Aero-engines are highly complex machines, and their reliability and lifespan directly impact flight safety. As a result, aero-engine reliability has become a significant research field. This paper aims to comprehensively summarize the progress in aero-engine reliability research. First, we analyzed the existing structures of aircraft engines, as well as the current research on reliability and commonly used estimation methods. Second, we reviewed the techniques employed for monitoring operational status and diagnosing faults in aircraft engines. Third, we summarized the optimization methods frequently used in fault diagnosis and lifespan prediction. Fourth, we conducted a bibliometric analysis. Finally, we identified potential challenges for future research. Based on our literature review, we found that: (1) mathematical modeling-based and data-driven approaches are currently the most commonly used methods for performance monitoring; (2) neural networks and deep learning are the most popular methods for fault diagnosis and lifespan prediction; (3) the bibliometric analysis reveals that China’s interest in aero-engine reliability research techniques is higher than that of other countries; and (4) further development is needed in the areas of overall system reliability, real-world usage scenario studies, and advanced simulation and modeling.

Bearing operating conditions are harsh and complex, with limited data available to effectively characterize bearing degradation processes during full-lifecycle condition monitoring. This makes it difficult to extract discriminative representations, severely impacting bearing remaining life prediction. Addressing the challenges of long lifecycles, subtle degradation features, and the physically inconsistent predictions in data-driven models for rolling bearings, this paper proposes a Physics-Informed Transformer (PIT) prediction framework. First, based on the physical properties of bearing degradation, a physics-informed feature selection criterion SC combining stationarity and correlation is constructed to screen high-confidence features. Second, a physics-data dual-stream residual architecture is designed. It explicitly models the macro-physical trends of degradation using a grey model GM(1,1) and replaces traditional recurrent networks with a Transformer encoder. Through a multi-head self-attention mechanism, it concurrently captures global long-term dependencies within complex data residuals. Most critically, a monotonicity-aware loss function was introduced, embedding the monotonicity regularization of degradation as soft constraints within the Transformer training process. Experiments demonstrate that this approach not only overcomes the vanishing gradient problem inherent in RNN-based models but also effectively eliminates non-physical fluctuations in prediction results, achieving an improved trade-off of accuracy, efficiency, and interpretability.

Remaining useful life (RUL) prediction plays a crucial role in prognostics and health management of aero-engines, as it directly supports condition-based maintenance and reliability-oriented decision-making. Although accurate RUL prediction is of great im-portance, existing approaches often struggle to simultaneously capture linear degradation trends and complex nonlinear degradation behaviors under varying operating conditions. To address this issue, this study proposes a hybrid ARIMA–Attention– LSTM framework for aero-engine RUL prediction, in which linear temporal characteristics and nonlinear residual dynamics are modeled in a decomposed manner. Specifically, an ARIMA model is employed to extract linear degradation trends, while an LSTM network with a multi-head attention mechanism is used to learn nonlinear residual dependencies, followed by a fusion strategy to integrate both predictions. The proposed method is evaluated on two public C-MAPSS subsets with different complexity levels and a private industrial dataset collected from in-service aero-engines. Experimental results demonstrate that the proposed framework consistently outperforms conventional statistical methods and representative deep learning models in terms of accuracy, robustness, and stability. The findings indicate that integrating linear trend modeling with attention-based nonlinear learning provides an effective and reliable solution for aero-engine RUL prediction and offers practical value for real-world PHM applications.

China’s economic development has achieved great success in recent years, but the problems of energy scarcity and environmental pollution have become increasingly serious. To enhance the reliability and efficiency between energy, the environment and the economy, sustainable development is an inevitable choice. In the context of measuring sustainability efficiency, a network data envelopment analysis model is proposed to formulate the two-stage process of energy use and operations management. A double frontier is derived to optimize the available energy for sustainable development. Due to nonlinearity, previous linear methods are not directly applicable to identify the double frontier and calculate stage efficiencies for inefficient decision-making units. To address this problem, this study develops the primal-dual relationship between multiplicative and envelopment network models based on the Lagrange duality principle of parametric linear programming. The newly developed approach is used to evaluate the sustainability efficiency of 30 administrative regions in China. The results show that insufficient sustainability efficiency is a systemic problem. Different regions should take different measures to conserve energy and reduce pollutant emissions for sustainable development. To increase sustainability efficiency, regions should support energy-saving and emission-reducing technologies in production processes and strengthen their capacity for technological innovation. Compared with energy use efficiency, operations management efficiency in China has a wider range of changes. During the operations management stage, there is not much difference between the capacity and quantity of each region. Based on benchmark regions at the efficiency frontier, there is an opportunity to improve operations management in the near future. Blockchain technology can effectively improve energy allocation efficiency.