基于交叉熵和空间分割的全局可靠性灵敏度分析

Global reliability sensitivity analysis using cross entropy method and space partition

基于失效概率的全局灵敏度分析可以度量各个基本随机变量的不确定性对失效概率的影响程度,对如何降低结构的失效概率具有指导意义。基于交叉熵方法和空间分割提出一种新全局可靠性灵敏度分析方法。该方法采用交叉熵法自适应的确定重要抽样密度函数,有效地回避了传统重要抽样中设计点位置和个数求解的困难。基于评估失效概率所使用的样本,利用空间分割方法计算各个输入随机变量的全局可靠性灵敏度指标,能够提高样本的利用率和计算效率。文中利用一个数值算例和两个工程算例验证了所提方法的计算效率和精度。

Failure-probability-based sensitivity analysis is capable to measure the effects of uncertainties of input variables on failure probability,and can provide guidance on how to reduce the failure probability of a structure.In this paper,a new method is proposed to estimate the global reliability sensitivity indices,based on cross entropy method and space partition.The proposed method adaptively determines the important sampling density function by cross entropy method,avoiding the issue of determining the positions and number of the design points.Based on the identical set of samples used to estimate failure probability,the global reliability sensitivity index of each input random variable is calculated by the space partition method,which significantly improves the utilization of the samples and computational efficiency.A numerical and two engineering examples are used to illustrate the accuracy and efficiency of the proposed method.