Xiaolong Wang

In order to tackle the problems of precisely identifying fault modes and accomplishing cross-condition diagnosis using limited data under the background of imbalanced rolling bearing data, this paper comprehensively integrates transfer learning techniques and feature enhancement strategies. We present two feature enhancement modules: the Neural Ordinary Differential Equations-based Temporal Feature Enhancement Module (NODE-TFEM) and the Path Signatures-based Spatial Feature Enhancement Module (PS-SFEM). Firstly, the residual-enhanced CNN (ResCNN) architecture is used to extract local features from vibration signals. Then the NODE-TFEM utilizes the local features as initial values, and then models the feature space as the systems of ordinary differential equations. By solving the systems, this module can capture the temporal evolution of ResCNN features. On the other hand, the PS-SFEM regards each vibration signal as a mathematical path. Through calculating its iterative integral, the module acquires a spatial feature representation of the entire vibration signal. This feature has a clear geometric meaning in mathematical terms, further enhancing the interpretability of the model. The validity of the proposed methodology has been meticulously verified on the Paderborn University bearing dataset, the Jiangnan University bearing dataset and the laboratory-acquired bearing dataset. These experiments comprehensively probed into the performance of the methodology, manifesting its potential to surmount the challenges in the domain of rolling-bearing fault diagnosis and furnishing robust evidence for its practical implementation in real-world mechanical maintenance scenarios.

Efficient methods for solving the Fokker–Planck (FP) equation are crucial for studying stochastic systems. This paper proposes a transfer learning method to solve the FP equation, enabling the training process to proceed without starting from the beginning. The equivalent linearization is first applied to unify a class of stochastic differential equations into a single simplified form. Subsequently, a pre-trained neural network framework, inspired by transfer learning, is designed based on the FP equation of the simple system. By leveraging the pre-trained neural network, the solving process is accelerated by starting from a more advanced state. Finally, numerical experiments are conducted to verify the proposed approach, including one- and two-dimensional stochastic systems as well as a system driven by both Gaussian and Lévy noise. Results show that the contours of the FP equations can be learned by the network very expeditiously, greatly reducing training time while maintaining accuracy. The proposed method not only improves computational efficiency but also demonstrates strong generalization capabilities.

Reconstructing attractors of airfoil systems from observations facilitates understanding of aeroelasticity, especially the onset of flutter. However, it is generally difficult due to observation noise and the nonlinear nature of the underlying dynamics. In this study, a hybrid strategy is proposed which incorporates data preprocessing and next generation reservoir computing (NG-RC) for reconstructing attractors of an airfoil system. This approach first estimates the system states from noisy observations via a state estimation method and then trains the NG-RC model to predict the responses of the airfoil system. The NG-RC employs nonlinear functions of past states to approximate the dynamics, requiring less training data and fewer hyperparameters than the conventional reservoir computing. To reduce the model complexity, both [ ] and smoothed [ ] norm penalties are introduced to promote the sparsity of trainable weights, where the optimal weights are determined by simple iterative optimization. Simulation results show that the proposed method can predict various vibration patterns and reconstruct the attractors of the airfoil system from limited, noisy observations. The smoothed [ ] norm penalty can lead to sparser weights and, in some cases, enhance performance. The findings support applications of the present method like flutter boundary prediction and flight accident analysis.

Nonlinear dynamical systems with control parameters may not be well modeled by shallow neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions of the parameter-dependent Lorenz system are learned simultaneously via a very deep neural network. The proposed deep learning model consists of a large number of identical linear layers, which provide excellent nonlinear mapping capability. Residual connections are applied to ease the flow of information and a large training dataset is further utilized. Extensive numerical results show that the chaotic solutions can be accurately forecasted for several Lyapunov times and long-term predictions are achieved for periodic solutions. Additionally, the dynamical characteristics such as bifurcation diagrams and largest Lyapunov exponents can be well recovered from the learned solutions. Finally, the principal factors contributing to the high prediction accuracy are discussed.

The increasing number of satellites bring serious hazard for the on-orbit spacecraft. For the large malfunction satellites removal mission, multi-spacecraft cooperative pursuit and remove is an efficient approach. There are many constraints should be considered in the process of pursuit, including and no limit to, the collision constraints between service spacecraft, collision constraints between service spacecraft and target spacecraft, communication constraints between service spacecraft, and cooperative pursuit formation configuration constraints. It brings challenge to control the multiple satellites considered the multiple constraints at the same time in the process of formation reconfiguration and pursuit. For this problem, a novel cooperative control method based on task priority is proposed in this paper. Firstly, the dynamic equation of multi-spacecraft cooperative pursuit is developed. Secondly, the constraints of the failed spacecraft pursuit are analyzed, and the priority of each task is analyzed. The multi-spacecraft cooperative control approach based on the null-space behavior (NSB) method and the artificial potential function method are introduced. The advantage of the proposed method is that, it can avoid conflicts between the coordinated tasks, and meet the multiple constraints. In order to verify the proposed approach, a simulation of multiple satellites pursuit is provided, and the simulation results show the superiority and effectiveness of the method proposed.