Compound kriging-based importance sampling for reliability analysis of systems with multiple failure modes

The compound kriging-based importance sampling (IS) strategy is proposed for the efficient estimation of failure probability of systems with multiple failure modes. The proposed method is based on the IS probability density function of each failure mode constructed by the kriging model, where the probabilistic classification function is treated as a surrogate model for the actual failure indicator function. The whole algorithm of the proposed method can be divided into two stages. First, the kriging model is constructed to estimate the component augmented failure probabilities and obtain quasi-optimal IS samples. Secondly, the constructed kriging model is further refined based on these quasi-optimal IS samples to estimate the correction factor. Finally, the system failure probability is estimated by the product of the component augmented failure probabilities and the correction factor. The system reliability analysis results of the presented examples illustrate the feasibility of the proposed method.