多失效模式重要抽样法的方差分析及应用

在计算结构体系失效概率时,基于Monte-Carlo数值模拟的重要抽样技术已被实践证明是一种非常有效的方法。重要抽样法中估计量的方差是影响收敛速度和计算精度的重要指标,因此重要抽样法的方差分析是非常必要的。对于单模式而言,其方差分析比较容易。对于多模式情况,其方差分析有一定的困难。这有可能影响重要抽样法在多模式结构体系失效概率计算中的应用。本文详细推导了几种常见重要抽样法的方差计算公式。然后用方差分析的概念,阐明了多模式重要抽样法应用中的一些问题。

VARIANCE ANALYSIS AND APPUCATION TO IMPORTANCE SAMPLING FOR MULTIMODAL FAILURE

Importance sampling technique based on the Monte Carlo method is proved to be very efficient for evaluating the failure probability of a structural system. Variance analysis to evaluate the importance sampling is very essential owing to its effect on computational speed and precision, For single failure mode, this analysis is relatively easy, however, for multimodal failure, it is not so easy. In this paper, three variance formulas corresponding to different importance sampling methods have been derived analytically. In the paper, it also illustrates the application of the variance analysis to solve some of the problems of importance sampling for multimodal failure.