Interpretable physics-guided data augmentation for rotating machinery using empirical wavelet transform and sparse identification of nonlinear dynamics

Data scarcity limits the development of machine-learning-based fault diagnosis systems for rotating machinery, especially under noise and varying operating conditions. This paper presents an interpretable, physics-guided data augmentation framework in which empirical wavelet transform (EWT), time-delay embedding and sparse identification of nonlinear dynamics (SINDy) are combined so that the SINDy-identified equations serve not for prediction or control, but as a compact generative model that is perturbed to produce physically consistent synthetic vibration trajectories. Vibration signals are decomposed by EWT into noise-reduced, fault-sensitive modes, embedded in higher-dimensional state space, and governed by compact equations identified via SINDy. Synthetic trajectories generated by perturbing initial conditions preserve fault-related nonlinear features. The framework is evaluated on an experimental broken rotor bar test rig and a numerical rotor-bearing-disc finite element model. Across torsional loads from 1 to 4 N m and rotational speeds from 85 to 115 rad/s, the method contributes to classification accuracies between 95.6% and 100% using augmented data from 1-3 real observations per fault class. Results indicate that combining adaptive signal decomposition with parsimonious dynamical modelling enables effective data synthesis at 10 dB SNR for the tested rotor systems, offering an interpretable alternative to black-box generative models in similar applications.