Adaptive importance sampling approach for structural time-variant reliability analysis

A novel sampling approach, called adaptive importance sampling (AIS), is proposed to efficiently perform time-variant reliability analysis. In practice, structures are generally subject to time-variant deterioration processes and external loads, and the Time-variant Failure Probability Function (TFPF), which is the failure probability as a function of time, is a critical quantity of interest in engineering applications. The proposed approach leverages an adaptive strategy and an optimal combination algorithm to further improve the accuracy and efficiency of TFPF estimation using the importance sampling approach. The adaptive strategy is to seek for the best setting of importance sampling components to iteratively obtain estimator components of the TFPF. The optimal combination algorithm is to collect all these adaptive estimator components to form an overall estimator by its coefficient of variation (C.o.V.). The proposed approach outperforms traditional importance sampling methods in the sense that it ensures the convergence with minimal computational cost, specifically the C.o.V. of the TFPF estimator is below a predetermined threshold over the entire time domain. Therefore, the proposed approach offers an extension to traditional importance sampling methods for time-variant reliability assessment. Numerical examples are provided to demonstrate the effectiveness of the proposed approach in accurately estimating the TFPF of structures subjected to time-variant loads and deterioration processes.