(PES)forservice

componentsidentification,andthenevaluatedthecomprehensive

correlation between service components based on

interdepen-dencematrix,aswellasappliedthefuzzygraphtheoryforservice

modulepartition.Sakao,etal.(Sakaoetal.,2017)developedanew

practicalmethodthatsupportsdesignerstocreateservice

mod-ulesbyextendingthedesignstructurematrix(DSM).Sheng,etal.

(Shengetal.,2017)useddirectedgraphtodescribethe

relation-shipbetweenserviceactivities,andappliedDSMforserviceactivity

identification,employedthetransitiveclosuremethodtocluster

servicemoduleandproductmodule.Sun,etal.(Sunetal.,2017)

appliedfunctionalrequirementanalysis(FRA)toidentifyPSS

com-ponentswhichareclusteredintoservicemodulesusingthefuzzy

clusteringalgorithm.Zheng,etal.(Zhengetal.,2017)employed

theDSMtoevaluatecorrelationbetweenservicecomponentsand

appliedthegraphtheorytogenerateinitialservicemodules.Then,

thegeneratedmodularizationschemeisevaluatedusinga

multi-objectiveoptimizationmodel.Li,etal.(Lietal.,2018)appliedthe

morphologicalmatrixmethodtoobtainmodularservice

portfo-liosandusedanoptimizationmethod(costandprofitmethod)to

evaluatemoduledivisionschemes.Geng,etal.(Gengetal.,2019)

developed a result-orientedPSS modulardesign methodbased

onFuzzyDSM.Inthis study,a weighteddirectedgraphisused

torepresenttherelationshipsbetweenserviceactivities,andthe

absolutevaluereciprocalmethodisappliedtoclustertheservice

modules.Fargnoli,etal.(Fargnolietal.,2019)suggestedtousethe

QFDandDelphimethodstoidentifyPSScomponents,applyingthe

AxiomaticDesigntheorytodefineservicemodulesandemploying

theserviceblueprintfordefinitionofnewsolutions.

2.4. Researchgaps

Althoughthesestudiesdiscussedabovebroughtvaluable

explo-rationfortheimplementingmethodsofPSSmodularization,most

ofthemhave notyetconsideredsomecriticalcharacteristicsof

smartPSSmodularization.Table1showsthecomparativefeatures

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Table 1 Comparisons between product service modularization methods. Identification of service components Correlation evaluation for service components Service module partition References Method

Service operation process

Smart product service characteristic Method Intrapersonal uncertainty Interpersonal uncertainty Method Visualization Measurement Li, et al. ( Li et al., 2012 ) QFD × × Correlation matrix × × Mapping matrix × × Song, et al. ( Song et al., 2015 ) PES blueprint √ × Interdependence matrix × × Fuzzy graph √ × Sheng, et al. ( Sheng et al., 2017 ) Directed graph and DSM × × Fuzzy equivalent matrix √ × Transitive closure method × × Sun, et al. ( Sun et al., 2017 ) FRA × × Correlation intensity matrix × × Fuzzy clustering algorithm × √ Zheng, et al. ( Zheng et al., 2017 )– × × DSM × × Graph theory and multiple-objective optimization method √√ Li, et al. ( Li et al., 2018 )– × × – × × Morphological matrix and optimization method × √ Geng, et al. ( Geng et al., 2019 ) Weighted directed graph × × FDSM × × Transitive closure method × × Fargnoli, et al. ( Fargnoli et al., 2019 ) QFD and Delphi × × Axiomatic Design theory × × Axiomatic Design theory and service blueprint × √ This study SPS blueprint √√ Rough-fuzzy correlation matrix √√ Weighed complex network theory and modified GN algorithm √√

outbyusingkeywords“PSSandmodularization”,“modularization

ofproductextensionservice”,“modularizationofproductrelated

service”,“modularizationofproductservice”and“modularization

ofsmartproductservice”fromthe“Scopus”and“GoogleScholar”

database.First,themajorityofthepreviousmethodsforservice

component identificationdo notconsider theservice operation

processandemergingsmartproductservicecharacteristics.These

characteristicsrefertothesmartcapabilitiesofservicecomponents

(e.g.perceptible,communicable,diagnosable,predictableand

opti-mizable)(Chen etal., 2020b)and thecomplex interaction(e.g.

materialflow,functioncorrelation,dataflow,informationflowand

wisdomflow)betweentheservicecomponents(Songetal.,2015;

Zhengetal.,2018).Thesenovelcharacteristicsmakethe

identi-ficationofSPS componentstobemore complicatedinpractice.

However,theusedmethodsforidentificationoftraditionalservice

componentsarenotsuitableforSPScomponentidentification.For

example,theQFDandDSMcannotbeusedtodescribethespecific

operationprocessofaproductserviceactivityinwhichthe

inter-actionbetweenservicecomponentsintermsofcyberandphysical

flowareinvolved.Moreover,althoughtheweighteddirectedgraph

andserviceblueprintconsidertheinterrelationshipbetween

ser-vicecomponents,theycannotbecapableofrepresentingtheflow

ofdata, informationand wisdomacrossthecyberand physical

servicespace.Second,mostthepreviousmethodsforcorrelation

evaluationdonotconsidertheevaluationuncertaintyinvolvedin

thegroupdecisionprocess,whichmayleadtoinaccurate

correla-tionresultsandpartitionschemes.Inaddition,theefficiencyofthe

previouspartitionmethods,suchasclusteringalgorithm,mapping

matrix,fuzzygraph,transitiveclosuremethodandmorphological

matrix,willmarkedlydecreaseandeasilysufferinlocaloptima.

Moreover,suchmethodscannotprovideavisualizedindexasan

easy waytounderstandthepartition processand toselectthe

optimalscheme.

3. TheproposedframeworkforSPSmodularization

3.1. Overviewoftheproposedframework

ThispaperproposesahybridframeworkforSPS

modulariza-tion,integratingtheCPS-basedSPSblueprintforSPScomponents

identification(ResearchissueI),rough-fuzzynumberfor

evaluat-ingcorrelationbetweenSPScomponents(ResearchissueII)and

complexnetworktheoryforSPSmodulepartition(Researchissue

III).The frameworkconsistsof three stages(see Fig.1).StageI

mainlyfocusesondevelopingtheCPS-basedSPSblueprintinorder

toidentifySPScomponents.Asmentionedabove,thepreviousused

product-extensionserviceblueprint(Songetal.,2015)isfeasible

torepresenttheoperationprocessofconventionalproductservice,

butnoteffectivetomodeltheSPSoperationprocessbecauseof

themorecomplexinteractionbetweenSPScomponents.Therefore,

thisstageproposesageneralCPS-basedSPSblueprintby

integrat-ingthebasicstructureofcyber-physicalproductservicesystem

(Wiesner et al.,2017; Zhenget al., 2016)and traditional

prod-uctserviceblueprint(Songetal.,2015;Bitneretal.,2008).The

proposedCPS-basedSPSblueprintcanprovideaholistic

descrip-tion of thecyberand physicalservice operation process and a

visualrepresentationofthecomplexinteractionbetweeneachpair

ofSPS components.Withthis tool,theembeddedservice

com-ponents canbe clearly and accuratelyidentified by theservice

designers.Moreover,theevaluationprocessofcorrelationbetween

SPScomponentsinvolvesintrapersonallinguisticvaguenessand

interpersonalpreferencediversitywhichwouldleadtoinaccurate

correlationandpartitionresults.However,thepreviousresearch

rarelyfullyconsiderthesehybriduncertainties.Therefore,StageII

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Fig.1. TheproposedframeworkforSPSmodularization.

numberwithsimultaneouslyconsideringtheintrapersonal

linguis-ticvaguenessandinterpersonalpreferencediversity.Inaddition,

theefficiencyofthepreviouspartitionmethodswouldmarkedly

decreaseandeasilysufferinlocaloptima.Consequently,StageIII

firstlyappliesthecomplexnetworktheoryandmodifiedGN

algo-rithmfor SPSmodulepartition.Thecomplex networktheoryis

appliedtoestablishaSPSnetworkmodelandtheGNalgorithm

ismodified tobefeasibleforvisualSPSpartition.Then, a

mea-surementindexcalledasmodularityisintroducedtoevaluatethe

qualityofservicemodulepartitionschemesandselectthe

opti-malone.Thedetaileddescriptionoftheproposedframeworkis

introducedinthefollowingsections.

