加权随机模拟的时变可靠性分析方法

针对结构时变可靠性的随机模拟分析方法计算代价大的问题,在极值方法的基础上提出基于加权随机模拟的时变可靠性分析策略。时变可靠性分析需要计算在不同时间处的失效概率,通常需要进行多次可靠性分析,计算代价巨大。所提方法通过对常规静态可靠性的随机模拟方法进行改进拓展,运用加权策略分别发展了加权蒙特卡洛法和加权重要抽样法,使之能够高效分析计算时变可靠性问题。所提方法仅需一次常规可靠性分析模拟,即可得到时变失效概率函数估计。采用管状悬臂梁和十杆桁架两个算例进行验证。结果表明,基于加权思想的分析方法在能确保精确度的前提下能够大幅度减小计算量,提高计算效率。

Weighted stochastic simulation for time-variant reliability analysis

In order to solve the problem of high cost of structural time-variant reliability analysis, a time-variant reliability analysis strategy based on weighted stochastic simulation was proposed. Time-variant reliability analysis needs to calculate the failure probability of structure with respect to different times, which often requires multiple reliability analyses, involving hugh calculation cost. The proposed method improves and expands the conventional stochastic simulation method which is used to analyze the static reliability problem. The weighted Monte Carlo method and weighted importance sampling method respectively are developed respectively by using the weighting strategy to efficiently analyze and calculate the time-variant reliability problem. The proposed methods require only one conventional reliability analysis simulation to obtain the estimator of time-variant failure probability function. Two examples, a tubular cantilever beam and a ten-bar truss, are used for verification. Results show that the weighted methods can greatly ease the computational burden and improve the computational efficiency while ensuring the precision.