A single-loop Kriging model coupled with cross-entropy importance sampling for time-variant reliability analysis of rare events

Time-variant reliability analysis plays an essential role in improving the safety of structures during their service life. However, conventional time-variant methods for problems with low failure probability face two main issues: inaccurate analysis and high computational costs. In this work, a novel single-loop strategy is developed to address these challenges by combining the Kriging model with importance sampling (IS). Firstly, the cross-entropy-based importance sampling (CEIS) is extended to overcome the limitations of traditional IS in identifying failure regions for time-variant problems. The IS parameters are adaptively determined using the cross-entropy technique, ensuring coverage of the desired region and improving sampling efficiency. Furthermore, a new sampling criterion is presented to select the best training sample for sequentially refining the Kriging model. Four cases involving engineering and mathematical problems are used to verify the applicability of the proposed method. Results reveal that the proposed strategy delivers superior efficiency while maintaining the required level of accuracy.