Time and space-variant system reliability analysis through adaptive Kriging and weighted sampling

The performance of complex engineering systems often changes over time and space, potentially leading to multiple failure modes. Such time and space variance presents a challenge to reliability analysis and design methods. To address this issue, this paper first analyzes three categories of approaches to four types of time-variant reliability problems, and then develops an adaptive uniform design-based Kriging (AUDK) framework with an improved weighted sampling method (IWSM), termed the AUDK-IWSM. In particular, a Kriging response surface of the extreme function for time and space-variant limit states is constructed, and then an existing weighted sampling method is improved for high precision to prepare the sampling points for reliability analysis on the Kriging surface. To construct the AUDK model and update it with the most probable point, an adaptive iterative algorithm is developed based on the IWSM. Thus, through integrating the reliability index of the generated Kriging response surface, the resultant AUDK-IWSM algorithm improves reliability calculations and enhances computational efficiency of the reliability analysis. The AUDK-IWSM is illustrated, and its effectiveness is verified through four case studies for engineering practice, in comparison with a number of state-of-the-art techniques reported in the literature.