An efficient structural reliability analysis method with active learning Kriging-assisted robust adaptive importance sampling

Due to deterioration effects and a variety of manmade or natural hazards, structures and infrastructure systems can face serious challenges for the functionality and safety during the service life. Thus, it is crucial to accurately assess the structural reliability and perform reasonable management actions. Simulation methods can yield more accurate reliability analysis results compared with approximation methods. However, as structures and infrastructure systems become complex, evaluating the engineering models can be very time-consuming. To address the gap, this paper proposes an active learning Kriging-assisted method for efficient structural reliability analysis. The proposed method consists of two stages. In the first stage, Kriging-based random walk, i.e., MCMC, is performed to explore the failure domain. Then, in the second stage, a Gaussian mixture distribution is established as the quasi-optimal sampling distribution for importance sampling. With the active learning framework that enlarges the training database in the MCMC and importance sampling process, the proposed method can achieve robust exploration of the whole failure domain, and also accurate failure probability estimates. Two classical numerical examples first validate the performance and advantages of the proposed method for handling problems with multiple failure domains and rare events. Then, a real-world application demonstrates the feasibility of applying the proposed method for quantitatively assessing the failure risk for prestressed-concrete continuous rigid-frame bridges during the service life.