3.2. SPScomponentsidentificationwithCPS-basedsmartproduct

serviceblueprint

InaccordancewiththePSSmodularizationthinking(Songetal.,

2015; Songand Sakao, 2017), a product service canbe broken

downintomultipleservicemodules,andaservicemodulecanbe

decomposedintomultipleservicecomponents.Aservice

compo-nentisdefinedasabasicelementtoconstituteaproduct-extension

service.InthecontextofsmartPSS,aservicecomponentcanbe

consideredasaserviceactivity(e.g.,digitaltwin-basedsimulation,

physicalproductdisassembly,faultprediction)orserviceresource

(e.g.digital twinsystem,cyberservice system,physical service

resources)that resultsina uniquefunctionofthewholesmart

productservice.In addition,aservicemodulegenerallyconsists

ofasetofservicecomponentsamongwhichthereexiststrong

cor-relation.Theservicecomponentsbelongedtodifferentmodules

havealowerinterdependenceorconnectionthanthecomponents

belongedtothesamemodule.Thisfeatureprovidesabasistosolve

theproblemofservicemodulepartitionbyapplyingthe

commu-nitydetectionmethodofcomplexnetworktheory.

ToconstructSPSmodule,thefirsttaskisbreakingdownthe

target service intomultiple servicecomponents. However,it is

difficultto accuratelydescribe andquantitatively represent the

serviceprocess, servicefunctionand serviceactivitydue tothe

intangibilityofproduct-extension service.Furthermore,the

ser-viceoperationprocessandtherelationshipsbetweentheservice

componentshavesignificantlychangedwiththedeepapplication

ofsmarttechnologies.Theinteractionbetweenthephysicalservice

domainandthecyberservicedomainaddsmorecomplexityand

multidimensionalitytotheservicerepresentationanddescription.

Notonlythevisiblematerialflow,activityflowandresourceflow,

butalsotheinvisibledataflow,informationflowandknowledge

flowareinvolvedintheserviceoperationprocess.Anidentification

toolofsmartservicecomponentsnamedCPS-basedSPSblueprint

isprovided.Thistoolisappliedtoholisticallydescribethecyber

andphysicalserviceoperation.Throughthevisualrepresentation

oftheentireoperationprocess,alltherelatedserviceelementsare

coveredandpresented.Thus,theembeddedservicecomponents

canbeclearlyandaccuratelyidentifiedbytheservicedesigners.

Thissection proposeda general CPS-based SPSblueprint by

integratingthebasicstructure ofcyber-physicalproductservice

system(Wiesneretal.,2017;Zhengetal.,2016)andtraditional

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Fig.2.CPS-basedSPSblueprint.

showninFig.2,theSPSblueprintincorporatesfivemaindomains,

namely,physicalSCPoperationdomain,physicalserviceoperation

domain,physicalresourcedomain,cyberPSSoperationdomain,

andcyberresourcedomain.ThedomainofphysicalSCPoperation

is implemented torealize thespecific SCP’s function that

sup-portsboththecyberserviceandphysicalservice.Thedomainof

cyberPSSoperationisestablishedtoachievesmartfunctions(Chen

etal.,2020b)suchasreal-timeperception,interactiveconnection,

dynamicmonitor,informativediagnostic,accurateprediction,

opti-maldecision-making,andsmartprescription,etc.Itincludesfour

sub-domains,namely,SCPdatamanagementdomain,SCPdigital

twindomain,dataanalyticdomainandcyberservicedomain.The

domainofcyber resourceis designed toprovide therequested

virtual resources such as communication network, computing

infrastructure,virtualplatformandsystem,informationsystem,

knowledgebase,algorithmbase,etc.Itisfoundationofthedomain

ofcyberPSSoperationandthedomainofphysicalservice

opera-tion,sinceitprovidestheunderlyingserviceresourcestofacilitate

theproductandservicetowardsexpectedsmartcapabilities.The

domainofphysicalserviceoperationissettotakethephysical

ser-viceaction,andachievethegoalandfunctionofthephysicalservice

function.Inaddition,thephysicalresourcedomainmainlyaimsto

providesupportforthephysicalservice-relatedactivitiesoccurred

inthedomainofphysicalserviceoperation.WiththisSPSblueprint,

thedesignerscanclearlyunderstandandacquiretheSPSstructure.

It canbeseen in Fig.2,the SPSblueprint is splitinto eight

functionalareasbysixboundaries.Theseboundariesare

respec-tivelynamedasboundarybetweenproductandservice,boundary

betweenphysicalactivityandcyberactivity,boundarybetween

activityandcyberresource,boundarybetweenactivityand

physi-calresource,boundarybetweendataandsimulation,andboundary

betweendataandcyberservice.Theserviceelementsareclassified

into seven types, i.e. product-related activities (PRA),

service-relatedactivities(SRA),users-involvedPRA,users-involvedSRA,

cyberproduct-relatedresource,cyberservice-relatedresource,and

physicalresource.Alltheelementsarerepresentedbyuniqueand

standardsymbols (seeFig.2).Thearrow betweentheelements

denotestheirinteraction,whichcanbeidentifiedastheflowof

smartness(e.g.data,information, knowledge)orservice, orthe

correlationoffunctionorresource.Thedetaileddescriptionofthe

boundaryandsplitfunctionareaareintroducedasfollows.

First,theboundarybetweentheproductandservicedividesthe

wholeSPSblueprintintoproductoperationdomainand service

operationdomain,whichreflectsthedifferentscopesofthe

prod-uctandservice.Intheproductoperationdomain,theboundary

betweenphysicalactivityandcyberactivitydividesthe

product-relatedactivitydomainintophysicalproductactivitydomainand

cyberproductactivitydomain.Inaddition,thecyberproduct

oper-ationdomaincanbesplittomanagementdomainofproductdata

andsimulationdomainofproductdigitaltwinbytheboundary

betweendataandsimulation.Severalmainactivitiesareinherently

takenplaceinthedatadomain,suchascollection,processingand

storageofoperationaldata.Inthedigitaltwinactivitydomain,the

real-timemappingandvisualizationofthephysicalproduct

oper-ationareregardedasnecessaryactivitiesinacyberproductspace.

Thus,welisttheseelementsin theirdomainsastypical

obliga-torycomponents.Thephysicalproductoperationdomaininclude

product-relatedactivitiesandusersinvolvedPRAofwhich

exam-plescouldbetheproductadjustment.

