An improved importance sampling method for failure probability based global sensitivity analysis

In order to analyze the effect of input variable on the failure probability of the system and reduce the failure probability, a failure probability based global sensitivity is investigated. Generally Monte carlo based method is widely used to solve the failure probability sensitivity measure, but its large computational cost can not be afforded, especially for the low failure probability in computationally engineering demanding problems. To overcome the disadvantage of MC method, an improved importance sampling method for global sensitivity measure of failure probability is proposed combining with H-S method. The main idea of the proposed method is firstly generating samples in interesting region by efficient importance sampling (IS), then searching the proper estimator and establishing the relationship between failure probability based global sensitivity measure and the estimator, furthermore, obtaining the global sensitivity measure. Since the proposed method combines the fast convergence of H-S estimator and high efficient searching capability in interesting region of the IS. The proposed method is more efficient with enough accuracy, compared with the standard Sobol' method for the variance based on global sensitivity measure. Finally, two numerical examples and an engineering example are employed to demonstrate the reasonability of the proposed sensitivity measure and the efficiency of the proposed method.