An adaptive Bayesian Physics-Informed neural network model for predicting the fatigue life of high-strength steel under non-uniform corrosion

High-strength steel subjected to non-uniform corrosion exhibits substantial variability and randomness in fatigue life, creating significant challenges for ensuring the durability of large-scale infrastructure. The Bayesian Physics-Informed Neural Network (BPINN) framework offers a promising direction by combining the interpretability of Physics-Informed Neural Networks (PINNs) with the uncertainty quantification capabilities of Bayesian Neural Networks (BNNs). However, its reliance on normal-distribution priors limits its ability to capture uncertainties in complex environmental conditions. To address this, we propose an Adaptive-weighted Physics-Informed Bayesian Neural Network (A-BPINN) that embeds a Bayesian layer within each weight layer. This design captures cognitive uncertainty in structural performance degradation and observation noise through parameter randomization, thereby overcoming the limitations of fixed normal priors. The approach enables joint modeling of data-driven, physics-informed, and distribution-robust components. Comparative results show that, under identical data partitions, A-BPINN achieves the best balance between accuracy and uncertainty calibration. Compared with BPINN, A-BPINN reduced the MSE from 0.138 to 0.109 and produced a slightly wider but better-calibrated predictive interval, as indicated by improved interval coverage and probabilistic evaluation metrics. Although its coverage is slightly lower than that of a pure BNN, A-BPINN reduces MSE by 40% and produces substantially narrower confidence intervals. Compared to a PINN model, the MSE decreased by 30%. These findings demonstrate that A-BPINN delivers high accuracy without sacrificing reasonable uncertainty estimation, challenging the conventional belief that higher precision must come at the cost of greater uncertainty. This provides a more robust and reliable framework for assessing the fatigue life of corroded steel structures.