Purpose: As an advanced calculation methodology, reliability-based multidisciplinary design optimization (RBMDO) has been widely acknowledged for the design problems of modern complex engineering systems, not only because of the accurate evaluation of the impact of uncertain factors but also the relatively good balance between economy and safety of performance. However, with the increasing complexity of engineering technology, the proposed RBMDO method gradually cannot effectively solve the higher nonlinear coupled multidisciplinary uncertainty design optimization problems, which limits the engineering application of RBMDO. Many valuable works have been done in the RBMDO field in recent decades to tackle the above challenges. This study is to review these studies systematically, highlight the research opportunities and challenges, and attempt to guide future research efforts.Design/methodology/approach: This study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.Findings: First, the multidisciplinary design optimization (MDO) preliminaries are given. The basic MDO concepts and the corresponding mathematical formulas are illustrated. Then, the procedures of three RBMDO methods with different reliability analysis strategies are introduced in detail. These RBMDO methods were proposed for the design optimization problems under different uncertainty types. Furtherly, an optimization problem for a certain operating condition of a turbine runner blade is introduced to illustrate the engineering application of the above method. Finally, three aspects of future challenges for RBMDO, namely, time-varying uncertainty analysis; high-precision surrogate models, and verification, validation and accreditation (VVA) for the model, are discussed followed by the conclusion.Originality/value: The scope of this study is to introduce the RBMDO theory systematically. Three commonly used RBMDO-SORA methods are reviewed comprehensively, including the methods' general procedures and mathematical models.

Purpose: As a clean and renewable energy source, wind energy will become one of the main sources of new energy supply in the future. Relying on the stable and strong wind resources at sea, wind energy has great potential to become the primary energy. As a critical part of the wind turbine, the gearbox of a wind turbine often bears a large external load. Especially at sea, due to the effects of ocean corrosion, waves and wind, the burden of the wind turbine gearbox is greater, which brings great challenges to its reliability analysis. This study aims to systematically review the reliability research in wind turbine gearboxes and guide future research directions and challenges.Design/methodology/approach: This study systematically reviews some design requirements and reliability analysis methods for wind turbine gearboxes. Then, it summarizes previous studies on wind load uncertainty modeling methods, including the processing of wind measurement data and the summary of three different classifications of random wind speed prediction models. Finally, existing reliability analysis studies on two major parts of the gearbox are described and summarized.Findings: First, the basic knowledge of wind turbine gearboxes and their reliability analysis is introduced. The requirements and reliability analysis methods of wind turbine gearboxes are explained. Then, the processing methods of wind measurement data and three different random wind speed prediction models are described in detail. Furthermore, existing reliability analysis studies on two common parts of wind turbine gearboxes, gears and bearings, are summarized and classified, including a summary of bearing failure modes. Finally, three possible future research directions for wind turbine gearbox reliability analysis are discussed, namely, reliability research under the influence of multiple factors on gears, damage indicators of bearing failure modes and quantitative evaluation criteria for the overall dynamic characteristics of offshore wind turbine gearboxes and a summary is also given.Originality/value: This paper aims to systematically introduce the relevant contents of wind turbine gearboxes and their reliability analysis. The contents of wind speed data processing, predictive modeling and reliability analysis of major components are also comprehensively reviewed, including the classification and principle introduction of these contents.

Hydrogen has gradually become one of the indispensable sources of energy for mankind. Since the discovery of hydrogen embrittlement (hydrogen-induced degradation of material properties) more than 100 years ago, fatigue properties in hydrogen environments have been studied. Fatigue crack growth of materials in a hydrogen environment is a complex process involving the interaction of multiple factors. Hydrogen binds to atoms within the material, leading to diffusion and aggregation of hydrogen atoms, which causes an increase in internal stresses. These stresses may concentrate at the crack tip, accelerating the rate of crack expansion and leading to fatigue fracture of the material. The work of current researchers has summarised a number of fatigue models to help understand this phenomenon. This paper firstly summarises the existing hydrogen embrittlement mechanisms as well as hydrogen embrittlement experiments. It then focuses on the mechanism of fatigue crack propagation in hydrogen environments and related literature. It also analyses and summarises a cluster diagram of the literature generated using CiteSpace. The fatigue life prediction methods for materials in hydrogen environment are then summarised in this paper. It aims to provide some guidance for the selection and design of materials in developing fields such as fatigue materials in hydrogen environment. Finally, challenges in the current research on the fatigue properties of materials under hydrogen embrittlement conditions are pointed out and discussed to guide future research efforts.

The planetary gearbox is an important part of the wind turbine. There are many random uncertain factors in the process of design, production, installation, and use, and these uncertain factors greatly influence the service life and reliability of the planetary gearbox. Therefore, the influence of uncertain factors needs to be considered in the design process to reduce the risk of failure. In this paper, an uncertainty design optimization method based on evidence theory is proposed, which can consider both interval variables and random variables in the optimization process. Then the megawatt wind turbine planetary gearbox is taken as the research object to analyze its uncertainty sources. Finally, the planetary gearbox is optimized by the proposed method. By comparing the results, the design scheme obtained by the method proposed in this paper is more reliable.

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.