Second,intheleftsideoftheboundarybetweenproductand

service,therearefivedomainsrelatedwithserviceoperation.The

boundarybetweendataandcyberservicedividesthecyber

ser-viceactivitydomainintodataanalyticdomainandcyberservice

domain,whichdescribestheinteractionbetweencoredataanalytic

capabilityandsmartservicefunction.Theactivitiesofdescriptive

analytics,diagnosticanalytics,predictiveanalyticsand

prescrip-tiveanalyticsareidentifiedasthecoresmartservicecomponents,

sincetheyprovidebasistodeliverproductextensionserviceina

smarterway.Furthermore,theserviceactivitiesincyberservice

domainprovidesmartdecision-makingfortheexecutionof

phys-icalserviceactivities,withintegratingthedataanalyticcapability

andtheproduct-relatedprofessionalknowledge.Thisintegration

isconductedinthebigdataanalyticplatform,whichisconsidered

asbasiccomponentinthecyberresourcedomain.Corresponding

toeachactivityelementinthedomainofcyberservice,thereisa

supportingcyberresourcesystemtoachieveexpectedsmart

ser-viceresultsinthedomainofcyberresourcedomain.Inaddition,

thedomainofphysicaloperationdomainincludesinvisible

physi-calserviceactivitiesandvisibleserviceactivitieswhichusers.These

physicalserviceactivitiesaresupportedbythekeyphysicalservice

resources,suchas,spareparts,servicetools,serviceengineers,etc.,

whichareprovidedinthedomainofphysicalresource.

WithapplicationoftheproposedCPS-basedSPSblueprint,the

smartservicecomponentscanbeeasilyidentifiedandtheir

inter-relationshipcanbealsovisuallydescribed.Thedifferentboxesin

Fig.2separatelydenotedifferentservicecomponentstobe

identi-fied.Thisblueprintcanprovidenotonlytheapproachtomodeling

ofsmartproductservice,butalsothedetaileddescriptionofthe

(8)

designerstoidentifyalltypesofservicecomponents,andanalyze

theinteractionbetweentheidentifiedcomponents.

3.3. CorrelationevaluationforSPScomponentsbasedon

rough-fuzzynumber

Inthissection,therough-fuzzynumberproposedbyChen,etal.

(Chenetal.,2020a)isappliedintotheevaluationofcorrelation

betweenthesmartservicecomponents,withobjectiveof

simul-taneouslymanipulatingtheintrapersonallinguisticvaguenessand

interpersonalpreferencesubjectivity.

3.3.1. EvaluationcriteriaforcorrelationbetweenSPScomponents

Theoperationprocess ofsmart productservice involvesnot

only the specific physical service activities but also the

inter-action of smartness (i.e.data, information, wisdom) acrossthe

physical-cybersystem.Awholesmartproductserviceprocesscan

bedescribedasaprocessinwhichtheserviceresources(input)

supporttheserviceflow(process)undertheguidanceofsmartness

(decision)toachieveexpected servicefunction(output).

There-fore,inthisstudy,theevaluationcriteriaforcorrelationbetween

servicecomponentsincludefunctioncorrelation,service-flow

cor-relation,smartness-flowcorrelationandresourcecorrelation.The

descriptionforthesecriteriaarepresentedasfollows:

(1)Functioncorrelation:Theservicemoduleassembledwiththe

servicecomponentsthathavestrongerfunctioncorrelationcan

achievehigherfunctionalindependenceandthusobtainhigher

exchangeability.Thus,theservicecomponentsthatimplement

therelevantorsimilarfunctionshouldbeaggregatedintoone

servicemoduletoenhancethefunctionaldependencyofthe

moduleanddecreasethefunctionalredundancyofthesmart

productservice.

(2)Service-flowcorrelation:In thephysicaloperationdomain,

theinteractionbetweenservicecomponentscanbepresented

inthetransferprocessofasetofphysicalactivitiesormaterials.

Theservice-flowcorrelationbetweentwocomponentscanbe

identifiedifoutputofonecomponentflowintotheotherone.

(3)Smartness-flowcorrelation:Inthecyberoperationdomain,

theinteractionbetweenservicecomponentsareexhibitedin

the transmission of data, information and knowledge. This

typeoftransferinteractionisnamedassmartness-flow

cor-relation. If there exist exchange of data, information and

knowledgebetweentwoservicemodules,theyareregarded

tobesmartness-flowcorrelated.

(4)Resourcecorrelation:In thesmartproductserviceprocess,

twoservicecomponentsmayworkbasedonthesamephysical

orcyberresource.Theycanbeconsideredtoberesource

depen-dent.Forinstance,faultmonitorandfaultdiagnosissharethe

samecyberresource:bigdataanalyticplatform,sotheyare

resourcecorrelated.

3.3.2. EvaluationofcorrelationbetweenSPScomponents

In this section, an approach integrated with fuzzy set and

roughsetisproposedtoevaluatethecorrelationbetweenservice

components. The function correlation, service-flow correlation,

smartness-flowcorrelationandresourcecorrelationcanbe

respec-tively calculatedby thefollowing procedures.The procedureis

describedbytakingfunctioncorrelationasexamples.

3.3.2.1. Step 1: establish linguistic correlation matrix. A decision

groupconsistingofRDMsisinvitedtoevaluatethefunction

cor-relation among n service components (SCs). A set of linguistic

variablesareusedbytheDMstojudgethecorrelationstrength

(seeTable2).

Table2

Fuzzyscaleoflinguisticvariables.

Linguisticvariable Crispscore Triangularfuzzynumber Verystrong(VS) 1 (0.75,1,1) Strong(S) 0.75 (0.5,0.75,1) Middle(M) 0.5 (0.25,0.5,0.75) Weak(W) 0.25 (0,0.25,0.5) Veryweak(VW) 0 (0,0,0.25) No(No) 0 (0,0,0)

ThelinguisticcorrelationmatrixCsfwhichismadebythesthDM isestablishedasfollows: Csf =

0 c12fs ··· c1nfs cfs21 0 ··· c2nfs . . . ... . .. ... cfsn1 cn2fs ··· 0

(1)

wherecijfsrepresentsthelinguisticcorrelationstrengthbetweenSCi andSCj,andcfsij =cfsji (i =/ j),ands=1,2,...,R.

3.3.2.2. Step2:Formfuzzycorrelationmatrix. Followingthefuzzy scaleinTable2,theelementcijfsofthelinguisticcorrelationmatrix

Csf isconvertedto ˜c fs ij=(lsij,m s ij,u s ij),wherel s ij,m s ijandu s ij denotes

thelowboundary,mediumboundaryandupboundaryoftheTFN,

respectively.Then,thefuzzycorrelationmatrix ˜C

f sisestablishedas follows: ˜ C f s=

0 ˜cfs12 ··· ˜cfs1n ˜cfs21 0 ··· ˜cfs2n . . . ... . .. ... ˜cfsn1 ˜cfsn2 ··· 0

(2)

3.3.2.3. Step3:constructgroupfuzzycorrelationmatrix. By

gather-ingthefuzzycorrelationmatricesthatareconstructedbyRDMs

intoasupermatrix,thegroupfuzzymatrices ˆC

f canbeformedas follows: ˆ C f =

0 ˆcf12 ··· ˆcf1n ˆcf21 0 ··· ˆcf2n . . . ... . .. ... ˆcfn1 ˆcfn2 ··· 0

(3) where ˆcfij=(ˆlij, ˆmij, ˆuij) ˆlij=



l1 ij,...,lsij,...,lRij

, mˆij=



m1 ij,...,m s ij,...,m R ij

, ˆuij=



u1 ij,...,u s ij,...,u R ij

,andthegroup

TFNscanalsobeexpressedas ˆcfij=



˜cijf1,..., ˜cfsij,..., ˜cfRij

.

