基于失效概率的全局重要性测度分析的交叉熵方法

Cross-Entropy Method for Failure Probability Based Global Importance Measure Analysis

输入随机变量对失效概率的贡献程度可以用基于失效概率的全局重要性测度来表征。引入交叉熵方法计算全局重要性测度,以解决传统重要抽样法存在重要抽样函数难以确定的困难。交叉熵方法是一种自适应重要抽样方法,通过渐进确定重要抽样函数的方法回避传统重要抽样法中设计点位置和个数求解的困难。通过比较重要抽样法和交叉熵方法的基本思想和算例结果可以发现:重要抽样法只适用于设计点位置和个数容易求得的情况,而对于多设计点和复杂极限状态函数的情况,交叉熵方法具有更高的效率和精度。

The contribution of input random variables to failure probability of an uncertain system can be characterized by failure probability based global importance indices. In this paper, cross entropy method （CEM） is introduced to calculate global importance indices to address the issue of constructing an appropriate importance sampling probability density function （PDF） in the traditional important sampling method. In essential, CEM is an adaptive important sampling method which selects a proper important sampling PDF in a progressive way to avoid the calculation of position and number of design points. Comparing the associate theories and computational results, it can be seen that the traditional importance sampling is applicable to simple cases where design points can be easily found only while CEM possesses high computational efficiency and accuracy for problems with multiple design points and complex limit state function.