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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering
ComparisonofNon-StandardSimulationMethodsforPerformingExtremelyLowProbabilityAssessments
RobertE.Kurth,CédricJ.Sallaberry
EngineeringMechanicsCorporationofColumbus(Emc2)3518RiversideDrive-Suite202
Columbus,OH43221-1735Phone:(614)459-3200Fax:(614)459-6800
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 2
PSAM 14 – Los Angeles (CA)
• In1985,theNRCproposedaModificationofGeneralDesignCriterion(GDC)4RequirementsforProtectionofDynamicEffectsofPostulatedPipeRupturesin10CFRPart50.▫ TheproposedamendmentswouldmodifyGDC4toallowforthedemonstrationof
pipinganalysestoserveasabasisforexcludingconsiderationofdynamiceffectsassociatedwithcertainpiperuptures.
▫ Theseanalysesconstitutewhatiscommonlyreferredtoastheleak-before-break(LBB)concept.
• Thefinalrulerequiresadeterministicfracturemechanicsanalysis• Thesupportingsafetyanalysismustdemonstratethatasubstantialrangeofstablepipecracksizescanexistwithdetectableleaks• Thattheprobabilityoffluidsystemspipingruptureisextremelylowunderconditionsconsistentwiththedesignbasisforthepiping.• Thedefinitionof“extremelylowprobability”ofpiperuptureisgivenontheorderof10-6perreactoryearwhenallpiperupturelocationsareconsidered.• Thisprobabilityincludestheprobabilityofaninitiatingeventoccurringsuchasanearthquakeoranaccident.
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 3
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• Presently,theStandardReviewPlan(SRP)3.6.3doesnotallowforassessmentofpipingsystemswithactivedegradationmechanisms,suchasPrimaryWaterStressCorrosionCracking(PWSCC),whichhasoccurredinsystemsthathavepreviouslybeengrantedLBBexemptions
• Along-termgoalhasbeentodevelopamodular-based,probabilisticfracturemechanicscodecapableofdeterminingtheprobabilityofruptureforReactorCoolantSystem(RCS)components.
▫ Theneedforthismodular-basedcodeisstronglydrivenbytheneedtoquantitativelyassessanLBB-approvedpipingsystem’scompliancewithGDC-4onaninterval(time)basis.
▫ BasedontheterminologyofGDC-4,thisprogramandcodeisentitledExtremelyLowProbabilityofRupture(xLPR).
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 4
• xLPR2.0hasbeencompleted▫ ItemploystheGoldSim®platformfortheprobabilisticcalculations▫ ItisafullyQA’edcodeforuseinregulatoryassessments▫ Becauseofthisoverheadeachsimulation,whichcoverstheentirepipelinelife,
takesapproximately4seconds
• BecausetheabilitytocomplywithGDC4implies,forasimplerandomsamplingmethod,5to10millionsimulationswouldbeneededalternativestrategieshavebeendeveloped▫ Simplerandomsampling▫ LatinHypercubeSampling(LHS)▫ ImportanceSampling▫ AdaptiveImportancesampling*
• Thefocusofthispaperisontheadaptiveimportancesampling
PSAM 14 – Los Angeles (CA)
*DetailsofthesetopicscanbefoundinPSAM103:“Efficientsamplingstrategiestoestimateextremelylowprobabilities”,C.Sallaberry,R.Kurth,F.Brust,E.Twombly
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 5
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SRS LHS DPD
Better multi-dimensional coverage for DPD. Helps in conjoint influence
Densely cover of each input with LHS. Helps if extreme value are needed
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 6
• Thedetailsofthemethodology,whichislabeledGRC(GoldenRuleClusteringsincethemethodisbasedontheFibonaccisequence)• Insteadweillustratetheapplicationtotwoproblems:▫ AtheoreticalproblemtoillustratetheGRCmethod▫ Ananalysisoftheapipingproblemwhere
! Timetofirstcrackinitiation! Timetofirstleakage! Timeofpipefailure
arecalculated
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 7
• GRCmethodis▫ Variancereductiontechnique▫ Purposeistooversampletheregionofinterestandunder-sampletheregions
withnoevents.
