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.

为提高模糊仿真在估计含模糊不确定性结构失效可能性时的计算效率，提出了一种模糊重要性抽样方法。该方法首先将失效域相关指标函数与模糊模型输入的联合隶属函数的乘积推导出用于估计失效可能性的最优重要性采样密度。随后，采用马尔可夫链模拟和自适应核采样方法，按照最优重要性采样密度渐近地生成一组样本。基于这组样本，构造了最优重要性采样密度表达式的近似表达式。最后，通过使用由近似最优重要性采样密度生成的少量样本，可以有效地估计失败的可能性。三个算例的结果表明，与原始模糊仿真方法相比，所提出的方法是一种更有效、更稳健的故障可能性估计方法。