3.3.2.4. Step4:Formtherough-fuzzycorrelationmatrix. Thegroup

fuzzyTFNs ˆcfijcanbeconvertedtorough-fuzzynumberfollowing

theoperationproposedbyChen,etal.(Chenetal.,2020a).The

calculationstepsareasfollows:

(1)Step4.1:Obtainthelowerandupperapproximationsofeach

(9)

ForthegroupTFNs ˆcfij=



˜cfij1,..., ˜c fs ij,..., ˜c fR ij

,thelowerand

upperapproximationsofthesthTFN ˜cfsijcanbeobtainedasfollows:

Lowerapproximation: Apr(˜cfsij)=∪

˜cftij ∈ ˆcfij/˜c ft ij ≤ ˜c fs ij

(4) Upperapproximation: Apr(˜cfsij)=∪

˜cftij ∈ ˆcfij/˜c ft ij ≥ ˜c fs ij

(5)

where Apr(˜cfsij) and Apr(˜cfsij) denotes the lower and the upper

approximationoftheTFN ˜asij,respectively.

(2)Step4.2:Obtainthelowerlimitandtheupperlimitofeach

TFN

ThenthelowerlimitandtheupperlimitofTFN ˜cfsij aredefined

asLim(˜cfsij)andLim(˜cfsij)asfollows:

Lim(˜cfsij)=(Lim(lijs),Lim(m

s ij),Lim(u s ij)) =

1 NL s NL s



k=1 xlk, 1 NL s NL s



k=1 xkm, 1 NL s NL s



k=1 xuk

(6)

Lim(˜cfsij)=(Lim(lijs),Lim(msij),Lim(usij))

=

1 NU s NU s



k=1 ylk, 1 NU s NU s



k=1 ymk, 1 NU s NU s



k=1 yku

(7) wherexl k,x m k,andx u

karerespectivelytheelementsoflower

approx-imationforlowboundary,mediumboundary,andupboundaryof

TFN ˜cfsij,yl

k,y m k,andy

u

karerespectivelytheelementsofupper

approx-imationforlowboundary,mediumboundary,andupboundaryof

TFN ˜cfsij,NL

sandNsUarethenumberofobjectsincludedinthelower

approximationandupperapproximationofTFN ˜cfsij.

(3)Step4.3:ConverteachTFNintorough-fuzzyform

Therough-fuzzynumberformRF(˜cfsij)of ˜cfsij canbedescribedas

follows: RF(˜cfsij)=



˜cfsLij , ˜cfsUij



=



(lsL ij,msLij,usLij),(lijsU,msUij ,usUij )



(8)



˜cfsLij , ˜cfsUij



=



Lim(˜cfsij),Lim(˜cfsij)



(9) (lsL

ij,msLij,usLij)=(Lim(lsij),Lim(msij),Lim(usij)) (10)

(lsU

ij ,msUij ,usUij )=(Lim(lsij),Lim(msij),Lim(usij)) (11)

where ˜cfsLij and ˜cfsUij arethelowerlimitandupperlimitof

rough-fuzzynumberRF(˜cfsij);lsL

ij andlsUij arethelowerlimitandupperlimit

ofroughnumberRN(ls

ij);m sL ij andm

sU

ij arethelowerlimitandupper

limitofroughnumberRN(ms

ij);u sL ij andu

sU

ij arethelowerlimitand

upperlimitofroughnumberRN(us

ij).

(4)Step4.4:Obtainrough-fuzzyintervalnumberofgroupTFNs

Therough-fuzzyintervalnumberRF(ˆcfij)ofthegroupTFNs ˆc

f ij=



˜cfij1,..., ˜c fs ij,..., ˜c fR ij

canbeacquiredbyusingroughcomputation

principlesasfollows: RF(ˆcfij)=



cijfL,cijfU



(12) cfLij =(lL ij,mLij,uLij) =



1 R R



s=1 lsLij,1 R R



s=1 msLij,1 R R



s=1 usLij



(13) cfUij =(lU ij,m U ij,u U ij) =



1 R R



s=1 lsUij ,1 R R



s=1 msUij ,1 R R



s=1 usUij



(14)

wherecfLij and cijfU are thelowerand upperlimitofrough-fuzzy

intervalnumberRF(ˆcfij);lL

ijandl U

ij arethelowerandupperlimitof

roughintervalRN(ˆlij);mLijandmUij arethelowerandupperlimitof

roughintervalRN( ˆmij);uLijanduUij arethelowerandupperlimitof

roughintervalRN( ˆuij).

(5)Step4.5:Obtainrough-fuzzycorrelationmatrix

AfterthegroupTFNs ˆcfijareaggregatedintoarough-fuzzy

num-berRF(ˆcfij),thegroupfuzzycorrelationmatrix ˆC

f

canbeconverted

torough-fuzzycorrelationmatrixRF( ˆC

f )asfollows: RF( ˆC f )=

0 RF(ˆcf12) ··· RF(ˆcf1n) RF(ˆcf21) 0 ··· RF(ˆc f 2n) . . . ... . .. ... RF(ˆcfn1) RF(ˆc f n2) ··· 0

(15)

3.3.2.5. Step5:constructtherough-fuzzycomprehensivecorrelation

matrix. The weights of the four criteria of correlation between

servicecomponentsareobtainedbyapplyingtherough-fuzzy

pair-wise comparison methodproposedbyChen,et al. (Chen etal.,

2019).Theweightsaresatisfiedwiththefollowingcondition:

wf+wse+wsm+wr=1 (16)

where wf, wse,wsm and wr separately denotes weightof

func-tion correlation, weight of service-flow correlation, weight of

smartness-flowcorrelationandweightofresourcecorrelation.

Therough-fuzzycomprehensivecorrelationmatrixRF( ˆC

f

)can

beacquiredbyweightedsumofthecorrespondingelementofthe

fourrough-fuzzycorrelationmatricesasfollows:

RF(ˆcij)=wfRF(ˆc f ij)+wseRF(ˆc se ij)+wsmRF(ˆc sm ij )+wrRF(ˆc r ij) (17)

where RF(ˆcij) represents the rough-fuzzy correlation strength

betweentheithservicecomponentandthejthone;RF(ˆcseij),RF(ˆc

sm ij )

andRF(ˆcrij)separatelydenoteselementofrough-fuzzycorrelation

matrixofservice-flow,smartness-flowandresource,whichare

cal-culatedusingEq.(1)∼(15).

3.3.2.6. Step 6: obtain crisp comprehensivecorrelation matrix. To

(10)

components,thecomprehensive correlationstrength shouldbe

transformedtocrispform.AccordingtoChen,etal.(Chenetal.,

2019), the crisp comprehensive correlation strength cij can be

obtainedasfollows: cij=(clLij +4cmLij +cuLij +cijlU+4cijmU+cuUij )/12 (18) where clL ij, c mL ij and c uL

ij separately denotes the low boundary,

mediumboundaryandupboundaryofthelowerlimitofRF(ˆcij);

clU

ij ,cmUij andcuUij respectivelydenotesthelowboundary,medium

boundaryandupboundaryoftheupperlimitofRF(ˆcij).

3.4. SPSmodulespartitionbasedonweightedcomplexnetwork

In this section,the comprehensivestrength matrix of smart

servicecomponents isused toinforma complex unidirectional

weightednetworkmodel (Strogatz,2001), sincethematrixis a

symmetricadjacencymatrix.Then,theGNalgorithm (Newman,

2006;NewmanandGirvan,2004)ismodifiedforSPSmodule

par-titionbased onthecommunity detectiontechnique incomplex

networktheory.

3.4.1. ConstructionofcomplexnetworkmodelforSPS

components

Inthissection,thecrispcomprehensivecorrelationmatrixis

regardedastheadjacencymatrixofaweightedunidirectional

com-plexnetworkmodel.Thisnetworkmodelisrepresentedbyfollows:

GSPS=(V,E,W ) (19)

whereV={SC1,SC2,...,SCn}isanodessetoftheidentified

ser-vice components set, in which the node SCi denotes the ith

service component; E={e12,...,e1i,...,eij,...,enn−1} is a set

of edges between the service component nodes, in which the

edge eij represents the link between SCi and SCj; and W=

{w12,...,w1i,...,wij,...,wnn−1}isasetofedges’weights,inwhich

the weight wij is the value of the comprehensive correlation

betweenSCiand SCj,i.e.,wij=cij,andit isalsoanrealnumber

attachedtotheedgeeij.Fig.3depictsanexamplediagramof

com-plexnetwork modelofthesmartproductservice.Therednode

representsaservicecomponent,andtheblacklinebetweentwo

servicecomponentsshowsthelinkbetweenthetwocomponents.

