Although data-driven machine learning methods have been successfully applied to predict complex nonlinear dynamics, forecasting future evolution based on incomplete past information remains a significant challenge. This paper proposes a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct a robust model where LightGBM builds a fitting function to capture and simulate the complex coupling relationships among variables in dynamically evolving chaotic systems. This approach enables the reconstruction of missing data, restoring sequence completeness and overcoming the limitations of existing chaotic time series prediction methods in handling missing data. We validate the proposed method by predicting the future evolution of variables with missing data in both dissipative and conservative chaotic systems. Experimental results demonstrate that the model maintains stability and effectiveness even with increasing missing rates, particularly in the range of 30% to 50%, where prediction errors remain relatively low. Furthermore, the feature importance extracted by the model aligns closely with the underlying dynamic characteristics of the chaotic system, enhancing the method’s interpretability and reliability. This research offers a practical and theoretically sound solution to the challenges of predicting chaotic systems with incomplete datasets.

Fractional-order chaotic systems describe complex dynamic processes with memory effects and long-range correlations, while integer-order chaotic systems are generally viewed as a special case of fractional-order counterparts. This close relationship often renders the two difficult to distinguish in practice. However, existing studies mostly design analytical methods for integer-order or fractional-order chaotic systems separately, lacking a unified classification framework that does not rely on prior assumptions about the system order. In this paper, we propose a multi-branch deep learning model integrating a multi-scale convolutional neural network, time–frequency analysis, Transformer blocks, and dynamic memory network to classify integer-order chaos, fractional-order chaos, and steady states. Experiments are conducted on time series from canonical chaotic systems—including the Lorenz, Rössler, Lü, and Chen systems—in both integer- and fractional-order formulations, under two data generation protocols: varying initial conditions and varying system parameters. We evaluate the model under two scenarios: (1) assessing baseline classification performance on noise-free data and (2) testing robustness against increasing levels of Gaussian, salt-and-pepper and Rayleigh noise. The model achieves classification accuracy above 99% on noise-free data across all tested systems. Under noise interference, it demonstrates strong robustness: accuracy remains above 89.7% under high-intensity Gaussian noise. Moreover, we demonstrate that the model trained with fixed system parameters but varying initial conditions generalizes poorly to unseen parameter settings, whereas training with diverse system parameters—while fixing initial conditions—markedly improves generalization. This work offers a data-driven framework for distinguishing integer- and fractional-order chaos and highlights the critical role of training data diversity in building generalizable classifiers for dynamical systems.

Early fault prediction of wind turbines is critical for ensuring wind farm safety and reducing operation and maintenance costs. However, the latent and progressive nature of incipient faults, together with concurrent failures across multiple subsystems, makes accurate root-cause identification challenging. In addition, severe class imbalance between normal and faulty samples further degrades prediction performance, particularly for minority fault types. To address these challenges, this paper proposes a novel fault prediction model, M²ANet, using SCADA data within a 30-min pre-fault window. The model combines a dual-memory module with progressive dilated convolutions to efficiently capture multi-scale temporal dependencies from high-dimensional operational variables. An entropy-bias penalty is further introduced into the loss function to adaptively regularize the predicted probability distribution, alleviating overconfidence under imbalanced data conditions and improving the recognition of minority faults. Experiments on a real-world wind farm dataset show that M²ANet achieves an overall accuracy of 90.73% and a weighted F1-score of 90.62% in multi-class fault prediction, outperforming 10 representative baseline models. In addition to these aggregate metrics, per-class evaluation confirms the model’s robustness under class imbalance. Notably, for yaw system faults, which account for only 1.9% of the samples, M²ANet achieves a recall of 95.92% with a 30-min-ahead warning. These results demonstrate its effectiveness and reliability for early fault prediction in practical wind turbine applications.