Cross-entropy-based adaptive importance sampling for time-dependent reliability analysis of deteriorating structures

Time-dependent reliability analysis of deteriorating structures is important in their performance evaluation and maintenance. Various definitions and methods have been used by researchers to predict the time-dependent reliability of structures. In the present study, these methods are first critically reviewed and examined. Among these methods, the stochastic-process-based method is theoretically the most rigorous but also computationally the most expensive. To facilitate the wide application of the stochastic-process-based method in complex problems, an efficient importance sampling method is then proposed in this paper. The proposed method includes a number of improvements formulated to enhance the efficiency and robustness of an existing method proposed by Kurtz and Song, leading to more efficient solutions of time-dependent reliability problems of structural systems with multiple important regions. The validity and efficiency of the new method is demonstrated through three numerical examples.