Time-dependent reliability analysis by a single-loop Bayesian active learning method using Gaussian process regression

• Published in: Computer methods in applied mechanics and engineering Vol. 444; p. 118092
• Main Authors: Dang, Chao, Valdebenito, Marcos A., Faes, Matthias G.R.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2025
• Subjects: Bayesian active learning; Gaussian process regression; Learning function; Stopping criterion; Time-dependent reliability analysis; Gaussian process regression; Bayesian active learning; Learning function; Time-dependent reliability analysis; Stopping criterion
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2025.118092

Time-dependent reliability analysis has proven to be an invaluable tool for assessing the safety levels of engineering structures subject to both randomness and time-varying factors. In this context, single-loop active learning Kriging methods have demonstrated a favorable trade-off between efficiency and accuracy. However, there remains significant potential for further improvement, particularly in addressing computationally expensive time-dependent reliability problems. This paper introduces a novel single-loop Bayesian active learning method using Gaussian process regression (GPR) for time-dependent reliability analysis, termed ‘Integrated Bayesian Integration and Optimization’ (IBIO). The key idea is to integrate the Bayesian integration method originally developed for static reliability analysis and the Bayesian optimization for solving the global optima of expensive black-box functions. First, we introduce a pragmatic estimator for the time-dependent failure probability. Second, a new stopping criterion is proposed to determine when the active learning process should be terminated. Third, three learning functions as three alternatives are developed to identity the best next time instant where to evaluate the performance function. Fourth, one new learning function is presented to select the best next sample for the random variables and stochastic processes given the time instant. Five numerical examples are presented to demonstrate the effectiveness of the proposed IBIO method. It is empirically shown that the method can produce accurate results with only a small number of performance function evaluations. •Single-loop Bayesian active learning method for time-dependent reliability analysis.•Proposed method integrates Bayesian integration and Bayesian optimization.•A novel stopping criterion proposed to halt the active learning process.•Three new learning functions proposed to identify the optimal next time instant.•A new learning function introduced to identify the best next sample given the time instant.