ML19011A427
| ML19011A427 | |
| Person / Time | |
|---|---|
| Issue date: | 01/16/2019 |
| From: | Office of Nuclear Regulatory Research |
| To: | |
| Nathan Siu 415-0744 | |
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| Download: ML19011A427 (32) | |
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Uncertainty and UncertaintiesLecture 3-21 Key TopicsTypes of uncertainty (as treated in NPP PRA): aleatory and epistemicEpistemic uncertaintyCharacterization (subjective probability)Magnitude for typical parametersTypes: completeness, model, parameter2Overview ResourcesG. ApostolakissubjectivisticNuclear Safety, 9, 305315, 1978.G. ApostolakisScience, 250, 13591364, 1990. DecisionmakingNUREG-2201, U.S. Nuclear Regulatory Commission, September 2016.Uncertainties Associated with PRAs in Risk-NUREG-1855, Revision 1, March 2013.National Academy of Sciences Proceedings (NASP), 111, No. 20, 7176-7184, May 20, 2014.3Overview Other ReferencesA. Mosleh, et al., Model Uncertainty: Its Characterization and Quantification, Center for Reliability Engineering, University of Maryland, College Park, MD, 1995. (Also available as NUREG/CP-0138)N. Siu, D. Karydas, and J. Temple, "Bayesian Assessment of Modeling Uncertainty: Application to Fire Risk Assessment," in Analysis and Management of Uncertainty: Theory and Application, B.M. Ayyub, M.M. Gupta, and L.N. Kanal, eds., North-Holland, 1992, pp. 351-361.E. DroguettRisk Analysis, 28, No. 5, 1457-1476, 2008.https://nrcoe.inl.gov/resultsdb/RADS/https://nrcoe.inl.gov/resultsdb/AvgPerf/4Overview Other References (cont.)W.E. VeselyNUREG/CR-3385, July 1983.Proceedings 5th International Topical Meeting on Nuclear Thermal Hydraulics, Operations, and Safety (NUTHOS-5), Beijing, China, April 14-18, 1997, pp. L.4-1 through L.4-6.American Nuclear Society and the Institute of Electrical and -2300, January 1983.a thermal-Nuclear Engineering and Design, 241, 310-327, 2011.5Overview The Big Picture (Level 1)CDF is a measure of uncertaintyRandom variables:number of core damage eventstime to a core damage event6How well do we know CDF?Motivation Types of Uncertainty Addressed by NPP PRA/RIDMAleatory (random, stochastic)Irreducible Examples:How many times a safety relief valve (SRV) operates before failingHow long it takes for operators to initiate a fire response procedureModeling addressed in Lecture 3-1Epistemic (state-of-knowledge)ReducibleExamples:7Types of Uncertainty Indicators of UncertaintyPercentilesth, 95th)MomentsGeneralMeanVariance8 950%95%could easily be above or below 4.6E-5 (the median)Very confident is below 7.8E-5 (the 95thpercentile)Subjective ProbabilityProbability is an internal measure of degree of belief in a propositionTo be useful, need:Consistent scale for comparing judgmentsConvergence with classical (relative frequency) probabilities given enough dataprobabilities conform to the laws of probabilityEpistemic Uncertainty: Characterization Qualitative to Quantitative: Examples10National Academy of Sciences Proceedings (NASP), 111, No. 20, 7176-7184, May 20, 2014.Epistemic Uncertainty: CharacterizationNUREG/CR-6771 Aleatory vs. Epistemic Relationship Subjective view: all uncertainties are epistemic. Aleatory modelsupports quantificationsupports communication regarding model parametersCoin toss exampleUncertain proposition X: observation of nmtosses (trials)P{XlC,H} can include consideration of conditions: fairness of coin, tossing, measurement; whether outcomes are truly binaryaleatory (binomial) distribution:If there is uncertainty in the conditions, as reflected by a probability distribution for , the total probability is the expectation of the aleatory result:11epistemic distribution for Types of Uncertainty Aleatory vs. Epistemic Uncertainty Commentary and ObservationsExample: Weld crack propagation depends on local material conditions (e.g., Cu content, flaw geometry).Aleatory model: conditions have a statistical distribution. Epistemic model: local conditions are knowable (in principle).at a randomly sampled location vs. conditions at a specific location).Practice of distinction is generally accepted, has proven useful in RIDM.modeling convention (used in these lectures).Terminology has been (and remains) a source of angst.Some arguments in the broader risk community for alternate measures of epistemic uncertainty (e.g., possibility, degree of membership)12Types of Uncertainty PRA Uncertainties Various Studies13Epistemic Uncertainty: Magnitude NUREG-1150 Uncertainties Another View140.0E+005.0E+041.0E+051.5E+052.0E+052.5E+051.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03Probability Density FunctionCDF (/ry)Surry InternalSurry EQSurry FireSurry TotalEstimatedEpistemic Uncertainty: Magnitude NUREG-1150 Uncertainties Another View150.0E+005.0E+041.0E+051.5E+052.0E+052.5E+050.E+002.E-054.E-056.E-058.E-051.E-04Probability Density FunctionCDF (/ry)Surry InternalSurry EQSurry FireSurry TotalEstimatedEpistemic Uncertainty: Magnitude PRA Uncertainties Indian Point (1980s)16Epistemic Uncertainty: Magnitude Knowledge CheckWhy do the NUREG-1150 curves get progressively taller with smaller values of CDF?What does this tell you about the Indian Point graph?17Epistemic Uncertainty: Characterization Types of Epistemic UncertaintyCompletenessModelCompeting modelsParameter Conditioned on model18Epistemic Uncertainty: Types Parameter