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.