Active evolutionary Gaussian process for structural large-scale full-field reliability analysis and critical domain prognosis with only few initial samples

Abstract

Reliability analysis is crucial for ensuring structural integrity, yet it requires repeated, time-consuming evaluations of responses and multivariate limit state functions, while struggling to provide full-field estimations efficiently. Therefore, we propose an active evolutionary reduced Gaussian Process framework (AER-GP) for fast and large-scale full-field reliability analysis and critical domain prognosis, utilizing only a few initial samples. In which we first define a novel probability indicator of erroneously evaluating the sign of the minimum of the full-field limit state function. Based on this, we then develop an efficient convergence criterion that relies on the expected error in failure probability estimates. Furthermore, we advance the dual order-reduced Gaussian process coupled Monte Carlo methods to accurately predict the large-scale full-field stochastic response under material and load uncertainty. Where the preliminary design of experiments starts from a significantly small number of sets (e.g.,5), and is progressively added by those samples containing the most information to distinguish the failure boundary. More importantly, we propose a novel mechanism for structural critical domain prognosis mechanism based on the failure probability of each single material point within the entire field, and make accurate critical domain prognosis. Real-world examples, including a car wheel hub and a single-tower cable-stayed bridge, demonstrate that the proposed algorithm achieves high prediction accuracy, computational efficiency, and robustness in large-scale structural reliability analysis and critical domain prognosis. It consistently outperforms widely used methods such as AK-MCS, EFF-MCS, ERF-MCS, and H-MCS. Notably, the proposed AER-GP method requires only a small number of initial DoE samples (fewer than 40), and through adaptive learning, it can reliably produce results with very low errors (typically less than 2%).