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A surrogate method for density-based global sensitivity analysis

机译：基于密度的全局灵敏度分析的替代方法

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摘要

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 L-1-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. (C) 2016 Elsevier Ltd. All rights reserved.
机译：本文介绍了一种精确且计算效率高的替代方法，称为多项式维分解（PDD）方法，用于估计基于密度的f敏感度指数的一般类别。与基于方差的Sobol指数不同，f敏感度指数适用于依从和独立概率分布的随机输入。所提出的方法涉及感兴趣的高维随机响应的PDD近似，从而形成替代的输入输出数据集。根据替代数据集对输出概率密度函数进行核密度估计；以及随后的蒙特卡洛积分，用于估计f灵敏度指数。该方法是针对任意凸函数f和输入变量的任意概率分布而开发的，能够计算各种敏感度或重要程度，包括互信息，平方损失互信息和基于L-1距离的信息。重要程度。三个数值例子说明了该方法在计算灵敏度指数时的准确性，效率和收敛性，该灵敏度指数是从三个显着的发散或距离测度得出的。对杠杆进行了基于有限元的全局敏感性分析，证明了该方法解决工业规模工程问题的能力。 （C）2016 Elsevier Ltd.保留所有权利。

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