Reliability and global sensitivity analysis based on importance directional sampling and adaptive Kriging model

This paper adopts importance directional sampling (IDS) and adaptive Kriging model for reliability and global sensitivity analysis. IDS is the combination of importance sampling (IS) and directional sampling (DS) by establishing directional vector in the importance region, which has the advantages of both IS and DS. A novel stopping criterion which tries to minimize the difference between the real failure region and fitted failure region is proposed based on the idea of auxiliary region to increase the efficiency of active learning. An improved active learning strategy is proposed based on the combination of optimization and learning function to synchronize the calculation process of design point and Kriging model updating, so as to ensure the accuracy of both Kriging model and importance directional density function. Different learning functions are adopted to select the most suitable active learning function of IDS. The global sensitivity index is calculated through failure probability and Bayes theorem based on Gaussian mixture model (GMM). The results show that: Through the proposed auxiliary region-based stopping criterion, the efficiency of active learning in IDS can be improved. The proposed active learning strategy can obtain high accuracy importance directional density function and failure probability with lower required function calls. Considering the accuracy and robustness of failure probability and global sensitivity index, U and EFF functions should be adopted on IDS.