Thewidthofthelinepresentsthecorrelationstrengthbetweenthe

twolinkednodes.

3.4.2. SPSmodulepartitionbasedonthemodifiedGNalgorithm

In this section, the traditional GN algorithm (Newman and

Girvan,2004)is modifiedtofindtheproperservicemodulefor

smartproductservicenetwork.First,thebasicformoftheGN

algo-rithmisdescribedasfollows:(1)determinetheedgebetweenness

Fig.3. ExampleofSPSnetwork.

scoreofalledgeswithintheSPSnetwork,and(2)findtheedge

thathasthelargestbetweennessandeliminatethisedgefromthe

network,then(3)reloaddeterminationofedgebetweennessfor

allunremovededges,and(4)repeatfromstep2untiltheexpected

servicemodulenumberisacquiredorthemaximummodularity

is reached. Based onthis procedure, theGN algorithm is

mod-ified with redefiningthe edge betweennessby introducing the

edgeweight(i.e.,thecomprehensivecorrelationbetweeneachpair

ofservicecomponents)inthecalculationofbetweenness.Inthe

traditionalGNalgorithm,theedgeswithlargerbetweennessare

selectedtoberemoved,whichmeanstheconnectionbetweenthe

pairofnodeslinkedwiththisedgeisweaker.However,inthecase

ofSPSnetwork,thelargeredgeweightimpliesastronger

connec-tionbetweenthispairofservicecomponents,andtherebytheedge

shouldnotbeeliminated.Iftheedgeweightisconsideredasa

pos-itivefactorinthecalculationofedgebetweenness,theedgeswith

higherweightwillberemoved,whichisreversedwiththeactual

situationofSPSmodularization.Tosolvethisproblem,a

modifi-cationmethodisproposed.First,theinitialedgebetweennessis

obtainedbyusingtheoriginalshortest-pathbetweennessmethod

withoutconsideringtheedgeweight.Then, anewbetweenness

canbecalculatedthroughdividingtheoriginalbetweennessbythe

edgeweight.Thisnewbetweennesscanservetobethecriterionto

removetheedge.Withthisoperation,theedgebetweenthe

ser-vicecomponentswithastrongercorrelationstrengthhasasmaller

possibilitytoberemoved.Basedonthismodification,arevisedGN

algorithmisdescribedasfollows:

3.4.2.1. Step1:assignscorevaluetoallverticesbasedonbreadth-first

searchalgorithm. ByrepeatingtheprocessdepictedinAlgorithm1

forallnsourcevertices(servicecomponents)intheSPScomplex

network,thescorevalueforallverticesareassigned.Fig.4(a)∼

(b)presentanexampleprocesstoassignvaluesi.e.,distanceand

weight,toeachvertexinanexamplenetworkconsistingofeight

verticesamongwhichvsisthesourcevertex.

(11)

3.4.2.2. Step2:calculatetheinitialedgebetweenness. Byrepeating

theprocessdepictedinAlgorithm2forallnsourcevertices(service

components)intheSPScomplexnetwork,theinitialbetweenness

canbedetermined.Fig.4(b)(c)presentanexampleprocessto

calculatetheedgebetweenness.Generally,inthetraditionalGN

algorithm,theedgewiththehighestinitialbetweennesswillbe

removedapproachingtoapartitionedSPSnetwork.However,as

mentionedabove,inordertohandletheactualsituationoftheSPS

network,anewbetweennesswillbeproposedbasedontheinitial

edgebetweennessinthenextstep.

3.4.2.3. Step3:determinetherevisededgebetweenness. Therevised

edgebetweennessisdeterminedbyfollows:

BRij=Bij/wij (20)

where BR

ij is therevised edge betweennessand wij is the edge

weight.

3.4.2.4. Step4:eliminatetheedgewiththelargestrevised

between-ness. Basedontheoutputresultsofprecedingstep,theedgewith

thelargestrevisedbetweennessBR

ij isidentified and thustobe

removed.

3.4.2.5. Step5:recalculatethebetweennessofallremainingedges.

Alltheremainingedgesandverticesinstep4canbedeemedan

updatednetwork,thenthisstepistoreloaddeterminationofedge

betweennessforallunremovededgesbyrepeatingstep1∼3.

3.4.2.6. Step6:determinethemodularity. Theoutputofthe

mod-ifiedalgorithmisintheformofadendrogramwhichdescribesa

globalhierarchyofthepossiblemodulepartitionsfortheSPS

net-work(NewmanandGirvan,2004).Theissuetobesolvedishow

torecognizethebestonefromthepossiblepartitions,i.e.where

thedendrogramshouldbecuttoacquireanoptimaldivisionof

thenetwork.Accordingto(Newman,2006;NewmanandGirvan,

2004),theconceptofmodularityisproposedasacriticalcriterionto

evaluatethequalityofaspecificpartitionofanetwork.Generally,

theoptimalpartitionisacquiredwhenthecorresponding

modu-larityisthelargestoneoverotherpartitions.Theusedmodularity

Q(Newman,2006)inthissectionisdefinedasfollows:

Q= 1 4m



ij



Aij− kikj 2m



(sisj+1) (21)

whereAijistheelementoftheunweightedmatrixoftheadjacency

matrix(i.e.comprehensivecorrelationmatrix),whichiscalculated

usingEq.(22);kiandkjseparatelydenotesthedegreeofthevertex

i(SCi)andvertexj(SCj),whichcanbedeterminedaski=



jAij;m

representsthetotalnumberofedgesintheoriginalnetwork,which

isequalto



iki/2;andsisj=1ifthevertexiandvertexjareinthe

samemodule,otherwisesisj=-1.

Aij=



1, ifwij=/0;

0, ifwij=0.

(22)

Finally,byfollowingthesixstepsabove,aSPScomponent

(12)

Fig.5.CPS-basedsmartgearboxmaintenanceserviceblueprint.

thebestmodularity.Theobtainedpartitionschemewillprovide

basisforthefurthersmartPSSconfigurationwork.

4. Casestudy

Inthissection,thefeasibilityandeffectivenessoftheproposed

modularizationmethodaredemonstratedthroughthemethod’s

applicationintothedesignofsmartmaintenanceservicesystem

forthegearboxofportcontainercrane(PCC).APCCmanufacturer

Zisaworldclassmanufacturerofheavyconstructionmachinery,

whoiscommittedtoprovidingportcustomerswithvarioustypesof

portcontainercranesandtherelatedservice.Thedeepconvergence

ofadvancedsmarttechnologiesandtraditionalcraneindustryhas

boostedthecompanyZtotransformitsvaluepropositionsfrom

product-soldtoservice-soldsoastoobtainhighercompetiveness

andincreasethecustomers’experience.PCCisacriticalfacilityfor

theport,sinceitsperformancedeterminetheoperationcondition

oftheport.Unexpectedstoppageofthegearboxwillcausehigh

riskand operationcost forthePCCinthetransportationofthe

goodsbetweenthefreightersandports.Timelyrepairand

predic-tivemaintenancecanmarkedlyreducetheoccurrencefrequency

oftheunexpectedstoppageandtheircausedcost.Owingtothe

applicationofsmarttechnologies,asmartmaintenanceservicecan

beprovidedwiththeportoperatorinordertoeffectivelyprevent

theunexpectedfailureandoptimizePCCoperation.However,the

designofpersonalizedmaintenanceserviceforeachindividualPCC

customerisnotaneconomicway.Therefore,companyZattempts

toapplytheSPSmodularizationmethodtoacquiretheoptimal

par-titionschemeforthesmartgearboxmaintenanceservice(SGMS)

modules.Thepurposeoftheapplicationoftheproposedmethod

in thecase studyis topresent itscalculationprocess and

vali-dateitsfeasibilitythroughsomecomparisonswithothermethods.

