A multi-level adaptive GP-VM algorithm for composite system reliability evaluation considering rare events

Variance Minimization (VM) technique is one of the most popular methods for importance sampling (IS), but it has never been successfully applied to composite (generation and transmission) system reliability evaluation due to the difficulty of solving. In this paper, Geometric Programming (GP) is firstly introduced to repeatedly solve the VM optimization model in multi-levels to adaptively obtain the optimal IS parameters used in a IS-Monte Carlo Simulation (MCS) based composite system reliability evaluation considering rare events. Then, the IEEE Reliability Test System and its modified version are used to test the proposed methodology, and the proposed method is compared with another important technique for IS of Cross-Entropy (CE) in estimation accuracy and convergence performance.