Accurate remaining useful life (RUL) prediction for bearings remains challenging when operating conditions differ from those encountered during training. Changes in vibration distributions limit model generalization, while sequence-level RUL labels provide limited guidance on degradation evolution within each input sequence. To address these limitations, this paper proposes a physics-constrained generalization damage-dynamics network (PCGDN), a framework combining multi-source domain generalization with a learnable physical constraint. A shared bidirectional gated recurrent unit extracts temporal features for RUL estimation and auxiliary latent-damage modeling. Multi-kernel maximum mean discrepancy reduces feature-distribution differences among source conditions, supporting generalization without access to target-condition data during training. A learnable Kachanov-type constraint links a vibration-derived load proxy to latent damage evolution, guiding the shared representation without requiring measured stress, damage labels, or calibrated material constants. Experiments on the PHM 2012 bearing dataset show that PCGDN achieves lower average prediction errors than representative baselines under unseen operating conditions. 

Remaining useful life prediction; rolling bearings; physics-informed learning; domain generalization; Kachanov damage model