Thecasestudyincludesthreeparts:identificationofSGMS

compo-nents,correlationevaluationforSGMScomponentsandpartition

ofSGMSmodules.TheidentificationofSGMScomponentsis

con-ductedbyfieldsurveyingthepracticalserviceprocessofthesmart

maintenanceofcompanyZ.Then,theproposedSPSblueprintis

usedforrepresentingtheSGMSoperationprocessintodetailed

dia-gram.FromtheestablishedCPS-basedsmartgearboxmaintenance

service blueprint,all thenecessary SGMS componentsare thus

identified.ForthecorrelationevaluationforSGMScomponents,in

ordertocollecttheopinionsfrommultiplestakeholders,a

deci-sionteamconsistingof5DMsisinvitedtoconducttheevaluation.

TheseDMsinclude2experiencedPCCdesigners,2serviceexperts

and 1 PCC operator. Afterthequestionnaires are collected, the

rough-fuzzycomprehensivecorrelationmatrixisconstructedby

transformingthegrouplinguisticcorrelationjudgementto

rough-fuzzynumbers.Then,therough-fuzzymatrixisconvertedintoa

complexnetworkmodelbyusingtheproposedmethod,andthe

finalSGMSpartitionresultisobtainedbyusingthemodifiedGN

algorithm.

4.1. IdentificationofSGMScomponents

Consideringtheactualserviceprocessandresourceofthesmart

gearboxmaintenanceofcompanyZ,theCPS-basedSPSblueprint

isappliedtodisplaythegeneralandtypicaloperationprocessof

smartgearboxmaintenanceservice,asshowninFig.5.Fiftyfour

SGMScomponentsareidentifiedwiththeproposedSPSblueprint,

asshowninTable3.

4.2. CorrelationevaluationforSGMScomponents

Theproposedrough-fuzzymethodis usedtoassessthe

cor-relationbetweeneachpairoftheservicecomponentsidentified

inTable3.ByapplyingEq.(1)∼(15),thegrouplinguistic

evalua-tionmatricesofthefunctioncorrelation,service-flowcorrelation,

smartness-flowcorrelationandresourcecorrelationareseparately

transformedtotheformofrough-fuzzycorrelationmatrix.Then,

usingtherough-fuzzypair-wisecomparisonmethod,theweights

of thefunction correlation,service-flow correlation,

smartness-flowcorrelationandresourcecorrelationaredeterminedas0.176,

0.494,0.226and0.104,respectively.Finally,byusingEq.(17)∼(18),

thecrispcomprehensivecorrelationbetweeneachcoupleofservice

componentsisacquiredinTable4.

4.3. PartitionofSGMSmodules

4.3.1. ConstructionofSGMSnetworkmodel

Inaccordancewiththedescriptioninsection3.4.1,theobtained

comprehensivecorrelation matrix of SGMS componentscan be

used as the adjacency matrix of a weighted complex network

model,asshowninFig.6.Thenodesymbols refertotheSGMS

components,andtheedgesdenotethelinkbetweeneachpairof

nodes.Thecorrelationstrengthbetweenthecomponentsis

repre-sentedbythewidthoftheedgeinthenetworkmodel.Thegreater

(13)

Table3

Servicecomponentsofsmartgearboxmaintenance.

No. Name Type Domain

SC01 SmartPCCoperating UsersinvolvedPRA PhysicalSCPoperationdomain SC02 Gearboxsensorssystemoperating Product-relatedactivity PhysicalSCPoperationdomain SC03 Speedsensorsoperating Product-relatedactivity PhysicalSCPoperationdomain SC04 Temperaturesensorsoperating Product-relatedactivity PhysicalSCPoperationdomain SC05 Ultrasonicdefectsensorsoperating Product-relatedactivity PhysicalSCPoperationdomain SC06 Soundsensorsoperating Product-relatedactivity PhysicalSCPoperationdomain SC07 Communicatorsoperating Product-relatedactivity PhysicalSCPoperationdomain SC08 NB-IoTcommunicatorrunning Product-relatedactivity PhysicalSCPoperationdomain SC09 5Gcommunicatorrunning Product-relatedactivity PhysicalSCPoperationdomain SC10 Datacollectionsystem Cyberproduct-relatedresource CyberPSSplatform

SC11 Gearboxdatacollection Product-relatedactivity SCPdatamanagementdomain SC12 Digitaltwinofgearboxsystem Cyberproduct-relatedresource CyberPSSplatform

SC13 DT-basedsimulation Product-relatedactivity SCPdigitaltwindomain SC14 Dataprocesssystem Cyberproduct-relatedresource CyberPSSplatform

SC15 Gearboxdataprocessing Product-relatedactivity SCPdatamanagementdomain SC16 DTanalysissystem Cyberproduct-relatedresource CyberPSSplatform

SC17 DT-basedvisualization Product-relatedactivity SCPdigitaltwindomain SC18 Datawarehouse Cyberproduct-relatedresource CyberPSSplatform

SC19 Gearboxdatastorage Product-relatedactivity SCPdatamanagementdomain SC20 Physical-cyberinteractionsystem Cyberproduct-relatedresource CyberPSSplatform

SC21 Fusionofphysicalandcyberdata Product-relatedactivity SCPdatamanagementdomain SC22 Faultmonitorsystem Cyberservice-relatedresource CyberPSSplatform

SC23 Descriptiveanalytics Service-relatedactivities Dataanalyticdomain

SC24 Faultmonitor Service-relatedactivities Cyberservicedomain

SC25 Faultdiagnosissystem Cyberservice-relatedresource CyberPSSplatform SC26 Diagnosticanalytics Service-relatedactivities Dataanalyticdomain SC27 Faultdiagnosis Service-relatedactivities Cyberservicedomain SC28 Faultprognosissystem Cyberservice-relatedresource CyberPSSplatform SC29 Predictiveanalytics Service-relatedactivities Dataanalyticdomain SC30 Faultprognosis Service-relatedactivities Cyberservicedomain SC31 Cognitiveoptimizesystem Cyberservice-relatedresource CyberPSSplatform SC32 Prescriptiveanalytics Service-relatedactivities Dataanalyticdomain SC33 Operationoptimization Service-relatedactivities Cyberservicedomain SC34 Bigdataanalyticplatform Cyberservice-relatedresource CyberPSSplatform SC35 Serviceexecutionsystem Cyberservice-relatedresource CyberPSSplatform

SC36 Generatingmaintenancesolution Service-relatedactivities Physicalserviceoperationdomain SC37 Serviceresourcemanagesystem Cyberservice-relatedresource CyberPSSplatform

SC38 Dispatchingserviceengineer Service-relatedactivities Physicalserviceoperationdomain SC39 Trainingserviceengineer Service-relatedactivities Physicalserviceoperationdomain SC40 Smartmaintenance UsersinvolvedSRA Physicalserviceoperationdomain SC41 Schedulingserviceresource Service-relatedactivities Physicalserviceoperationdomain SC42 ARmaintenancetoolaiding Service-relatedactivities Physicalserviceoperationdomain SC43 Servicequalitymanagesystem Cyberservice-relatedresource CyberPSSplatform

SC44 Serviceevaluation UsersinvolvedSRA Physicalserviceoperationdomain

SC45 Serviceengineers Physicalresources Physicalresourcedomain

SC46 Smartservicetools Physicalresources Physicalresourcedomain

SC47 Spareparts Physicalresources Physicalresourcedomain

SC48 Gearboxclean UsersinvolvedSRA Physicalserviceoperationdomain

SC49 Gearboxrepair UsersinvolvedSRA Physicalserviceoperationdomain

SC50 Gearboxreplace UsersinvolvedSRA Physicalserviceoperationdomain

SC51 Gearboxupdate UsersinvolvedSRA Physicalserviceoperationdomain

SC52 PCCadjustment UsersinvolvedPRA PhysicalSCPoperationdomain

SC53 PCCinstallation UsersinvolvedPRA PhysicalSCPoperationdomain

SC54 Actuatoroperating Product-relatedactivity PhysicalSCPoperationdomain

Fig.6.TheSGMSnetworkmodel.

