A novel β hyper-plane based importance sampling method

A novel β hyper-plane based importance sampling method is presented to estimate failure probability of structure. Based on β section, a virtual hyper-plane tangent to the failure surface, the variable space is separated into the importance region R and the unimportance region S, on which the truncated importance sampling functions h_R(x) and h_S(x) are established respectively. The sampling numbers generated from h_R(x) and h_S(x) are dependent on the contributions of R and S to the failure probability, and they are determined by the iterative simulations. The formulae of the failure probability estimation, the variance and the coefficient of variation are derived for the presented β hyper-plane importance sampling method. The presented method is suitable for the failure probability estimation of both a single failure mode and multiple failure modes in parallel. The examples show that the presented method is more efficient than the traditional importance sampling method.