An adaptive Kriging-based method for reliability analysis with a new learning strategy

Abstract

This study proposes a novel active learning-based method for reliability analysis, termed AK-EIG-ESC. The method integrates the adaptive Kriging metamodel with Monte Carlo simulation to estimate the probability of failure and, most importantly, introduces a novel active learning strategy to guide the selection of training samples. To achieve this, a random variable associated with the probability of failure is introduced and demonstrated to follow a Gaussian distribution according to the Central Limit Theorem. Building on this formulation, a new learning strategy is designed by quantifying the expected information gain from a hypothetical experiment. The information gain is expressed as the Kullback-Leibler divergence between the prior and posterior distributions of the introduced random variable associated with the probability of failure. Following this active learning strategy, a sequential sampling scheme is used to actively select new training samples, and the Kriging model is adaptively updated after each new sample is acquired. An error-based stopping criterion is adopted to evaluate the convergence of the proposed algorithm. Several illustrative examples are then used to assess the proposed AK-EIG-ESC algorithm, and the results show that the proposed algorithm exhibits high accuracy and efficiency for reliability analysis.