A surrogate method for density-based global sensitivity analysis

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.