A surrogate method for density-based global sensitivity analysis

Sharif Rahman

Reliability Engineering and System Safety, 2016, vol. 155, issue C, 224-235

Abstract: This paper describes an accurate and computationally efficient surrogate method, known as the polynomial dimensional decomposition (PDD) method, for estimating a general class of density-based f-sensitivity indices. Unlike the variance-based Sobol index, the f-sensitivity index is applicable to random input following dependent as well as independent probability distributions. The proposed method involves PDD approximation of a high-dimensional stochastic response of interest, forming a surrogate input–output data set; kernel density estimations of output probability density functions from the surrogate data set; and subsequent Monte Carlo integration for estimating the f-sensitivity index. Developed for an arbitrary convex function f and an arbitrary probability distribution of input variables, the method is capable of calculating a wide variety of sensitivity or importance measures, including the mutual information, squared-loss mutual information, and L1-distance-based importance measure. Three numerical examples illustrate the accuracy, efficiency, and convergence properties of the proposed method in computing sensitivity indices derived from three prominent divergence or distance measures. A finite-element-based global sensitivity analysis of a leverarm was performed, demonstrating the ability of the method in solving industrial-scale engineering problems.

Keywords: f-Divergence; f-Sensitivity index; Hellinger distance; Kernel density estimation; Kullback–Leibler divergence; Polynomial dimensional decomposition; Total variational distance (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:155:y:2016:i:c:p:224-235

DOI: 10.1016/j.ress.2016.07.002

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