An adaptive truncated importance sampling for fuzzy and random reliability of structure

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.