Construction of adaptive Kriging metamodel for failure probability estimation considering the uncertainties of distribution parameters

A critical problem in engineering reliability analysis is obtaining an accurate failure probability with a high computational efficiency. This study aims to present failure probability estimation under the conditions of uncertain input variables and their uncertain distribution parameters. An adaptive Kriging model of failure probability with respect to distribution parameters (FP-DP model) is developed, which avoids coupling modeling among the distribution parameters, input variables, and failure probability. An improved U-learning function that simultaneously considers the statistical information of uncertain distribution parameters and failure probability is proposed to select new sampling points for the FP-DP model. The stopping criteria based on sample distances and relative errors of the predicted failure probability are constructed to improve the convergence performance around the limit state function. Three numerical and four engineering examples with different complexities are considered to verify the effectiveness of the proposed adaptive FP-DP Kriging metamodel. The results show that the proposed method can obtain an accurate failure probability with fewer sampling points of uncertain distribution parameters than some existing methods, indicating that the proposed method can be efficiently integrated into reliability-based design optimization problems considering both the uncertainties of input variables and their distribution parameters.

Automated summary

This study presents a failure probability estimation method under the conditions of uncertain input variables and their uncertain distribution parameters. By developing an adaptive Kriging model and using an improved U-learning function and stopping criteria, the computational efficiency and convergence performance can be improved. The results of numerical and engineering examples demonstrate that the proposed method can obtain accurate failure probabilities with fewer sampling points.