As the core component of aircraft systems, aeroengines require accurate Remaining Useful Life (RUL) prediction to ensure flight safety, which serves as a key part of Prognostics and Health Management (PHM). Traditional RUL prediction methods primarily fall into two main categories: physics-based and data-driven approaches. Physics-based methods mainly rely on extensive prior knowledge, limiting their scalability, while data-driven methods (including statistical analysis and machine learning) struggle with handling high-dimensional data and suboptimal modeling of multi-scale temporal dependencies. To address these challenges and enhance prediction accuracy and robustness, we propose a novel hybrid deep learning framework (CLSTM-TCN) integrating 2D Convolutional Neural Network (2D-CNN), Long Short-Term Memory (LSTM) network, and Temporal Convolutional Network (TCN) modules. The CLSTM-TCN framework follows a progressive feature refinement logic: 2D-CNN first extracts short-term local features and inter-feature interactions from input data; the LSTM network then models long-term temporal dependencies in time series to strengthen global temporal dynamics representation; and TCN ultimately captures multi-scale temporal features via dilated convolutions, overcoming the limitations of the LSTM network in long-range dependency modeling while enabling parallel computing. Validated on the NASA C-MAPSS data set (focusing on FD001), the CLSTM-TCN model achieves a root mean square error (RMSE) of 13.35 and a score function (score) of 219. Compared to the CNN-LSTM, CNN-TCN, and LSTM-TCN models, it reduces the RMSE by 27.94%, 30.79%, and 30.88%, respectively, and significantly outperforms the traditional single-model methods (e.g., standalone CNN or LSTM network). Notably, the model maintains stability across diverse operational conditions, with RMSE fluctuations capped within 15% for all test cases. Ablation studies confirm the synergistic effect of each module: removing 2D-CNN, LSTM, or TCN leads to an increase in the RMSE and score. This framework effectively handles high-dimensional data and multi-scale temporal dependencies, providing an accurate and robust solution for aeroengine RUL prediction. While current performance is validated under single operating conditions, ongoing efforts to optimize hyperparameter tuning, enhance adaptability to complex operating scenarios, and integrate uncertainty analysis will further strengthen its practical value in aircraft health management.

Mathematical models and methods serve as fundamental tools for studying ice-related phenomena in the Yellow River. River ice is driven and constrained by hydrometeorological and geographical conditions, creating a complex system. Regarding the Yellow River, there are some uncertainties that manifest in unique features in this context, including ice–water–sediment mixed transport processes and the distribution of sediment both within the ice and on its surface. These distinctive characteristics are considered to different degrees across different scales. Mathematical models for Yellow River ice developed over the past few decades not only encompass models for the large-scale deterministic evolution of river ice formation and melting, but also uncertainty parameter schemes for deterministic mathematical models reflecting the Yellow River’s particular ice-related characteristics. Moreover, there are modern mathematical results quantitatively describing these characteristics with uncertainty, allowing for a better understanding of the unique ice phenomena in the Yellow River. This review summarizes (a) universal equations established according to thermodynamic and hydrodynamic principles in river ice mathematical models, as well as (b) uncertainty sources caused by the river’s characteristics, ice properties, and hydrometeorological conditions, embedded in parametric schemes reflecting the Yellow River’s ice. The intractable uncertainty-related problems in space–sky–ground telemetric image segmentation and the current status of mathematical processing methods are reviewed. In particular, the current status and difficulties faced by various mathematical models in terms of predicting the freeze-up and break-up times, the formation of ice jams and dams, and the early warning of ice disasters are presented. This review discusses the prospects related to the uncertainties in research results regarding the simulation and prediction of Yellow River ice while also exploring potential future trends in research related to mathematical methods for uncertain problems.

Statistical optimization methods serve as fundamental tools for studying sea-ice-related phenomena in the polar regions. To comprehensively analyze the spatial distributions of ice ridge keels, including the draft and spacing distributions, a statistical optimization model was developed with the aim of determining the optimal keel cutoff draft, which differentiates ice ridge keels from sea ice bottom roughness. By treating the keel cutoff draft as the identified variable and minimizing the relative errors between the theoretical and measured keel spatial distributions, the developed model aimed to seek the optimal keel cutoff draft and provide a precise method for this differentiation and to explore the impact of the ridging intensity, defined as the ratio of the mean ridge sail height to spacing, on the spatial distributions of the ice ridge keels. The utilized data were obtained from observations of sea ice bottom undulations in the Northwestern Weddell Sea during the winter of 2006; these observations were conducted using helicopter-borne electromagnetic induction (EM-bird). Through rigorous analysis, the optimal keel cutoff draft was determined to be 3.8 m, and this value was subsequently employed to effectively differentiate ridge keels from other roughness features on the sea ice bottom. Then, building upon our previous research that clustered measured profiles into three distinct regimes (Region 1, Region 2, and Region 3, respectively), a detailed statistical analysis was carried out to evaluate the influence of the ridging intensity on the spatial distributions of the ice ridge keels for all three regimes. Notably, the results closely matched the predictions of the statistical optimization model: Wadhams’80 function (a negative exponential function) exhibited an excellent fit with the measured distributions of the keel draft, and a lognormal function proved to effectively describe the keel spacing distributions in all three regimes. Furthermore, it was discovered that the relationship between the mean ridge keel draft and frequency (number of keels per kilometer) could be accurately modeled by a logarithmic function with a correlation coefficient of 0.698, despite considerable data scatter. This study yields several significant results with far-reaching implications. The determination of the optimal keel cutoff draft and the successful modeling of the relationship between the keel draft and frequency represent key achievements. These findings provide a solid theoretical foundation for analyzing the correlations between the morphologies of the sea ice surface and bottom. Such theoretical insights are crucial for improving remote sensing algorithms for ice thickness inversion from satellite elevation data, enhancing the accuracy of sea ice thickness estimations.

This paper proposes a distributed relative-position-based cooperative pointing control scheme for stationary planar multi-agent systems toward a stationary target under switching topologies. First, the proposed scheme only requires the leaders' orientation angles and relative position measurements, without relying on the agents' states in a common global coordinate frame. Then, the cooperative control problem is decoupled into cooperative target localization and local pointing control. In the proposed scheme, the cooperative target localization problem is modeled as a distributed relative position estimation system, in which the system dynamics are determined by the switching topologies and the projection matrices induced by the leaders' orientation angles. Under minimal information conditions, sufficient conditions are established to ensure the convergence of the proposed scheme by developing a novel error estimator and multiple Lyapunov functions. As a result, the generated reference orientations converge to the desired ones, and the local pointing controllers track them asymptotically. Finally, numerical simulations validate the effectiveness of the proposed method.