A numerical algorithm for general failure probability with fuzzy basic variables and fuzzy states

For general reliability analysis with fuzzy basic variables and fuzzy failure domain, an improved numerical simulation algorithm is presented on the basis of simulated annealing optimization. During the simulation procedure, the importance sampling function, from which the samples for evaluation of the general failure probability are taken, is gradually optimized by Metropolis rule in the simulated annealing method. Due to fuzziness both in the basic variables and in failure domain, two factors, i. e., the equivalent joint probability density function of the basic variables and the membership of the state variable to the fuzzy failure domain,are taken into consideration in the construction of the importance sampling function. From the optimized importance sampling function, the samples contributing significantly to the general failure probability can be taken out with high probability. Hence the sampling efficiency and the precision of simulation are improved. In the present method, the information of the simulation obtained from the gradual optimization of importance sampling is sufficiently utilized, which improved the sampling efficiency further. Illustrations are used to explain the rationality and feasibility.