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Nicolas PERRY, Mehdi EL AMINE, Jérôme PAILHES - Exploring design space in embodiment
design with consideration of models accuracy - CIRP Annals - Manufacturing Technology - Vol.
64, n°1, p.181–184 - 2015
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Exploring
design
space
in
embodiment
design
with
consideration
of
models
accuracy
Nicolas
Perry
(2)
*
,
Mehdi
El
Amine,
Je´roˆme
Pailhe`s
ArtsetMe´tiersParisTech,I2M–UMR5295,F-33400Talence,France1. Introductionandstateofart
Life-cyclecostcanbeinfluencedupto70%bydecisionstaken
duringconceptualandembodimentdesignstages[1]. Theneedof
supportingdecisionmakingbyadequatetheoriesand
methodolo-giesisthusgreatestatthesestages.For manyyears,designhas
beenmostlydependentoncompanies’know-howanddesigners’
tacitknowledge[2]. Nowadays,agreatpartofdevelopmenttime
in design departments is spenton numerical calculationusing
behaviourmodels.Giventhemultitudehypothesis and
approx-imationsadopted inthesemodels,their capacity toadequately
representproductbehaviourshasalwaysbeenacriticalissuefor
designers. In addition, it is difficult to effectively qualify the
accuracy of results provided by these behaviour models. This
usuallyleadstoalong‘‘trial-and-error’’processinwhichseveral
physicalprototypesarerealizedandtested.Thisisafrequentcause
ofcost overrunsand scheduledelays. Moreover, it provides no
guaranteeofapproachingtheoptimalsolution.Withinthiswork,
the objective is to propose a multi-criteria decision-making
methodthataimstomaximizethesatisfactionofdesignobjectives
witha considerationoftheriskassociatedwiththeaccuracyof
behaviourmodels.
Multi-criteriadecision makingisa verycomplex problemin
modernindustry.AsclearlyexplainedbyKrauseandGolm[3]and
Elwanyet al.[4],itisprincipallyduetotheheterogeneousand
contradictorynatureofdesignobjectives,andtodataimprecision.
Intheframeworkofdecisionmakinginengineeringdesign,the
MethodofImprecision(MoI)proposedbyOttoandAntonsson[5]
hasdemonstrateditsefficiency.Itallowsdesignerstoformalize
imprecision in Design Alternative (DA) evaluation using fuzzy
logic.EachDAisthenevaluatedusingseveralpreferencevalues
which are finally aggregated into a generalized preference. In
addition, theMoIproposes axioms toprovide a framework for
applicationtothefieldofengineeringdesign,andtheabilitytouse
differentstrategiestoexpressthewillofdesigners.MoIprovides
solidtheoreticalbasisinthefieldofdecisionmakinginengineering
design.However,themainlimitofthisapproach,inourcontext
andforourpointofview,isthattheevaluationofDAdoesnottake
intoaccounttheaccuracydegreeofbehaviourmodels(ordata)
usedfortheevaluationofDA.Asanexample,twoDAmayillicitthe
same performance in term of achievementof design goals but
the risk related to the accuracy of behaviour models may be
different.TheattitudeofDecisionMaker(DM)inthiscasewillnot
bethesame.
Inaccuracy of behaviours models is due to: simplifying
hypotheses,uncertaintyintheidentificationofmodelparameters
and,inaccuracyofdigitalresolution[6].Evaluatingtheaccuracyof
abehaviourmodelisadifficulttask.Intheabsenceofsignificant
backgrounddata,statisticaltoolssuchacase-basedreasoningor
artificialneuralnetworkcannotbeused.Inthepresentcontext,we
supposethatreferencepointsexistandcorrespondtoresultsof
experimental testson realscale 1 prototype. Inthis case, it is
recommended to measure accuracy as the distance between
behavioursmodelresultandreferencepoints[7,8].Accordingto
Vernatet al.[7],theaccuracyestimationcriteriacanbelocalor
globalcriteria.Alocalerrorestimatecanbegiven,forexample,
throughthemaximum(Eq.(1))orminimumoftheabsoluteerror
inthemeasuredpoints,orsimplybytheerrorataparticularpoint.
