A novel physical constraint-guided quadratic neural networks for interpretable bearing fault diagnosis under zero-fault sample

To increase confidence in intelligent damage assessment models, research often emphasizes interpretability but neglects essential physical fault mechanisms. Addressing this gap, we propose a novel hybrid learning framework combining a dynamic physical model with a data-driven Quadratic Neural Network and Bidirectional LSTM (QNN-Bi-LSTM). Acceleration and velocity equations of the rolling element, derived physically, are embedded as constraints into the loss function, guiding learning. This Physical Constraint-Guided (PCG) learning aligns physical laws with features from real-world vibration data. To enhance generalization under zero fault samples, a genetic algorithm adaptively balances physical and cross-entropy losses. Experiments show the model achieves near 100% accuracy no-load and 95% heavy-load with zero fault samples, exhibiting strong robustness. Compared to conventional models, it significantly enhances interpretability, credibility, and reliability. This highlights a new direction for NDE and condition monitoring, especially for insufficient fault scenarios. Integrating physical principles and nonlinear feature learning offers a promising, generalizable solution for intelligent damage assessment in critical systems like rolling bearings.