UncertaintyTypically characterized using parametric distributions (e.g., beta, gamma, lognormal)Parameters estimated using Bayes Theorem (see Lecture 5-1)Statistical evidence (operational experience, test results); engineering judgment in processingLarge amounts of data => subjective probabilities converge with evidenceSmall amounts of data => large uncertaintiesNote: pooling data increases confidence in estimates for population, but not necessarily for NPP studied.19Epistemic Uncertainty: Types Generic Demand Failure Probabilities2015 Industry-wide estimates from: https://nrcoe.inl.gov/resultsdb/AvgPerf/Explosive valves: 3 failures in 713 trialsSBO EDGs: 12 failures in 419 trialsEDGs: 214 failures in 75,452 trials2001002003004005000.000.010.020.030.040.050.06Probability Density FunctionFailure ProbabilityDemand FailuresExplosive ValvesSBO EDGEDG01002003004005001.00E-041.00E-031.00E-021.00E-01Probability Density FunctionFailure ProbabilityDemand FailuresExplosive ValvesSBO EDGEDGEpistemic Uncertainty: Magnitude Generic Runtime Failure Rates212015 Industry-wide estimates from: https://nrcoe.inl.gov/resultsdb/AvgPerf/Service Water Pumps: 2 failures in 16,292,670 hour0.00775 days <br />0.186 hours <br />0.00111 weeks <br />2.54935e-4 months <br />sNormally Running Pumps: 225 failures in 59,582,350 hour0.00405 days <br />0.0972 hours <br />5.787037e-4 weeks <br />1.33175e-4 months <br />sStandby Pumps (1sthour operation): 48 failures in 437,647 hour0.00749 days <br />0.18 hours <br />0.00107 weeks <br />2.461835e-4 months <br />s0.000.200.400.600.801.001.00E-091.00E-081.00E-071.00E-061.00E-051.00E-041.00E-03Probability Density Function (Normalized)Failure Rate (/hr)Runtime FailuresService WaterNormally RunningStandbyalert user to potential irregularitiesEpistemic Uncertainty: Magnitude Model UncertaintyCurrently only requirements for characterization (not quantification)sensitivity studiesIf appropriately defined, uncertainties can be quantified and brought into the PRAFocus on observables, difference between prediction and Limited applications in practice22Epistemic Uncertainty: Types Thought ExerciseUnder what conditions could a flawed consensus 23Epistemic Uncertainty: Types Example Quantification of Model Uncertaintyestimates based on comparisons with experimentsDRM for cable fire propagation velocityUncertainty factor (a random variable)Note: bias in results indicates need for better DRM24N. Siu, D. Karydas, and J. Temple, "Bayesian Assessment of Modeling Uncertainty: Application to Fire Risk Assessment," in Analysis and Management of Uncertainty: Theory and Application, B.M. Ayyub, M.M. Gupta, and L.N. Kanal, eds., North-Holland, 1992, pp. 351-361.0.000.010.020.030.040.05020406080100Probability Density FunctionModel Uncertainty Factor055095E[]3.814.856.918.6Epistemic Uncertainty: Types Another Example Quantification of Model UncertaintyTime (s)Experiment (K)DRM (K)18040045036046551072053056084055056525E. DroguettRisk Analysis, 28, No. 5, 1457-1476, 2008.Notes:1)Bayesian methodology accounts for possibility of inhomogeneous data.2)Very large uncertainty bands might be unrealistic.Epistemic Uncertainty: Types Model Uncertainty Quantification Other ConsiderationsPerspective mattersModel developer ability of model to address phenomenaPRA user include user effectsUncertainties in unmeasured parametersSub-model limits of applicability26M.H. Salley-1824 Supplement 1/EPRI 3002002182, November 2016.Epistemic Uncertainty: Types Completeness Uncertainty Example Known SourcesIntentional acts (sabotage/terrorism)Operator errors of commissionOrganizational influencesSafety cultureExternal influences during an accidentDesign errorsPhenomenological complexitiesCombinations of severe hazardsNewly recognized hazards27Epistemic Uncertainty: Types Propagation of UncertaintiesEventual aim: state uncertainty in risk metric estimatescontributing parameters through PRA model28notation used to indicate epistemic distributionEpistemic Uncertainty: Overall Characterization Propagation of Uncertainties -MethodsMethod of momentsSamplingDirect Monte CarloLatin HypercubeAdvanced methods for computationally challenging situationsImportance sampling (line sampling, subset Surrogate models (response surface, Gaussian 29Epistemic Uncertainty: Overall Characterization Sensitivity AnalysisTypical approach for treating model uncertaintiesIn PRA/RIDM context, need to ensure analysis provides useful informationSpecific insights supporting decision problem (e.g., whether variation could lead to different decision)Importance measures, routinely available from current -at-a-sensitivity calculationsAdvanced tools (e.g., global sensitivity analysis) available but not routinely used30Epistemic Uncertainty: Overall Characterization Importance MeasuresSome notation: R = risk metric of interest, Pi= probability of event iCommon measures: 31MeasureDefinitionAlternateNotesFussell-Vesely(F-V)Same rankings as RRW and RRRBirnbaumNearly same rankings as RAW and RIRRisk Achievement Worth (RAW)Nearly same rankings as BirnbaumRisk Increase Ratio (RIR)Nearly same rankings as BirnbaumRisk Reduction Worth (RRW)Same rankings as F-VRisk Reduction Ratio (RRR)Same rankings as F-VEpistemic Uncertainty: Overall Characterization Once uncertainties are characterized, then what?See Lecture 8-132Epistemic Uncertainty: Overall Characterization