Aglobalerrorestimatecanbegivenforexamplebythesquared
error(Eq.(2))allowsforexampletoobtainageneraltrendofthe
errorontheentiredesignspace.Itisrecommendedtocompare
theobtaineddistancewithathresholdvalueoraccuracyobjective
[7,8]. EM¼maxiX˜iXi (1) Keywords: Decisionmaking Design Conceptsmaturity ABSTRACT
Reworktasksincollaborativedevelopmentprojectsdealingwithimmaturedesignconceptsarevery frequentandareresponsibleofcostoverrunsandscheduledelays.Takingintoaccountuncertaintyand accuracyofmodels(anddata)improvesdecisionmakingaccordingtostrategicorientationforproduct development.Basedonarealdesignoflight,slenderbutrigidsolarcollectorsupports,multipletoolshave beendevelopedandtestedtosupportdecisionmakingatdifferentstagesofdevelopmentprocess.The objectiveofthispaperistoinvestigatetheintegrationoftheseaccuracyevaluationsintothedesign process.Thisproposalisvalidatedbytheindustrialdevelopmentandvalidation.
* Correspondingauthor.
¯ E ¼X n i¼1 1 n X˜iXi (1’)
Thelimitofsuchameasureofaccuracyoccurswhenthereare
veryfewreferencepointsandalargedesignalternativesspaceto
explore.Inthiscase,itisverydifficulttojustifythevalidityofthis
accuracymeasureinalldesignalternativesspace.
2. Proposedapproach
Whenexploringthesetofpossibledesignalternativesusingthe
results of behaviour models, decision maker’s preferences are
drivenbytwomainconsiderations:(i)maximizingthesatisfaction
ofdesignobjectives,and(ii)minimizingtheriskassociatedtothe
inaccuracyofbehaviourmodelsused.Intheproposedapproach,
thesetwoconsiderationsarerepresentedbynumericalindicators
that are respectively Overall Desirability Indicator (ODI) and,
SafetyIndicator(SI).
2.1. Overalldesirabilityindicator(ODI)
ODI quantifythe generallevelof satisfactionachievedby a
DA.Themodelusedforitscalculation(Fig. 1)issimilartoMoI
[5]. Startingfrom agivenDA thatis definedbythechoice of
design parameters (structural dimensions, materials, etc.),
behavioursmodels areusedtodetermine thesetofquantities
needed to assessthe achievement of design objectives (mass,
maximumstress,carbonfootprint,etc.).Theresultingquantities
arecalledObservationVariables(OV).ForeachOV,aDesirability
Index(DI)between0and1 isthenaffectedtoexpressthelevel
ofsatisfactionofthecorrespondingdesignobjective(Fig. 2).In
our approach, this process is made using the adjustable
desirability function proposed by Harrington’s [9] because of
its ease of parametrization and its appropriateness to the
differentkindsofdesignobjectives.TheODIisobtainedbythe
aggregation of DI of each design objectives. The aggregation
function used is Generalized Ordered Weighted Averaging
(GOWA) operator (Eq. (4)) proposed by Yager [10]. This
functionwaschosensincetheaggregationstrategyis
complete-lyadjustable bythechoiceof:(i)designobjectivesweightswi
thatexpresstheirrelativesimportanceand,(ii)theparameters
that reflects the level of compensation between design
objectives. Scott [11] proves that any DA in Pareto front can
bereachedbyadjustingwiands. Theinterpretationofthegiven
weightsisnot absolutebutdependsonthelevelof
compensa-tion (expressed by s). Inother way, the method used for the
determination of weight musttake into account the value of
s. In order to respect this constraint, we use in this work
the method of indifference points [11] that is based on the
definitionofindifferencedesignalternativesthatelicitthesame
performance, to determine simultaneouslya unique value for
thetrade-offstrategyandfortheweightratio.
