Estimation of statistical moments of performance functions using efficient importance measure

Abstract

ABSTRACT This paper introduces an efficient methodology for evaluating the first four central moments of performance functions in structural reliability assessment. The procedure of the proposed method is divided into three major steps. First, a performance function is approximated as the sum of univariate and bivariate functions by the bivariate dimension-reduction method. Next, a new criterion based on importance measure analysis is proposed for dividing the bivariate functions into significant bivariate functions and non-significant bivariate functions, and then the new approximation of the performance function is obtained. Finally, formulas are derived for evaluating the first four central moments of the proposed performance function, in which the first four raw moments of the univariate and bivariate functions can be achieved by a point estimating method in a standard normal space. The effectiveness and efficiency of the proposed method are demonstrated through three numerical examples.