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.

摘要

本文介绍了一种有效的方法来评估结构可靠性评估中性能函数的前四个中心矩。所提出的方法的过程分为三个主要步骤。首先，通过双变量降维方法，将性能函数近似为单变量和双变量函数的总和。其次，提出了一种基于重要性度量分析的新准则，将双变量函数划分为显着双变量函数和非显着双变量函数，进而得到性能函数的新逼近。最后，导出了用于评估所提出的性能函数的前四个中心矩的公式，其中单变量和双变量函数的前四个原始矩可以通过标准正态空间中的点估计方法来实现。通过三个数值例子证明了所提出方法的有效性和效率。