Cédric J. Sallaberry

Survey of sampling-based methods for uncertainty and sensitivity analysis

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (1) Definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (2) Generation of samples from uncertain analysis inputs, (3) Propagation of sampled inputs through an analysis, (4) Presentation of uncertainty analysis results, and (5) Determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition.

Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models

The analysis of many physical and engineering problems involves running complex computational models (simulation models, computer codes). With problems of this type, it is important to understand the relationships between the input variables (whose values are often imprecisely known) and the output. The goal of sensitivity analysis (SA) is to study this relationship and identify the most significant factors or variables affecting the results of the model. In this presentation, an improvement on existing methods for SA of complex computer models is described for use when the model is too computationally expensive for a standard Monte-Carlo analysis. In these situations, a meta-model or surrogate model can be used to estimate the necessary sensitivity index for each input. A sensitivity index is a measure of the variance in the response that is due to the uncertainty in an input. Most existing approaches to this problem either do not work well with a large number of input variables and/or they ignore the error involved in estimating a sensitivity index. Here, a new approach to sensitivity index estimation using meta-models and bootstrap confidence intervals is described that provides solutions to these drawbacks. Further, an efficient yet effective approach to incorporate this methodology into an actual SA is presented. Several simulated and real examples illustrate the utility of this approach. This framework can be extended to uncertainty analysis as well.

Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty

Three applications of sampling-based sensitivity analysis in conjunction with evidence theory representations for epistemic uncertainty in model inputs are described: (i) an initial exploratory analysis to assess model behavior and provide insights for additional analysis; (ii) a stepwise analysis showing the incremental effects of uncertain variables on complementary cumulative belief functions and complementary cumulative plausibility functions; and (iii) a summary analysis showing a spectrum of variance-based sensitivity analysis results that derive from probability spaces that are consistent with the evidence space under consideration.

Extension of Latin hypercube samples with correlated variables

A procedure for extending the size of a Latin hypercube sample (LHS) with rank correlated variables is described and illustrated. The extension procedure starts with an LHS of size m and associated rank correlation matrix C and constructs a new LHS of size 2m that contains the elements of the original LHS and has a rank correlation matrix that is close to the original rank correlation matrix C. The procedure is intended for use in conjunction with uncertainty and sensitivity analysis of computationally demanding models in which it is important to make efficient use of a necessarily limited number of model evaluations.

Conceptual basis for the definition and calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada

Abstract A deep geologic repository for high-level radioactive waste is under development by the US Department of Energy (DOE) at Yucca Mountain (YM), Nevada. As mandated in the Energy Policy Act of 1992, the US Environmental Protection Agency has promulgated public health and safety standards (i.e., 40 CFR Part 197) for the YM repository, and the US Nuclear Regulatory Commission has promulgated licensing standards (i.e., 10 CFR Parts 2, 19, 20, etc.) consistent with 40 CFR Part 197 that the DOE must establish are met in order for the YM repository to be licensed for operation. Important requirements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. relate to the determination of expected (i.e., mean) dose to a reasonably maximally exposed individual (RMEI) and the incorporation of uncertainty into this determination. This paper is the first part of a two-part presentation and describes how general and typically nonquantitative statements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. can be given a formal mathematical structure that facilitates both the calculation of expected dose to the RMEI and the appropriate separation in this calculation of aleatory uncertainty (i.e., randomness in the properties of future occurrences such as igneous and seismic events) and epistemic uncertainty (i.e., lack of knowledge about quantities that are imprecisely known but assumed to have constant values in the calculation of expected dose to the RMEI). The second part of this presentation is contained in the following paper, “Computational Implementation of Sampling-Based Approaches to the Calculation of Expected Dose in Performance Assessments for the Proposed High-Level Radioactive Waste Repository at Yucca Mountain, Nevada,” and both describes and illustrates sampling-based procedures for the estimation of expected dose and the determination of the uncertainty in estimates for expected dose.

Computational implementation of sampling-based approaches to the calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada

Abstract A deep geologic repository for high-level radioactive waste is under development by the US Department of Energy (DOE) at Yucca Mountain (YM), Nevada. As mandated in the Energy Policy Act of 1992, the US Environmental Protection has promulgated public health and safety standards (i.e., 40 CFR Part 197) for the YM repository, and the US Nuclear Regulatory Commission has promulgated licensing standards (i.e., 10 CFR Parts 2, 19, 20, etc.) consistent with 40 CFR Part 197 that the DOE must establish are met in order for the YM repository to be licensed for operation. Important requirements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. relate to the determination of expected (i.e., mean) dose to a reasonably maximally exposed individual (RMEI) and the incorporation of uncertainty into this determination. This paper is the second part of a two-part presentation on the determination of expected dose to the RMEI in the context of 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. The first part of this presentation is contained in the preceding paper, “Conceptual Basis for the Definition and Calculation of Expected Dose in Performance Assessments for the Proposed High-Level Radioactive Waste Repository at Yucca Mountain, Nevada”, and describes how general and typically nonquantitative statements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. can be given a formal mathematical structure that facilitates both the calculation of expected dose to the RMEI and the appropriate separation in this calculation of aleatory uncertainty (i.e., randomness in the properties of future occurrences such as igneous and seismic events) and epistemic uncertainty (i.e., lack of knowledge about quantities that are poorly known but assumed to have constant values in the calculation of expected dose to the RMEI). The present paper describes and illustrates sampling-based procedures for the estimation of expected dose and the determination of the uncertainty in estimates for expected dose.

