Efficient Algorithm for Evaluation of Statistical Moments of Performance Functions

Abstract

Evaluating the statistical moments of performance functions from the perspective of balancing accuracy and efficiency remains a challenge. This paper proposes an efficient algorithm for evaluating the statistical moments of performance functions. The main procedure of the proposed method consists of three steps. First, based on the bivariate dimension-reduction method, the performance function is approximated by a summation of one-dimensional and two-dimensional functions. Next, according to the criterion of delineating the existence of cross terms, the two-dimensional functions are decomposed as functions including and excluding cross terms. Third, the one-dimensional point estimate method is used to evaluate the statistical moments of the one-dimensional functions and the two-dimensional functions without cross terms, whereas the two-dimensional sparse grid stochastic collocation method is applied to estimate the statistical moments of the two-dimensional functions with cross terms. Several numerical examples are presented to illustrate the efficiency, accuracy, and applicability of the proposed method. The results demonstrate that the proposed method achieves a good balance between accuracy and efficiency and provides a useful tool for evaluating the statistical moments of performance functions.