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Uniform sampling and saddlepoint approximation for probabilistic sensitivity analysis in engineering design. (English) Zbl 1266.62098

Fan, Jianqing (ed.) et al., Contemporary multivariate analysis and design of experiments. In celebration of Professor Kai-Tai Fang’s 65th birthday. Most of the papers are presented at the international conference on statistics, Hong Kong, China, June 20–24, 2005. Hackensack, NJ: World Scientific (ISBN 981-256-120-X/hbk; 978-981-256-776-5/ebook). Series in Biostatistics 2, 269-291 (2005).
Summary: Sensitivity analysis plays an important role to help engineers gain knowledge of complex model behaviors and make informed decisions regarding where to spend engineering effort. In designs under uncertainty, probabilistic sensitivity analysis (PSA) is performed to quantify the impact of uncertainties in random variables on the uncertainty in model outputs. One of the most challenging issues for PSA is the intensive computational demand for assessing the impact of probabilistic variations. An efficient approach to PSA is presented in this article. Our approach employs the Kolmogorov-Smirnov (KS) distance to quantify the importance of input variables. The saddlepoint approximation approach is introduced to improve the efficiency of generating cumulative distribution functions (CDFs) required for the evaluation of the KS distance. To further improve efficiency, optimized uniform samples are used to replace the direct Monte Carlo simulations for determining the cumulant generating function (CGF) in saddlepoint approximation. Efficient construction of a uniform design necessary to generate the “best” samples in a multidimensional space is presented. Our approach is illustrated with a structural design problem. It has the potential to be the most beneficial for high dimensional engineering design problems that involve expensive computer simulations.
For the entire collection see [Zbl 1078.62524].

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62D05 Sampling theory, sample surveys
62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods
65C60 Computational problems in statistics (MSC2010)
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