4.3.2. PartitionofSGMSmodules

BycalculatingthemodifiedGNalgorithminMATLABR2019a,

thedendrogramoftheSGMSmodulesandthepartition

modular-ityarepresentedinFig.7.Themodularityvariancegraphshows

thatthe modularityincrease withthedivisions’number before

theoptimaldivisionschemeisreached.Oneglobalpeakappearat

theoptimalpartitionscheme,andthenthemodularitydecreases

withtheincreasingpartitions.Inthissection,themodularization

schemeswithmodularityQ2=0.223,Q4=0.220,Q6 =0.320,Q8

=0.277andQ10=0.265arepresentedinTable5,wherethe

sub-scriptiofthesymbolQimpliesthatthereareipartitionedservice

modulesinthisscheme.Theresultsshowthatthemodularization

schemeofSGMSmoduleswithQ6=0.320istheoptimalone,and

(14)

Z. Chen, X. Ming, E. Vareilles et al. / Computers in Industry 123 (2020) 103302 13 Table4

Thecomprehensivecorrelationbetweenservicecomponents.

SC01 SC02 SC03 SC04 SC05 SC06 SC07 SC08 SC09 SC10 SC11 SC12 SC13 SC14 SC15 SC16 ... SC52 SC53 SC54 SC01 0 0.282 0.038 0.038 0.038 0.038 0.282 0.068 0.068 0.029 0 0.17 0 0 0 0.068 ... 0.319 0.159 0.319 SC02 0.282 0 0.282 0.282 0.282 0.282 0.211 0.068 0.068 0.029 0 0.17 0.029 0 0 0.068 ... 0.256 0 0 SC03 0.038 0.282 0 0.211 0.211 0.211 0.282 0.068 0.068 0.029 0 0.17 0.029 0 0 0.068 ... 0.256 0 0 SC04 0.038 0.282 0.211 0 0.162 0.162 0.225 0.038 0.038 0.018 0 0.121 0.018 0 0 0.038 ... 0.256 0 0 SC05 0.038 0.282 0.211 0.162 0 0.162 0.225 0.038 0.038 0.018 0 0.121 0.018 0 0 0.038 ... 0.256 0 0 SC06 0.038 0.282 0.211 0.162 0.162 0 0.225 0.038 0.038 0.018 0 0.121 0.018 0 0 0.038 ... 0.256 0 0 SC07 0.282 0.211 0.282 0.225 0.225 0.225 0 0.293 0.293 0.293 0.293 0.222 0.128 0.041 0.018 0.128 ... 0.256 0 0 SC08 0.068 0.068 0.068 0.038 0.038 0.038 0.293 0 0.27 0.27 0.27 0.2 0.113 0.034 0.018 0.113 ... 0.256 0 0 SC09 0.068 0.068 0.068 0.038 0.038 0.038 0.293 0.27 0 0.27 0.27 0.2 0.113 0.034 0.018 0.113 ... 0.256 0 0 SC10 0.029 0.029 0.029 0.018 0.018 0.018 0.293 0.27 0.27 0 0.27 0.27 0 0.2 0 0.113 ... 0 0 0 SC11 0 0 0 0 0 0 0.293 0.27 0.27 0.27 0 0 0.16 0.27 0.16 0 ... 0 0 0 SC12 0.17 0.17 0.17 0.121 0.121 0.121 0.222 0.2 0.2 0.27 0 0 0.27 0 0 0.27 ... 0 0 0 SC13 0 0.029 0.029 0.018 0.018 0.018 0.128 0.113 0.113 0 0.16 0.27 0 0 0 0.27 ... 0 0 0 SC14 0 0 0 0 0 0 0.041 0.034 0.034 0.2 0.27 0 0 0 0.27 0.034 ... 0 0 0 SC15 0 0 0 0 0 0 0.018 0.018 0.018 0 0.16 0 0 0.27 0 0 ... 0 0 0 SC16 0.068 0.068 0.068 0.038 0.038 0.038 0.128 0.113 0.113 0.113 0 0.27 0.27 0.034 0 0 ... 0 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . SC52 0.319 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0 0 0 0 0 0 0 ... 0 0.66 0.518 SC53 0.159 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... 0.66 0 0.66 SC54 0.319 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... 0.518 0.66 0

(15)

Table5

Themodularizationschemeswithdifferentmodularity.

Q2=0.223 Q4=0.220 Q6=0.320 Q8=0.277 Q10=0.265 Module1 {SC14,SC15,SC17, SC18,SC19,SC20,SC21, SC22,SC23,SC24,SC25, SC26,SC27,SC28,SC29, SC30,SC31,SC32,SC33, SC34,SC35,SC36,SC37, SC38,SC39,SC40,SC41, SC42,SC43,SC44,SC45, SC46,SC47,SC48,SC49, SC50,SC51,SC53, SC54} {SC15,SC18,SC19, SC20,SC21,SC22,SC23, SC24,SC25,SC26,SC27, SC28,SC29,SC30,SC31, SC32,SC33,SC34,SC35, SC36,SC37,SC38,SC39, SC40,SC41,SC42,SC43, SC44,SC45,SC46,SC47, SC48,SC49,SC50,SC51, SC53,SC54} {SC15,SC18,SC19, SC20,SC21,SC22,SC23, SC24,SC25,SC26,SC27, SC28,SC29,SC30,SC31, SC32,SC33,SC34} {SC15,SC19,SC20, SC21,SC22,SC23,SC24, SC25,SC26,SC27,SC28, SC29,SC30,SC31,SC32, SC33,SC34} {SC19,SC21,SC22, SC23,SC24,SC25,SC26, SC27,SC28,SC29,SC30, SC31,SC32,SC33, SC34} Module2 {SC1,SC2,SC3,SC4, SC5,SC6,SC7,SC8,SC9, SC10,SC11,SC12,SC13, SC16,SC52} {SC1,SC2,SC3,SC4, SC5,SC6,SC7,SC8,SC9, SC10,SC11,SC12,SC13, SC16,SC52} {SC35,SC36,SC37, SC38,SC39,SC40,SC41, SC42,SC45,SC46,SC47, SC48,SC49,SC50,SC51, SC53,SC54} {SC1,SC2,SC3,SC4, SC5,SC6,SC7,SC8,SC9, SC10,SC11,SC12,SC13, SC16,SC52} {SC1,SC2,SC3,SC4, SC5,SC6,SC7,SC8,SC9, SC10,SC11,SC12,SC13, SC16,SC52} Module3 / {SC14} {SC1,SC2,SC3,SC4, SC5,SC6,SC7,SC8,SC9, SC10,SC11,SC12,SC13, SC16,SC52} {SC35,SC36,SC37, SC38,SC39,SC40,SC45, SC48,SC49,SC50,SC51, SC53,SC54} {SC35,SC36,SC37, SC38,SC39,SC40,SC45, SC48,SC49,SC50,SC51, SC53,SC54} Module4 / {SC17} {SC43,SC44} {SC41,SC42,SC46, SC47} {SC41,SC42,SC46, SC47} Module5 / / {SC14} {SC43,SC44} {SC43,SC44} Module6 / / {SC17} {SC18} {SC15} Module7 / / / {SC14} {SC20} Module8 / / / {SC17} {SC18} Module9 / / / / {SC14} Module10 / / / / {SC17} Table6

ComparisonsbetweendifferentmethodsforSPScomponentsidentification.