ODI¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn j ðwjðDIjÞsÞ s v u u t (2)
The step of defining desirability functions and aggregation
function constitute a mean for capitalizing on knowledge
associated withdecision making.Italsoallows theautomation
thecalculation processvia theformalization ofdecision maker
preferences.ThisfacilitatesthetreatmentofseveralDA.Another
advantageofaggregationprocessisthatitrepresentsameanof
negotiating different and usually conflicting design objectives,
whichfacilitateinformationexchange,mutualunderstanding,and
jointdecision-makingincollaborativedevelopment[12].
2.2. Safetyindicator(SI)
Arecognizedprincipleinengineeringdesigndecisionsisthatof
annihilation [5,13,14]. It states that a minimum threshold is
required for each design objective, and if also one of these
thresholds is unmet, the DA is rejected regardless of the
satisfaction level of the otherdesign objectives.So, one of the
mainconcernsofdecisionmakersistoensurethesatisfactionof
these minimum thresholds. The proposed Safety Indicator (SI)
aims to assess the risk of not meeting the corresponding
acceptancethresholdduetotheinaccuracyofbehaviourmodels
used.Givenadesignalternative,aSafetyIndicator(SI)iscalculated
foreachdesignobjectiveanditsvalueistobemaximized.Inorder
tobeconservative,theminimumvalueisconsideredbetweenthe
differentSI.TheproceduretocalculateSIisinspiredfromFMEA
(Failure Mode Effects Analysis). Three factors are taken into
account:theoccurrenceoftherisk(O),thegravityofnotsatisfying
the acceptance threshold (G) and, the detectability (C). As the
classicFMEA,gravityisestimatedusinganumericalscale(from
Fig.1.EvaluationmodelofOverallDesirabilityIndicator.
Fig.2.Desirabilityandconfidencefunctions. 181–184
0.2 to1)associatedwithsemanticexpressions.Themethodsof
calculationofOandCareexplainedbelow.SIiscalculatedbythe
relation:
SI¼OGD (3)
2.2.1. Occurrenceoftherisk(O)
This factor is obtained by the relative distance between
Observation Variables (OV) calculated by behaviour model and
theacceptance threshold. Itis considered that thegreater this
distance is, the lower is the risk of not respecting acceptance
thresholdduetothelowaccuracyofbehaviourmodel.Inorderto
takeintoaccountthevaguenessofacceptancethreshold,amean
distancewascalculatedusingtwovaluesOV1
t andOVt2(Eq.(4)).
O¼1
2ðDðOVm0OV
1
tÞþDðOVm0OVt2ÞÞ (4)
whereDisthedistancedefinedby:
Dða;bÞ¼ ab j j b if a>b 0 if a<b 8 < : (5) 2.2.2. Detectability(D)
Inourcase,itisassumedthatatleastonedesignalternativehas
beenprototypedandtested.Itisconsideredasareferencepointto
evaluatetheaccuracyofbehaviourmodel.Foragivenobservation
variable, the accuracy of the model is given by the distance
betweenthevaluegivenbybehaviourmodel(OVi)andthevalue
givenbyexperimentalmeasuresonphysicalprototype ˜O ˜Vi. The
distanceusedis:
D0ðOV i; ˜O ˜ViÞ¼ OV ˜O ˜Vi ˜ O ˜Vi (6)
Theconditionsinwhichexperimentaltestsonprototypewas
performed may be different of real environment. Moreover,
measuring instruments always exhibit a certain imprecision.
Experimental measures ˜O ˜Vi are thus subject to imprecision.
