截断抽样在结构模糊随机可靠性中的应用研究

An Adaptive Truncated Importance Sampling for Fuzzy and Random Reliability of Structure

针对模糊变量和随机变量同时存在的混合可靠性问题,建立了模糊失效概率计算的自适应截断抽样法。所建方法在给定的隶属水平确定的模糊变量隶属区间内,遍历抽取模糊变量的样本。对于每一个模糊变量样本,采用自适应截断抽样法来计算随机变量作用下的失效概率,并求得给定隶属度水平下模糊失效概率的上下界。由于自适应截断抽样法在求解随机变量作用下的失效概率时具有高效和稳健的优点,因此基于该方法建立的模糊失效概率计算方法也继承了这些优点,并且这些优点也得到了算例的验证。

In order to solve mixed reliability including fuzzy variables and random variables,an adaptive truncated importance sampling is established to calculate fuzzy failure probability.In the established method,the fuzzy variables are screened by sampling in the membership interval corresponding to the given membership level.For each fuzzy sample,the adaptive truncated importance sampling method is used to analyze the failure probability in space of the random variables,and the upper and lower bounds are furthermore obtained for the fuzzy failure probability corresponding to the given membership level.The adaptive truncated importance sampling method is especially efficient and robust in calculating the failure probability in the space of the random variables,and these advantages are propagated to the fuzzy failure probability method based on it.Several examples are used to demonstrate the advantages of the method.