Physics-informed diffusion model for small-sample bearing fault diagnosis via signal generation

Rolling bearing fault diagnosis is fundamentally limited under small-sample conditions, where insufficient data hinder stable modeling of impact structures and modulation characteristics in nonstationary vibration signals. Existing generative approaches predominantly rely on distribution fitting, which, under data scarcity, often induces structural deviations that cause generated signals to deviate from underlying fault mechanisms, thereby degrading diagnostic performance. To address this limitation, we propose a physics-informed diffusion model that incorporates mechanism-related residuals into the diffusion training process, thereby imposing explicit constraints on the generated distribution and preserving consistency in impact–modulation structures. Methodologically, physical residuals are constructed based on envelope spectrum modulation, complemented by impulsiveness and sparsity features, to jointly constrain the frequency organization and temporal structure of signals, thereby capturing key representations of fault mechanisms. To mitigate the bias introduced by nonlinear residuals under mean estimation, a hybrid residual evaluation strategy is adopted to preserve critical structural information while maintaining training stability, enabling constraints to remain effective in low-noise regimes. Experimental results demonstrate that the proposed method effectively reduces distributional deviation under small-sample conditions and maintains stable performance across diverse operating conditions. The generated samples more closely resemble real signals in terms of impact structures and characteristic frequency organization, thereby improving the accuracy and robustness of downstream fault diagnosis. This method provides a principled modeling framework for fault signal generation under small-sample conditions, balancing distributional consistency and mechanism-based constraints.