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.

With the engineering system becoming more and more complex, the uncertainty factors have a more and more profound influence on the reliability and security of the engineering system. In recent years, Reliability-Based Design Optimization (RBDO) has been studied extensively in complex engineering system design. The research on reliability optimization design considering stochastic uncertainty has been comprehensive and widely used. However, the reliability optimization design considering mixed uncertainty has the disadvantages of large computation and imprecise convergence. This study proposes an RBDO method based on Particle Swarm Optimization (PSO) and Simulated Annealing (SA) to overcome this challenge. In the method, PSO is used to solve the most probable point, while SA has excellent global optimization capability to acquire the global optimal solution. Finally, three examples are given to illustrate the advantages of the proposed method.

In this paper, a novel MRGP-SS method is proposed to deal with the reliability analysis problems under multiple failure modes. First, a random moving quadrilateral grid sampling (RMQGS) method is proposed to improve the randomness and uniformity of initial samples. Second, an adaptive procedure, which combines the multiple response Gaussian process (MRGP) model and the novel active learning functions, is proposed to efficiently and accurately produce surrogate models for failure surfaces. In this regard, two novel learning functions are introduced to adapt to different iterative cycles, one is employed to correct the quality of samples, and the other is used to search for the samples closest to the limit state surface. Third, the subset simulation (SS) is integrated into the adaptive MRGP model to estimate the failure probability under multiple failure modes with fewer function calls and time consumption. Numerical and engineering case studies are finally provided to demonstrate the effectiveness of the proposed method.

In this study, material and dynamic stress experiments are combined with finite element (FE) simulations to reveal the fracture mechanism of the wheelset lifting apparatus, and a structural design optimization scheme based on the double-layer Kriging surrogate model is proposed. The fracture mechanism of the wheelset lifting apparatus is first clarified through the material analysis of macro/micro and dynamic stress tests. Static strength and modal analyses are then performed to perfect the mechanism analysis in terms of structural performance. An efficient, robust, fatigue design optimization method based on the double-layer Kriging surrogate model and improved non-dominated sorting genetic algorithm II (NSGA-II) is finally proposed to improve the original design scheme. For the wheelset lifting mechanism’s fracture, the crack source is found on the transition fillet surface of the lifting lug and lifting ring, where the fracture has the characteristics of two-way, multisource, high-cycle, low-stress fatigue. It is further revealed that the vibration fatigue occurring at the point of maximum stress is the main cause of the fracture. The effectiveness of the proposed design optimization method is validated via comparative analysis.