Assumingthatexperimentalmeasureiscomprisedbetween ˜O ˜V1i
and ˜O ˜V2i, we consider an average distance E obtained by the
followingequations: E¼ 1 ðD0ðOVi; ˜O ˜ViÞÞ D0 s if D0 ð ˜O ˜Vi;OViÞ<D0s 0 if D0ð ˜O ˜V i;OViÞ>D0s 8 > < > : (7) D0ðOVi; ˜O ˜ViÞ D E ¼D 0 ðOVi; ˜O ˜V 1 iÞþD 0 ðOVi; ˜O ˜V 2 iÞ 2 (8)
D0sisathresholddistanceoverwhichthemodelisconsidered
unusablebythedesigner.Inourcasestudy,weadoptavalueof
0.20 foreachobservationvariable.
The distance E is calculated for the design alternative
correspondingtotheprototype.Foradifferentdesignalternative,
in which different design parameters are used, this accuracy
measureisnolongervalid.Inordertocorrectthisindicator,itis
multiplied by a second term (Eq. (9)) that represents the
degradationofbehaviourmodelexactnessrelatedtothedistance
oftheevaluateddesignalternativefromthephysicalprototype.
D¼EY n i CDi¼ Yn i giðDPiDPoÞ (9)
n is the number of design parameters and CIi is a parameter
comprised between 0 and 1 and express the degradation of
measuredaccuracyE. Itiscalculatedusingconfidencefunctionsgi
(Fig. 2)thatexpressCDiasafunctionofthedistancebetweenthe
design parameter of the reference solution CDo and that of
candidate solution CDi. As shown in Fig. 2, this function is
parametrizedusing twopoints thatare estimatedby designers
involved in the development of the product. This additional
information allowsextendingtheuseof initialaccuracy
assess-menttoalldesignalternativesspace.
3. Applicationtotheindustrialcase
Inaconcentratedsolarpower(CSP)plant,themainfunctionof
solar collectors is to concentrate and redirect sunlight onto
absorbertubestoheatuptheworkingfluid.Thesolarcollectoris
composedofreflectiveplates(reflectiveglassesplatesorpolished
aluminiumplates)andasupportingstructurewhosefunctionisto
give andmaintain reflectiveplates shape (Fig. 3). A mounting
device is placed between the reflecting surface plates and the
supportingstructuretoensuretheconnectionbetweenthem.In
ourstudy,onlysupportingstructure isconsidered. Theconcept
selectedinconceptualdesignphaseistrussstructure.Thecostof
rawmaterialforthemanufacturingofsolarcollectorsrepresents
50%ofinvestmentcostforaCSPplant[15]. Itisthusimportantto
reducethestructuremass(objectiveDI3).Inaddition,inorderto
maintainagoodopticalperformance,elasticdeformationofthe
structuremustremainaslowaspossible(objectiveDI1).Finally,it
mustresistahighwindpressuretobeusableforamultitudeof
implementation sites (objective DI2). More details about the
productaregivenin[14].
A first behaviour model based on bars-type finite element
analysishasbeenproposedtoevaluateOV. Using thismodel,a
designofexperimentofdesignparametershasbeenperformedand
afirstDAhasbeenselectedforprototyping(Fig.3).Thecomparison
betweenmechanicaltestsandbehavioursmodelOVrevealsmajor
discrepancies(until35%oferror).Thefirstbehaviourmodelisnot
adapted to this structure since it does not correctly reproduce
physique phenomena in nods connexions, which are strongly
involved in the evaluation observation variables. A second
behaviourmodelhasbeenproposedusingshell-typefiniteelement
analysiswithahighlyrefined meshingin nodsconnexions.The
prototypetestingresultswereusedasareferencepointtotestthe
accuracyoftheimprovedbehaviourmodelandaseconddesignof
experiment procedure has been performed by varying design
parametersintheestablishedranges.EachofDAhasbeentestedin
termofODIandSI.Fig.4showstheresultsofdesignofexperiment.
