AES-AUBF: an adaptive ensemble surrogate framework with approximate upper bound function for efficient structural reliability analysis

Accurate and efficient estimation of structural failure probability often requires balancing predictive accuracy with computational cost, particularly when high-fidelity models are involved. To address this challenge, this study develops an adaptive ensemble of surrogates with approximate upper bound function (AES-AUBF) for reliability analysis. The proposed framework integrates multiple polynomial chaos Kriging (PCK) surrogates through a novel weighting scheme, enabling dynamic adjustment of model importance according to both global accuracy and local predictive uncertainty. An approximate upper bound function (AUBF) is introduced within a Bayesian active learning framework to guide the sequential selection of new informative samples, effectively reducing epistemic uncertainty in failure probability estimation. Furthermore, a reward-based learning function allocation strategy is proposed to adaptively select the most effective learning function from a portfolio, while a parallel enrichment mechanism accelerates convergence by adding multiple samples per iteration. A hybrid error-based stopping criterion ensures termination at an optimal balance between accuracy and efficiency. Three numerical examples, including a nonlinear oscillator, a multi-branch series system, and the fatigue reliability assessment of a monopile-supported offshore wind turbine, are employed to investigate the performance of AES-AUBF. Results show that AES-AUBF achieves accuracy comparable to direct Monte Carlo simulation while significantly reducing the number of function evaluations. The proposed framework provides a flexible and efficient tool for reliability analysis, and its modular structure allows seamless integration with dimension-reduction and advanced simulation techniques for future extension to high-dimensional or rare-event problems.