Hydrogen embrittlement poses a critical threat to the durability of metallic components in emerging hydrogen energy infrastructure. Reliable fatigue life assessment in hydrogen-rich environments is, however, severely constrained by the high cost and low throughput of high-pressure testing, resulting in characteristically sparse experimental datasets. Conventional empirical fatigue models struggle to capture hydrogen–mechanical coupling effects, while purely data-driven approaches often suffer from severe overfitting under data-scarce conditions. To address this challenge, this study develops a physics-enhanced learning framework that integrates established fracture mechanics principles with machine learning. Using high-strength GS80A steel as a case study, two complementary strategies are introduced. First, a physically augmented input strategy reformulates raw experimental variables into dimensionless physical descriptors derived from the Basquin and Goodman relations, thereby reducing the complexity of the learning space. Second, a physics-regularized ensemble strategy combines deterministic physical predictions with neural network outputs through a dual-pathway inference scheme, ensuring physically admissible behavior during extrapolation. An automated hyperparameter selection module is further employed to establish a robust data-driven baseline. Comparative evaluation against optimized multi-layer perceptron and support vector regression models demonstrates that the proposed framework significantly improves predictive robustness in small-sample regimes. Specifically, the coefficient of determination ($R^2$) exceeds 0.975, with the root mean square error (RMSE) reduced by approximately 70% compared to the pure data-driven baseline. By systematically embedding mechanistic priors into the learning process, the proposed approach provides a reliable and interpretable tool for fatigue assessment of metallic components operating in hydrogen environments.

In practical engineering, mechanical structures are affected by time-dependent uncertainties and by correlated failure modes. This study proposes an enhanced time-variant reliability analysis framework by coupling a mixed Archimedean Copula model with an adaptive Kriging model driven by the maximum expected prediction error (MEPE) learning function. The mixed Copula combines Gumbel, Clayton and Frank components, so that upper-tail, lower-tail and nearly symmetric dependence can be represented in one model. The MEPE function combines Kriging prediction variance and leave-one-out cross-validation error through a dynamic balance factor, which guides early global exploration and later refinement near the most probable point trajectory. For the planar three-bar structure, the mixed-Copula failure probability at t = 7 is 0.4078, close to the direct-MCS benchmark 0.4059, with a relative error of 0.47%; the number of original limit-state evaluations decreases from 1.00 × 10⁶ to 326, corresponding to a 99.97% reduction. For the two-rod parallel structure, the mixed-Copula failure probability at T = 2 is 0.0987, close to the direct-MCS benchmark 0.0992, with a relative error of 0.50%; the number of original limit-state evaluations decreases to 284. The calculated upper- and lower-tail dependence coefficients of the mixed Copula are 0.1345 and 0.2985 for the planar three-bar structure and 0.0003 and 0.3709 for the two-rod parallel structure. These quantitative results show that the proposed framework can describe nonlinear failure dependence more flexibly than a single Copula while retaining high computational efficiency.

This paper proposes an adaptive subregion-based active Kriging (AS-AK) surrogate modeling approach. Firstly, an adaptive subregion decomposition strategy is developed to partition the candidate sample space into multiple concentric subregions, significantly enhancing the efficiency and accuracy of sampling. Subsequently, an active Kriging surrogate model is constructed, where the surrogate model is sequentially updated by iteratively selecting critical samples within each subregion to precisely approximate the highly nonlinear limit state function. Moreover, a collaborative multi-output surrogate modeling framework is further established to systematically handle correlations among multiple failure modes. Four benchmark numerical examples and an engineering application involving an aeroengine rigid-flexible coupling system illustrate that the proposed AS-AK method significantly outperforms existing reliability methods in both computational efficiency and accuracy.