Adaptive importance sampling method for reliability and reliability sensitivity analysis based on mixture density function estimator

A fast finite mixture density function based adaptive importance sampling method is proposed to analysis structure failure probability and reliability sensitivity. The proposed method employs the finite mixture density estimators to obtain the density function of the points pre-sampling in failure region. The density function is used as the importance sampling density. The pre-sampling points are simulated as the states of a Markov chain, the resulting density tends to the optimal importance sampling density. Moreover, the method has been extended to analyze the structure reliability sensitivity. The proposed method is more efficient than traditional importance sampling method, and can handle the multi-mode system structure. The examples demonstrate the accuracy and efficiency of the method.