Estimating predictive failure probability and its update under newly available observations by a layered cluster importance sampling algorithm - Li, Zhen; Lu, Zhenzhou (Reliability engineering & system safety, 2026)
When there is uncertainty in the input variables and their corresponding distribution parameters, the predictive failure probability (PFP) is used to quantify the structural safety level. After obtaining the newly available observations during the service period, it is necessary to study the algorithm for updating the PFP to calibrate the structural safety level. However, for the common problem with small PFP and its update in engineering, the development of corresponding efficient algorithms remains an unsolved issue in current research. Therefore, this paper proposes a layered cluster importance sampling (LC-IS) algorithm to estimate the PFP and its updated value. In LC-IS, the difficulty of exploring the rare augmented failure domain (AFD) is reduced by adaptively dividing it into a set of layered structures where the PFP decreases in descending order. Additionally, through cluster analysis for failure samples of each layer, an explicit regular IS density is gradually established, thereby reducing the variance of estimating PFP. To further improve computational efficiency, the proposed method employs adaptive Kriging model to replace the computation of the real performance function, thereby significantly reducing the evaluation of the performance function. Experimental results show that the proposed method achieves higher computational efficiency than existing methods with similar accuracy.