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).
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
caDepartmentofIndustrialEngineeringandManagement,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
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
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
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
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
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
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
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 ukarerespectivelytheelementsoflower
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) (lsLij,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 ijcanbeacquiredbyusingroughcomputation
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
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.
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=1ifthevertexiandvertexjareinthesamemodule,otherwisesisj=-1.
Aij=
1, ifwij=/0;
0, ifwij=0.
(22)
Finally,byfollowingthesixstepsabove,aSPScomponent
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
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
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
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
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