Contrastive learning and dynamics embedding neural network for label-free interpretable machine fault diagnosis

Industrial machinery often produces vibration signals that can serve as indicators of underlying faults. However, these signals often need to be labeled, presenting a challenge for accurate and interpretable fault diagnosis. While supervised learning methods, such as deep neural networks, have been applied for fault diagnosis, they need help in effectively distinguishing between different vibration-related faults. In response to this issue, our study introduces an innovative approach for automatic fault diagnosis through the application of the Bootstrap Your Own Latent and Dynamical Systems Model Discovery algorithm (BYOLDIS). This method not only addresses the challenge of unlabelled signals but also provides readily interpretable results. The proposed methodology consists of three fundamental steps. First, we derive a matrix of differential equations to capture the dynamic behavior of faulty bearings. Second, we employ a contrastive learning network alongside a time-delay embedding matrix to reconstruct the coordinates of the fault-dynamical system. Lastly, we construct a library of fault machine dynamic polynomial equations, incorporating prior constraints based on physical models. To assess the effectiveness and robustness of our proposed method, we conducted both simulations and experiments. The results of these case studies affirm that BYOLDIS can accurately diagnose bearing faults and offer dynamic explanations for the diagnostic outcomes. This suggests that BYOLDIS holds substantial promise as a diagnostic tool for processing unlabelled vibrational data.