Adaptive Kriging-based method with learning function allocation scheme and hybrid convergence criterion for efficient structural reliability analysis

Abstract Structural reliability analysis poses a considerable challenge in engineering practice, leading to the development of various state-of-the-art methods. Active learning methods, known for their superior performance, have been extensively investigated for assessing failure probabilities in structural reliability analysis. This paper aims to develop an efficient and accurate Kriging-based active learning method for structural reliability analysis, incorporating a novel learning function allocation scheme and a hybrid convergence criterion. Specifically, a novel learning function allocation scheme is introduced to address the challenge of no single learning function demonstrating superior performance across various engineering contexts. Six active learning functions, including EFF, H, REIF, LIF, FNEIF, and KO, are used to form a portfolio of functions in the allocation scheme. The use of the U learning function initiates the active learning process with a truncated candidate sample pool, alleviating computational burden while maintaining accuracy. Additionally, a hybrid convergence criterion, combining the error-based stopping criterion with a stabilization convergence criterion, is proposed to terminate the active learning process at an appropriate stage. The performance of the proposed method is evaluated through four numerical examples and one engineering case, demonstrating its accuracy and efficiency.