Conceptual structure and computational organization of the 2008 performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada

Abstract Extensive work has been carried out by the U.S. Department of Energy (DOE) in the development of a proposed geologic repository at Yucca Mountain (YM), Nevada, for the disposal of high-level radioactive waste. This presentation describes the overall conceptual structure and computational organization of the 2008 performance assessment (PA) for the proposed YM repository carried out by the DOE in support of a licensing application to the U.S. Nuclear Regulatory Commission (NRC). The following topics are addressed: (i) regulatory background, (ii) the three basic entities underlying a PA, (iii) determination of expected, mean and median dose to the reasonably maximally exposed individual (RMEI) specified in the NRC regulations for the YM repository, (iv) the relationship between probability, sets and scenario classes, (v) scenario classes and the characterization of aleatory uncertainty, (vi) scenario classes and the determination of expected dose to the RMEI, (vii) analysis decomposition, (viii) disjoint and nondisjoint scenario classes, (ix) scenario classes and the NRC’s YM review plan, (x) characterization of epistemic uncertainty, and (xi) adequacy of Latin hypercube sample size used in the propagation of epistemic uncertainty. This article is part of a special issue of Reliability Engineering and System Safety devoted to the 2008 YM PA and is intended as an introduction to following articles in the issue that provide additional analysis details and specific analysis results.

Expected Dose for the Early Failure Scenario Classes in the 2008 Performance Assessment for the Proposed High-Level Radioactive Waste Repository at Yucca Mountain Nevada.

Extensive work has been carried out by the U.S. Department of Energy (DOE) in the development of a proposed geologic repository at Yucca Mountain (YM), Nevada, for the disposal of high-level radioactive waste. In support of this development and an associated license application to the U.S. Nuclear Regulatory Commission (NRC), the DOE completed an extensive performance assessment (PA) for the proposed YM repository in 2008. This presentation describes the determination of expected dose to the reasonably maximally exposed individual (RMEI) specified in the NRC regulations for the YM repository for the early waste package (WP) failure scenario class and the early drip shield (DS) failure scenario class in the 2008 YM PA. The following topics are addressed: (i) properties of the early failure scenario classes and the determination of dose and expected dose the RMEI, (ii) expected dose and uncertainty in expected dose to the RMEI from the early WP failure scenario class, (iii) expected dose and uncertainty in expected dose to the RMEI from the early DS failure scenario class, (iv) expected dose and uncertainty in expected dose to the RMEI from the combined early WP and early DS failure scenario class with and without the inclusion of failures resulting from nominal processes, and (v) uncertainty in the occurrence of early failure scenario classes. The present article is part of a special issue of Reliability Engineering and System Safety devoted to the 2008 YM PA; additional articles in the issue describe other aspects of the 2008 YM PA.

Uncertainty and Sensitivity Analysis for the Igneous Scenario Classes in the 2008 Performance Assessment for the Proposed High-Level Radioactive Waste Repository at Yucca Mountain Nevada.

Extensive work has been carried out by the U.S. Department of Energy (DOE) in the development of a proposed geologic repository at Yucca Mountain (YM), Nevada, for the disposal of high-level radioactive waste. In support of this development and an associated license application to the U.S. Nuclear Regulatory Commission (NRC), the DOE completed an extensive performance assessment (PA) for the proposed YM repository in 2008. This presentation describes uncertainty and sensitivity analysis results for the igneous intrusive scenario class and the igneous eruptive scenario class obtained in the 2008 YM PA. The following topics are addressed for the igneous intrusive scenario class: (i) engineered barrier system conditions, (ii) release results for the engineered barrier system, unsaturated zone, and saturated zone, (iii) dose to the reasonably maximally exposed individual (RMEI) specified in the NRC regulations for the YM repository, and (iv) expected dose to the RMEI. In addition, expected dose to the RMEI for the igneous eruptive scenario class is also considered. The present article is part of a special issue of Reliability Engineering and System Safety devoted to the 2008 YM PA; additional articles in the issue describe other aspects of the 2008 YM PA.

Uncertainty and sensitivity analysis for the nominal scenario class in the 2008 performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada

Extensive work has been carried out by the U.S. Department of Energy (DOE) in the development of a proposed geologic repository at Yucca Mountain (YM), Nevada, for the disposal of high-level radioactive waste. In support of this development and an associated license application to the U.S. Nuclear Regulatory Commission (NRC), the DOE completed an extensive performance assessment (PA) for the proposed YM repository in 2008. This presentation describes uncertainty and sensitivity analysis results for the nominal scenario class (i.e., for undisturbed conditions) obtained in the 2008 YM PA. The following topics are addressed: (i) uncertainty and sensitivity analysis procedures, (ii) drip shield and waste package failure, (iii) engineered barrier system conditions, (iv) radionuclide release results for the engineered barrier system, unsaturated zone, and saturated zone, and (v) dose to the reasonably maximally exposed individual specified in the NRC regulations for the YM repository. The present article is part of a special issue of Reliability Engineering and System Safety devoted to the 2008 YM PA; additional articles in the issue describe other aspects of the 2008 YM PA.