Methods Blueprintsstructures Interactionpresentation Applicationscope Traditionalservice

blueprint(Bitneretal., 2008)

Fourdomains:customeractiondomain, onstage/visibleactiondomain,backstage/ invisibleactiondomainandsupport domain.

Itmainlyaddressesthepureservice operationprocesswithoutconsideringthe characteristicsoftheproduct-based service,letalonethefeaturesofsmart productservice.

Conventionalconsumerserviceandother pureservice,e.g.,bookingservice, supermarketsservice.

Threeboundaries:lineofinteraction,line ofvisibilityandlineofinternalinteraction. PESblueprint(Song

etal.,2015)

Fivedomains:productusingdomain, productmanagementdomain,visualized servicedomain,invisibleservicedomain anddomainofresources.

Itprovidesthreecriticaltypesof interactioninterdependencesbetweenthe servicecomponents,namely,

function-basedinterdependency,service flow-basedinterdependencyand resource-basedinterdependency. However,theeffectofsmarttechnologies ontheinteractionisnotconsidered.

Physicalproductservicesuchasafter-sale installationservice,repairservice,and sparepartsdistribution.

Fiveboundaries:boundarybetween productandservice,boundarybetween activityandresource,boundaryofusing andboundaryofvisualization. CPS-basedSPS

blueprint

Fivemaindomains:physicalSCP operationdomain,cyberPSSoperation domain(includingSCPdatamanagement domain,SCPdigitaltwindomain,data analyticservicedomainandcyberservice domain),cyberresourcedomain,physical serviceoperationdomainandphysical resourcedomain.

Inadditiontothecorrelationsof function,service-flowandresource, thesmartness-flowcorrelationis consideredwithhandlingthefeatures ofsmartPSSandtheimpactofsmart technologies.Moreover,theCPS structureanddigitaltwinconceptare integratedintheblueprintsoasto accuratelyandeffectivelydescribethe operationprocessofsmartproduct serviceandrepresenttheinteraction betweenthephysicalandcyberservice spaces.

Smartproductservicesuchas real-timerepairservice,predictive maintenanceservice,product operationoptimizationservice,user behavioroptimizationserviceandso on.

Sixboundaries:boundarybetween productandservice,boundarybetween physicalactivityandcyberactivity, boundarybetweenactivityandcyber resource,boundarybetweenactivityand physicalresource,boundarybetweendata andsimulation,andboundarybetween dataandcyberservice.

5. Comparisonsanddiscussions

In this section, the feasibility and effectiveness of the

pro-posedmodularizationframeworkisdemonstratedthroughthree

comparisonswith other methods. The first comparison is

con-ducted topresent thedifferences betweentheidentification of

SPScomponentswithconventionalserviceblueprint(Bitneretal.,

2008),theproduct-extensionservice(PSE)blueprint(Songetal.,

2015)and theproposed SPSblueprint. The second comparison

servestoillustratethedifferentpartitionresultscausedby

differ-entcorrelationevaluationmethods(i.e.crispnumber-based,fuzzy

number-based, rough number-based and the proposed

rough-fuzzynumber-based).Thethirdcomparisonaimstouncoverthe

differencesbetweenthemodularizationresultsoftheclassicalGN

algorithm(NewmanandGirvan,2004)andtheproposedmodified

(16)

Fig.7.ThedendrogramofSGMSmodulespartition.

5.1. ComparisonsbetweendifferentmethodsforSPScomponents

identification

Comparedwiththetraditionalserviceblueprint(Bitneretal.,

2008)andthePSEblueprint(Songetal.,2015),theproposed

CPS-basedSPSblueprintembedsthepropertiesofsmartcapabilitiesand

considersthechangesofserviceoperationundertheapplicationof

smarttechnologies.Theproposedblueprintcanreflectthe

com-plexinteractionsbetweenthephysicalproduct/serviceoperation

spaceandcyberproduct/serviceoperationspace.The

compar-ative resultsin Table6 shows that theproposedSPS blueprint

presentsmoreadaptivenessandfeasibilitytoidentifythesmart

servicecomponentsinthecontextofsmart PSSfromthreekey

aspects:blueprintsstructures,interactionpresentationand

appli-cationscope,comparedwiththetraditionalserviceblueprintand

PSEblueprint.

Fig.8.Themodularitydistributionwithdifferentmethods.

5.2. Comparisonsbetweendifferentmethodsforcorrelation

evaluation

This comparison mainly reveals the strength of the

pro-posed rough-fuzzy number-based evaluation method in the

manipulationofintrapersonallinguisticuncertaintyand

interper-sonalpreferencediversitycomparingwiththecrisp-based,fuzzy

number-basedandrough-basedmethodsinthesamecase.The

lin-guisticresponsesfrommultipleexpertsarerespectivelyconverted

intoanaveragenumber,triangularfuzzynumber,roughnumber

andrough-fuzzynumber.Incrisp-basedapproach,thejudgements

entered intotheevaluation process arethearithmetical means

ofthefiveDMs’initialscores.Inthefuzzy-basedapproach, the

groupaveragefuzzyintervalsnumberisacquiredbycalculatingthe

arithmeticalmeanvalueofthegroupfuzzyjudgements.Moreover,

aroughprocedureisadoptedforaggregatinggroupcrisp

judge-mentstoinformthegroupaverageroughintervalsnumberinthe

rough-basedmethod.

Fig.8presents therelationshipbetweenthemodularityand

themodularizationschemeswithdifferentmethods.Theabscissa

MSi representsthemodularization schemewithiservice

mod-ules, and theordinate denotes the modularity of the obtained

partitionscheme.Thedistributioncurvemarkedas“rough-fuzzy

correlationandmodifiedGN”isobtainedbyusingtheproposed

rough-fuzzynumber-basedevaluationmethodandtheproposed

modifiedGNalgorithm.Similarly,thecurvesmarkedascrisp,fuzzy

and roughcorrelationandmodified GNareseparatelyacquired

byusingthecrispnumber-based,fuzzynumber-basedandrough

number-basedevaluationmethods,withthesamemodifiedGN

algorithm.Theresultsshowthatthemodularitypresentedwith

thefourevaluationmethodshaveasimilarchangetrend,i.e.the

parabolagoingdownwardsinonedirection.However,theoptimal

modularityobtainedintheproposedrough-fuzzymethodemerges

atthemodularizationschemewithsixservicemodules,whilethe

optimaloneacquiredintheotherthreemethodsuniformlyoccur

atthemodularizationschemeswithfourservicemodules.In

addi-tion,asshowninFig.9(a),(c)and(d),theoptimalmodularization

schemewiththeproposedrough-fuzzymethodisdifferentwith

the onesobtainedwith theother three methods. For instance,

theoptimalschemewiththerough-fuzzymethodhavesix

ser-vicemodules,amongwhichtheSGMScomponentsSC43andSC44

emergeinthesameindependentmodule.However,allthe

Figure

Fig. 1. The proposed framework for SPS modularization.
Fig. 2. CPS-based SPS blueprint.
Fig. 4. Example process of edge betweenness determination.
Fig. 5. CPS-based smart gearbox maintenance service blueprint.
+3

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