一种新的多输出重要性测度及其高效计算方法

基本变量重要性测度分析是结构安全评估以及工程优化设计的一项必要工作。本文结合矩独立重要性测度思想和基于方差的重要性测度思想,提出了一种新的适用于多个输出的重要性测度。所提测度利用概率积分转化(Probability integration transformation,PIT),将输出的不确定性由输出的联合分布函数来表征。在多输出情况下,相比单纯基于方差的重要性测度,所提测度能够同时包含各个输出的不确定性及其相关性。而相比单纯的矩独立重要性测度,由于它使用方差来衡量变异性,因而求解过程更为简便。在计算多输出的分布函数时,本文采用基于分数矩的极大熵方法结合Nataf变换法,在保证求解精度的同时大大降低了模型调用次数。数值和工程算例说明了该测度的合理性以及计算方法的高效性。

New Importance Measure for Multivariate Output and Its Effective Solution

Importance measure for input random variables is a necessary component of safety evaluation and optimization design in engineering. In this paper, a new importance measure for multivariate output is introduced by combining notions of the moment-independent importance measure and the variance-based importance measure synthetically. The new measure is based on the multivariate probability integration transformation (PIT), in which the uncertainty of the multivariate output is represented in the form of its joint cumulative distribution function (CDF). Compared with variance-based measures, the new measure can take into account both of the uncertainty and the correlation information in the multivariate output. Compared with moment-independent measures, the solution procedure of new measure is more simple because the variability of the joint CDF is measured by variances. In this paper, maximum entropy method based on fractional moments and Nataf transformation are proposed to reduce model calls when the joint CDF is calculated. The calculation cost is saved without decreasing its accuracy. A numerical example and an engineering example are given to show the reasonableness of the proposed measure and the efficiency of the algorithm.