A Physics-Informed Neural Network Framework Leveraging Deterministic Learning and Statistical Constraints for Bearing Fault Diagnosis

Abstract

Recently, physics-informed learning-based intelligent bearing fault diagnosis methods have demonstrated great potential in improving diagnostic accuracy and physical consistency. Nevertheless, the practical deployment of conventional physics-informed neural networks typically relies on explicit partial differential equations (PDEs), which are generally difficult to acquire in real industrial scenarios. To address this limitation, a PDE-free physics-informed bearing fault diagnosis framework is proposed based on deterministic learning and statistical constraints. In the proposed framework, deterministic learning is adopted to extract nonlinear dynamic trajectories from multi-directional bearing vibration signals. The residuals between sample dynamic trajectories and class-specific standard trajectories are further converted into probabilistic statistical soft constraints. Accordingly, the system evolution mechanism embedded with physical dynamic characteristics is incorporated into the model training process, eliminating the need for explicit PDE constraints. In addition, a composite loss function is constructed by integrating the supervised classification loss with dynamic trajectory-based statistical constraint terms. This enables the network optimization process to be jointly guided by classification error and physical dynamic consistency. Finally, the effectiveness of the proposed method is validated through simulation and experimental studies. The results reveal that the average discernibility of dynamic trajectories reaches 0.3614, representing respective improvements of 122% and 68.6% over time-domain and frequency-domain signals. The proposed method achieves an effective balance among diagnostic accuracy, inference speed, and model complexity, with its average parameter volume reduced by approximately 93.9% relative to the comparative methods. These results demonstrate that the proposed method is applicable to bearing fault diagnosis scenarios where explicit PDE information is unavailable.