基于子集模拟和重要抽样的可靠性灵敏度分析方法

针对工程实际中大量存在的小失效概率问题，提出了基于子集模拟和重要抽样的可靠性灵敏度分析方法. 在子集模拟重要抽样可靠性分析方法中，通过引入合理的中间失效事件，将小的失效概率表达为一系列较大的条件失效概率的乘积，而较大的条件失效概率则可通过构造中间失效事件的重要抽样密度函数来高效求解. 基于子集模拟重要抽样可靠性分析的思想，论文将可靠性灵敏度转化为条件失效概率对基本变量分布参数的偏导数形式，推导了基于子集模拟和重要抽样的可靠性灵敏度估计值及估计值方差的计算公式，并采用算例对所提方法进行了验证. 算例结果表明所提方法具有较高的计算精度和效率，并且适用单个和多个失效模式系统. 

RELIABILITY SENSITIVITY ANALYSIS BASED ON SUBSET SIMULATION AND IMPORTANCE SAMPLING

Reliability sensitivity algorithm is presented on the basis of subset simulation and importance sampling due to the small failure probability highly experienced in engineering. Firstly, a small failure probability is expressed as a product of larger conditional failure probabilities of some intermediate failure events. Secondly, the larger conditional failure probabilities can be estimated efficiently by constructing the importance sampling density functions of the intermediate failure events. Thirdly, the reliability sensitivity is transformed into the partial derivatives of conditional failure probabilities with respect to the distribution parameters of the basic variables in the paper. The estimation of the reliability sensitivity and its variance are then derived for the presented algorithm. The results from several cases show that the present method is efficient, precise and applicable to the structural system with single and multiple failure modes.