Time-dependent reliability analysis under random and interval uncertainties based on Kriging modeling and saddlepoint approximation

Time-dependent reliability analysis is capable of evaluating the reliability of the system over its full life cycle, which is of highly concerned for designers. In practice, some uncertainties cannot be simply described by a deterministic distribution due to lack of knowledge or information, and generally, their upper and lower bounds can be obtained. Thus, this paper develops a novel computational method for time-dependent reliability under random and interval uncertainties. The first step of the proposed method is to construct the Kriging surrogating model of the most probable point trajectory, with which the bound of the limit-state function can be efficiently recast as an equivalent Gaussian process. In this case, the computation of the bound of time-dependent failure probability (TDFP) is converted to a high-dimensional Gaussian integral problem. To solve this problem, the expansion optimal linear estimation, sparse-grid Gaussian quadrature technique and saddlepoint approximation method are integrated so that the above integral can be efficiently computed. Finally, four engineering examples are studied to demonstrate the effectiveness of the proposed method by comparison with previous methods. The results show this novel method can provide accurate and efficient time-dependent reliability analysis in terms of random and interval uncertainties.