Enhanced generalized subset simulation with multiple importance sampling for reliability estimation

In structural reliability estimation, generalized subset simulation (GSS) method is used to estimate failure probabilities of multiple performance functions simultaneously by a single run. However, compared with the original subset simulation (SuS), although GSS has reduced the computational cost, the uncertainty and unbiasedness of the estimation results is still inferior in some cases. In this paper, we propose a reliability estimation method combined GSS with multiple importance sampling (GSS-MIS), which enhances the performance of failure probability estimation of GSS without changing the iterative process of sample generation. This method uses a balance heuristic strategy to assign weights to samples from all the unified intermediate distributions in the estimation of the failure probabilities. The proposed GSS-MIS is verified in four representative examples and the estimation results are compared with that of original SuS and GSS, showing its improvement on the performance of the failure probability estimation with similar computational cost.