Bearing Dynamics Identification with SINDy-Based Neural Network and Physics Model

Deep neural networks can fit nonlinear bearing vibration responses, but their learned parameters are difficult to relate to contact deformation, rolling element angular position, and other acceleration-generating mechanisms. To improve physical traceability in data-driven bearing dynamics identification, this study develops a physics-informed SINDy-NN with a mechanism-guided feature library. This paper presents a novel approach for constructing a physics-informed SINDy-NN (Sparse Identification of Nonlinear Dynamics-based Neural Network) and demonstrates its application in identifying bearing dynamics. A 5-DoF (five Degrees of Freedom) bearing dynamics model is built, and the primary components influencing the acceleration response are analyzed. This analysis forms the basis for defining a physics-explainable basis function library for the SINDy-NN. For comparison, widely used polynomial and Fourier libraries are also employed to evaluate modeling accuracy and convergence speed. Furthermore, to address the limited number of bearing data, virtual states are generated by applying multiple finite differences to the acceleration signal, expanding the dimensionality of the model and enabling the use of a Multi-Input–Multi-Output (MIMO) model in SINDy-NN. Finally, experimental data from the FEMTO bearing test bench are utilized for validation. The results demonstrate that the physics-informed SINDy-NN offers superior modeling efficiency, with sufficient accuracy and improved interpretability compared to general SINDy-NN.