基于自适应Kriging代理模型的交叉熵重要抽样法

To solve the reliability analysis of the coupling of complex failure domain and small failure probability, an improved method shortened as CE-IS-AK is proposed by combining Cross-Entropy Importance Sampling (CE-IS) with the Adaptive Kriging (AK) model on the existing CE-IS. In the proposed CE-IS-AK, the Gaussian mixed model suitable for complex failure domain is used to approximate the optimal Importance Sampling Density Function (IS-DF), and in the approximation process, the AK model is used to iteratively update the parameters of the Gaussian mixed model, so the efficiency of CE-IS is improved by the modification. In addition, the convergence criterion of the existing CE-IS is improved by CE-IS-AK for avoiding redundant iterations and expanding the applicability of the existing CE-IS. Since the AK model is nested into the CE-IS, the efficiency of constructing IS-DF is improved by the CE-IS-AK while ensuring the accuracy. Compared with the widely applicable AK based on Monte Carlo Simulation (AK-MCS), the size of the candidate sample pool for training AK in the CE-IS-AK is greatly reduced due to the variance-reduced strategy of IS in the case of that the number of training samples keeps almost equivalent, and the introduction of the Gaussian mixed model makes the proposed CE-IS-AK applicable for the multiple complex failure domain. The presented examples demonstrate the superiority of the CE-IS-AK.