Research on mechanical fault diagnosis method based on federated differential equations

The existing fault diagnosis methods based on federated learning mainly focus on the privacy, data heterogeneity, and communication efficiency, while neglecting the problem related to memory consumption, computational costs, and interpretability in the federated learning diagnostic model. To overcome these deficiencies, neural networks are re-examined from the perspective of dynamic systems in this paper. However dynamic systems are closely related to differential equations, and dynamic problems can usually be described by establishing differential equations. Therefore, a mechanical fault diagnosis based on federated differential equations (FDEs) is proposed. In the proposed FDE-based method, the complex calculation process between neurons and network layers can be replaced by a differential equations solver, which greatly reduces memory consumption and the number of model parameters, increases the interpretability of the diagnostic model, and establishes a connection between mechanical dynamics and the federated learning; the deep integration of mechanical dynamics and federated learning is greatly prompted. Finally, the proposed FDE method has been successfully applied to fault diagnosis of aero-engine, and the proposed method is compared with the fault diagnosis method based on federated learning. The experimental results show that the proposed method not only has a satisfactory fault recognition rate but also has the ability of continuous dynamic learning. The number of model parameters is greatly reduced, and the interpretability of the diagnostic model is greatly enhanced. The research in this paper has important theoretical value and engineering application value for the deep integration of mechanical dynamics and artificial intelligence.