截断正态分布情况下失效概率计算的截断重要抽样法

Truncated importance sampling method for failure probability estimation with truncated normal distribution

截断重要抽样法是在传统的重要抽样方法的基础上,引入截断抽样函数来计算结构的失效概率,本文运用此方法来解决工程中普遍存在的截断分布问题。首先将截断分布情况下的可靠性模型转化为非截断分布情况下的多模式并联系统的可靠性模型,然后采用截断重要抽样法求解,推导了截断分布可靠性估计值的方差分析公式。文中给出的算例结果表明:截断重要抽样法适用于截断分布的可靠性分析,且在相同的计算精度下,截断重要抽样法比传统的重要抽样法效率要高。

Based on the traditional importance sampling （IS）, truncated importance sampling（TIS） has been proposed to calculate the failure probability by adopting the truncated importance sampling function, this paper utilizes TIS to solve truncated normal distribution commonly existing in the engineering structures. The original reliability with the truncated normal distribution is transformed to the system reliability with multiple parallel failure modes and non-truncated distribution, then TIS is employed to estimate the system reliability, and the variances of the reliability estimations by TIS are derived approximately. The results of the examples show that TIS is applicable to reliability analysis with truncated normal distribution, and compared to traditional IS, in the case of the same precision, the efficiency of TIS is higher than that of traditional IS.