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

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

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

Developers of computer codes, analysts who use the codes, and decision makers who rely on the results of the analyses face a critical question: How should confidence in modeling and simulation be critically assessed? Verification and validation (V&V) of computational simulations are the primary methods for building and quantifying this confidence. Briefly, verification is the assessment of the accuracy of the solution to a computational model. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In verification, the relationship of the simulation to the real world is not an issue. In validation, the relationship between computation and the real world, i.e., experimental data, is the issue.

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Verification, Validation, and Predictive Capability in Computational Engineering and Physics

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant

https://digital.library.unt.edu/ark:/67531/metadc707340/m2/1/high_res_d/755476.pdf

Uncertainty and sensitivity analysis for two-phase flow in the vicinity of the repository in the 1996 performance assessment for the Waste Isolation Pilot Plant: disturbed conditions

Uncertainty and sensitivity analysis techniques based on Latin hypercube sampling, partial correlation analysis, stepwise regression analysis, and examination of scatterplots are used in conjunction with the BRAGFLO model to examine two-phase flow (i.e., gas and brine) at the Waste Isolation Pilot Plant, which is being developed by the US Department of Energy as a disposal facility for transuranic waste, to provide insights on factors that are potentially important in showing compliance with applicable regulations of the US Environmental Protection Agency. Specific regulations include Petitions to Allow Land Disposal of a Waste Prohibited Under Subpart C of Part 268 (40 CFR 268.6), which implements the Resource Conservation and Recovery Act and establishes maximum environmental concentrations for regulated chemicals such as volatile organic compounds (VOCs) and heavy metals, and Environmental Standards for the Management and Disposal of Spent Nuclear Fuel, High-Level and Transuranic Radioactive Wastes (40 CFR 191, Subpart B), which places a probabilistic limit on allowable radioactive releases from a disposal facility over a 10,000-yr time period. The primary topics investigated are (a) gas production due to corrosion of steel, (b) gas production due to microbial degradation of cellulosics, and (c) gas migration into anhydrite marker beds in the Salado Formation,more » which is the host unit into which the waste will be emplaced. Gas production and movement is of particular importance in establishing compliance with 40 CFR 268.6 because of its influence on the movement of VOCs. Important variables identified in the analysis include (a) initial brine saturation of the waste, (b) stoichiometric terms for corrosion of steel and microbial degradation of cellulosics, and (c) gas barrier pressure in the anhydrite marker beds.« less

J. D. Schreiber

Papers

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant

Uncertainty and sensitivity analysis for two-phase flow in the vicinity of the repository in the 1996 performance assessment for the Waste Isolation Pilot Plant: disturbed conditions

Uncertainty and sensitivity analysis for gas and brine migration at the waste isolation pilot plant : fully consolidated shaft