Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol’ variance decomposition, and fast probability integration. Desirable features of Monte Carlo analysis in conjunction with Latin hypercube sampling are described in discussions of the following topics: (i) properties of random, stratified and Latin hypercube sampling, (ii) comparisons of random and Latin hypercube sampling, (iii) operations involving Latin hypercube sampling (i.e. correlation control, reweighting of samples to incorporate changed distributions, replicated sampling to test reproducibility of results), (iv) uncertainty analysis (i.e. cumulative distribution functions, complementary cumulative distribution functions, box plots), (v) sensitivity analysis (i.e. scatterplots, regression analysis, correlation analysis, rank transformations, searches for nonrandom patterns), and (vi) analyses involving stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty. Published by Elsevier Science Ltd.

/pdf/latin-hypercube-sampling-and-the-propagation-of-uncertainty-k6f019s9h6.pdf

Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems

https://digital.library.unt.edu/ark:/67531/metadc891681/m2/1/high_res_d/886897.pdf

Survey of sampling-based methods for uncertainty and sensitivity analysis

Identification and qualitative comparison of sensitivity analysis methods that have been used across various disciplines, and that merit consideration for application to food-safety risk assessment models, are presented in this article. Sensitivity analysis can help in identifying critical control points, prioritizing additional data collection or research, and verifying and validating a model. Ten sensitivity analysis methods, including four mathematical methods, five statistical methods, and one graphical method, are identified. The selected methods are compared on the basis of their applicability to different types of models, computational issues such as initial data requirement and complexity of their application, representation of the sensitivity, and the specific uses of these methods. Applications of these methods are illustrated with examples from various fields. No one method is clearly best for food-safety risk models. In general, use of two or more methods, preferably with dissimilar theoretical foundations, may be needed to increase confidence in the ranking of key inputs.

Identification and Review of Sensitivity Analysis Methods

https://cfwebprod.sandia.gov/cfdocs/CompResearch/docs/Storlie_SAND_20086570.pdf

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

High-order compact finite difference schemes for two-dimensional convection-diffusion-type differential equations with constant and variable convection coefficients are derived. The governing equations are employed to represent leading truncation terms, including cross-derivatives, making the overall O(h4) schemes conform to a 3 × 3 stencil. We show that the two-dimensional constant coefficient scheme collapses to the optimal scheme for the one-dimensional case wherein the finite difference equation yields nodally exact results. The two-dimensional schemes are tested against standard model problems, including a Navier-Stokes application. Results show that the two schemes are generally more accurate, on comparable grids, than O(h2) centred differencing and commonly used O(h) and O(h3) upwinding schemes.

Differential‐equation‐based representation of truncation errors for accurate numerical simulation

The Waste Isolation Pilot Plant (WPP) is located in southeastern New Mexico and is being developed by the U.S. Department of Energy (DOE) for the geologic (deep underground) disposal of transuranic (TRU) waste. A detailed performance assessment (PA) for the WIPP was carried out in 1996 and supports an application by the DOE to the U.S. Environmental Protection Agency (EPA) for the certification of the WIPP for the disposal of TRU waste. The 1996 WIPP PA uses a computational structure that maintains a separation between stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty, with stochastic uncertainty arising from the many possible disruptions that could occur over the 10,000 yr regulatory period that applies to the WIPP and subjective uncertainty arising from the imprecision with which many of the quantities required in the PA are known. Important parts of this structure are (1) the use of Latin hypercube sampling to incorporate the effects of subjective uncertainty, (2) the use of Monte Carlo (i.e., random) sampling to incorporate the effects of stochastic uncertainty, and (3) the efficient use of the necessarily limited number of mechanistic calculations that can be performed to support the analysis. The use of Latin hypercube sampling generates a mapping from imprecisely known analysis inputs to analysis outcomes of interest that provides both a display of the uncertainty in analysis outcomes (i.e., uncertainty analysis) and a basis for investigating the effects of individual inputs on these outcomes (i.e., sensitivity analysis). The sensitivity analysis procedures used in the PA include examination of scatterplots, stepwise regression analysis, and partial correlation analysis. Uncertainty and sensitivity analysis results obtained as part of the 1996 WIPP PA are presented and discussed. Specific topics considered include two phase flow in the vicinity of the repository, radionuclide release from the repository, fluid flow and radionuclide transport in formations overlying the repository, and complementary cumulative distribution functions used in comparisons with regulatory standards (i.e., 40 CFR 191, Subpart B).

/pdf/uncertainty-and-sensitivity-analysis-results-obtained-in-the-5dn67rdfa0.pdf

Uncertainty and Sensitivity Analysis Results Obtained in the 1996 Performance Assessment for the Waste Isolation Pilot Plant

A class of finite-element methods for elliptic problems is shown to exhibit nodal superconvergence in the approximate solution, and some equivalence properties to familiar finite-difference operators are demonstrated. The superconvergence property is exploited in a Taylor series analysis to demonstrate Gauss-point superconvergence for the derivatives of the approximation. A post-processing formula for the derivative at the nodes is constructed and shown to exhibit superconvergence. The nodal superconvergence property can be exploited recursively to further enhance the finite-element or finite-difference solution. Supporting numerical studies are given.

Nodal Superconvergence and Solution Enhancement for a Class of Finite-Element and Finite-Difference Methods

The primary objective of this study is to investigate the feasibility and utility of developing a defensible safety case for disposal of United States Department of Energy (U.S. DOE) high-level waste (HLW) and DOE spent nuclear fuel (SNF) in a conceptual deep geologic repository that is assumed to be located in a bedded salt formation of the Delaware Basin. A safety case is a formal compilation of evidence, analyses, and arguments that substantiate and demonstrate the safety of a proposed or conceptual repository. A safety case also provides the necessary structure for organizing and synthesizing existing knowledge in order to help DOE prioritize its future research and development (R&D) activities. We conclude that a defensible initial safety case for potential licensing could be readily compiled by capitalizing on the extensive technical basis that exists from prior work on the Waste Isolation Pilot Plant (WIPP), work on other repository development programs, and the work published through international efforts in salt repository programs such as in Germany. It should be emphasized that the DOE has not made any decisions regarding the disposition of DOE HLW and DOE SNF. This study provides additional information that could be used to inform DOE‘s decision making regarding management of this waste. Furthermore, the safety case discussed herein is not intended to either site a repository in the Delaware Basin or preclude siting in other media at other locations. Rather, this study simply presents an approach for accelerated development of a safety case for a potential DOE HLW and DOE SNF repository using the currently available technical basis for bedded salt. This approach includes a summary of the regulatory environment relevant to disposal of DOE HLW and DOE SNF in a deep geologic repository, the key elements of a safety case, the evolution of the safety case through the successive phases of repository development and licensing, and the existing technical basis that could be used to substantiate the safety of a geologic repository if it were to be sited in the Delaware Basin. We also discuss the potential role of an underground research laboratory (URL). Towards a Defensible Safety Case for Deep Geologic Disposal of DOE HLW and DOE SNF in Bedded Salt

/pdf/towards-a-defensible-safety-case-for-deep-geologic-disposal-41233b5b8d.pdf

Towards a Defensible Safety Case for Deep Geologic Disposal of DOE HLW and DOE SNF in Bedded Salt

Deep Borehole Disposal Safety Analysis.

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