At this stage of development, decisionsare required on the
evolution of actual DA (prototyped alternative) and on the
developmenttasksneededtothisdecision.Trade-offmustbedone
betweenODIandSI.Manyelementsaretobetakenintoaccount.In
thisparagraph,generalguidelinesarederived.Inthecasewhere
thedeadline of validating theproduct is approaching, decision
wouldpreferasolutioninZone1(Fig. 4)sincehavingafeasible
solutionisapressingissueinthiscase.Inothercircumstances,DM
wouldprefertoexploreDAwithhigherODI(Zone2 orZone3)
even with a low SI. But such a decision implies further
investigationsandfurthertimetoimproveSIofchosenDA.These
couldbedoneeitherbyimprovingbehaviourmodelssothatthe
accuracycomparedwithreferencepointwillbetterorbyrealizing
otherprototypesandothermechanicaltestsfortheselectedDA.In
ourcase,wecanobserveinFig. 4thatanimportantgapbetween
ODIofthereferencepointandthemaximumODIachievableduring
theseconddesignofexperiment.Suchapotentialofimprovement
cannotbeignored.DesignalternativeswithhighODIelicitalowSI
whichpreventstheirdirectvalidation.Furtherdevelopmenttasks
mustbedoneinourcasetoimprovethisSI.
Alternative structure that has already been developed and
testedinanexperimentalCSPplanthastobetakenintoaccountin
reasoning.ItsODIisestimatedto0.53butitsmainadvantageisits
highmaturitylevel.Itrepresentsaguaranteefordecisionmakers
sinceitcanbedirectlyintroducedtothesystem.Inthiscase,itis
moreacceptableforthecaseoftrussstructuretoexploreDAwith
lowSI.Thisscenarioisverycommonindesigndepartments.They
are usually encouraged to have a feasible solution with high
maturitydegreetoreducerisk.
Inourindustrialcase,thestrategicdecisionistoadopta
low-cost CSP plant. In the proposed approach, it is expressed by
assigninghighweighttotheobjectiveofstructuremassreduction
comparedwiththeotherdesignobjectives.Inmanysituations,the
decision maker wishes to know the effect of giving more
importance to some design objectives compared to others.
Thereby, we haveconsidered a second scenarioin which more
importanceisgiventoopticalperformance(whichimpactsenergy
efficiencyoftheCSPplant) comparedtostructuremass.Fig. 5
showstheresultsofODIandSIcalculationforthisscenario.Itcan
be seen that the cartography of ODI and SI changed. Such a
modificationindevelopmentstrategycanbedoneatearlyphases
ofdevelopmentprocessandimplyhavingaholisticviewofthe
global system by trying to understand how individual design
decisionsimpacthigh-levelattributesofthesystem[16].
4. Conclusionandfutureworks
Inthiswork,amulti-criteriadecisionmakingmodelisproposed
andtestedfortheselectionofdesignparameters.Itisbasedonthe
maximization of the satisfaction of design objectives and
minimization of the risk associated with the low accuracy of
behavioursmodels.Theconstructionofproposedindicatorspasses
through the formalization of preferences associated with the
achievementofdesignobjectivesaswellasthedecisionmaker
attitudetowardsrisk.Thedevelopmentcostofthismulticriteria
decision model is counterbalanced by the capitalization on
knowledge associated with decision making and the ability to
treat a broad spectrum of design alternatives. The strength of
proposedaccuracymeasure(detectability)is tocombine onthe
onehandanobjectivemeasurethat istheerrorfromreference
pointandontheotherhandasubjectivemeasurethatexpressthe
degradation of the initial accuracy measure in function of the
distance of DP from reference point. This combination allows
havinganaccuracymeasurethatcoversalldesignspace.Afuture
stepistoprovidethresholds forSIinordertoidentifyadesign
alternativethatcanbedirectlyintroducedtothesystemandto
treatothercasestudies.
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Fig.4.ODIandSIforeachcandidatesolutionforthefirstscenario.
