An Efficient and Versatile Kriging-Based Active Learning Method For Structural Reliability Analysis

Abstract

In structural reliability analysis, the development of an efficient and versatile active learning method that is applicable to problems of varying complexity is still a challenging task. The critical contribution of this work is an elegant implementation of the Kriging-based importance sampling and dimension reduction technique in an active learning framework. Specifically, a dimension reduction technique that accounts for the contributions of important and unimportant random variables is employed to enable the proposed algorithm with the capability to deal with high-dimensional problems. To exploit the merits of the adaptive Kriging method, the quasi-optimal importance sampling density is established based on the predictive information provided by the Kriging model. Besides, a new learning function derived from a folded normal distribution is developed for selecting new samples near the LSS with significant contributions to the failure probability. Moreover, an efficient stopping criterion is introduced to terminate the active learning process at an appropriate stage effectively. In other words, the proposed method inherits the merits of Adaptive Kriging, Dimension Reduction, and Importance Sampling, thus is called AK-DRIS in this study. The overall performance of the AK-DRIS is verified through several numerical examples of different complexity.

Keywords: Structural reliability; Kriging model; Active learning method; Importance sampling;Dimension reduction