Fuzzy importance sampling method for estimating failure possibility

To improve the computational efficiency of the fuzzy simulation in estimating failure possibility of the structure containing fuzzy uncertainty, a fuzzy importance sampling method is proposed in this paper. In the proposed method, the optimal importance sampling density for estimating failure possibility is deduced as the product of the indicator function related to failure domain and the joint membership function of fuzzy model inputs at first. Subsequently, the Markov chain simulation and an adaptive kernel sampling method are employed to generate a group of samples asymptotically following the optimal importance sampling density. Based on this group of samples, an approximate expression of the optimal importance sampling density expression is constructed. Finally, the failure possibility can be efficiently estimated by using a small number of samples generated by the approximate optimal importance sampling density. Results of three examples demonstrate that the proposed method is a more efficient and robust method for estimating the failure possibility estimation compared with the original fuzzy simulation method.