▫ InthetheoreticalproblemThreeareasofinterest,morethantwostandarddeviationsfromthecentroid,needtohavetheirprobabilityofoccurrenceestimated
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 8
• Forthetheoreticalproblemwewishtofindthepeaks• Adaptivesamplingfocusestheinputsontheareaswheretheresponseis“ofinterest”
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• Inthepictureonthebottomleftthe3DsurfaceisprojectedontotheX-Yplane▫ RedpointsareSRS▫ Bluepointsareadaptive
• Onthebottomrightthevaluesbelowalowerlimitareremoved
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 9
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• AcomparisonofthenormaldistributiontheoreticalCDF,theDPDrepresentation,andtheGRCrepresentationareshowntotheleft
• BoththeDPDandGRClieonthetheoreticalline.Agoodstart.
• TheDPDpoints,shownasanopenblackcircle,areuniformlyspacedalongthexaxisandthenmovedtotheconditionalmeanvalue
• TheGRCpointsdependonthevalueoftheinputwhenaresponseofinterestisfound
• Forthissampletheinputwasat~15%value
• 50%oftheGRCpointsareplacedbelowthisvalue,theremainderabove
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 10
PSAM 14 – Los Angeles (CA)
• TheCDFandCCDFareshownfortheyieldstrength
• The“pivot”pointisnearthemean
• ThepointsaretheDPDvaluesaftertheadaptivealgorithmhasbeenapplied
• ClearlytherewillbemoresamplestakennearthepivotpointwhenthesamplingisbasedonthesimplerandomsamplingoftheintervalnotonthevalueoftheCDF
• TheDPDPDFareusedtofindtheweightingvaluefortheresponse
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 11
• BecausethefocusofGRC4isonanextremelylowprobabilityofrupturethreequantitiesareexamined▫ Timetofirstcrackinitiation▫ Timetofirstleakage▫ Timeofrupture
• BecauseoftheQArequirementsofxLPRtheGoldSim®platformcannotimplementtheGRCmethod
• Therefore,apreprocessortoxLPRhasbeenwrittenwhichimplementstheGRCmethod
• ThispreprocessoriscallPROMETHEUSandhasbeenreleasedasabetaversion,PROMETHEUS1.0
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 12
• Acomparisonoftheresultsforaprobabilisticanalysisisshown
• 2,500simulationusingSRSwithLHSxLPR2.0(dottedline)
• 100,000SRSsample(dashedline)
• 2,500GRCsample(solidline)
• All3methodsconvergetosample60yearresult
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• GRCresultestimatesthe100,000SRSresultthroughtheentirerange• Theuncertaintyislarger• Theabilitytoestimatethe1in100,000pointallowsthexLPRcodetofocus
samplingusingstandardimportancesamplingmethods
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Materials,StructuralIntegrityandReliabilitySolutionsThroughInnovativeEngineering 13
• Theuseofavarietyofsamplingmethodshavebeenstudiedtoallowefficientanalysisschemestobedevelopedto▫ Estimateextremelylowprobabilitiesofavarietyofevents▫ Identifytheareasoftheinputspacewhichleadtheeventsofinterest
• Muchsmallersamplesizescanbeusedtoidentifyareasofinterestforfocusedsampling• Comparisonofthemethodsshowsthat▫ TheSRS,LHS,andDPDmethodsallleadtostatisticallyequivalentmeanresults▫ TheGRCmethodfindsverylowprobabilityeventsmoreefficientlybutthecost
islargeruncertainty
• TheuseoftheGRCmethodallowslessefficient(basedonthenecessarynumberofsimulations)tobefocusedontheregionsoftheinputspaceleadingtorareevents• Thisfocusincreasestheefficiencyofthesecodes
PSAM 14 – Los Angeles (CA)