A Physics-Informed Temporal-Enhancing Neural Network for Remaining Useful Life Prediction of Rolling Bearing

Fluctuations in rolling bearing vibration signals, induced by stage-dependent degradation dynamics and stochastic disturbances under varying operating conditions, pose significant challenges for remaining useful life (RUL) prediction. Consequently, this nonstationarity masks subtle early degradation cues, hinders stage-transition modeling, and often causes purely data-driven methods to produce physically implausible RUL decay trajectories. Moreover, interpretability remains limited when learned degradation representations are weakly connected to physically meaningful decay dynamics. To overcome these challenges, a physics-informed temporal-enhancing neural network (PI-TENN) is developed for estimating the RUL of rolling bearings across multi-stage degradation regimes. Specifically, a temporal-enhancing degradation feature fusion module is constructed by coupling a multi-layer long short-term memory (LSTM) temporal dependency encoder with an attention-enhancing block. In this way, the multi-layer LSTM encoder captures long-range temporal dependency, while the attention-enhancing block suppresses noise-dominated time steps and highlights degradation-relevant patterns, thereby producing latent degradation representations that are stable across degradation stages. Furthermore, a universal partial differential equation (PDE) is constructed to explicitly relate the latent degradation representation to the decay rate of RUL, which enables the learning of stage-wise RUL evolution patterns across distinct degradation stages. Meanwhile, model optimization is guided by a data–physics fusion loss integrating data fitting, PDE residual, and monotonicity regularization, so that predictive accuracy and physically consistent stage-wise decay are jointly ensured. Finally, experiments on full-life-cycle steel and ceramic bearing datasets demonstrate improved accuracy, robustness under complex operating conditions, and enhanced physical consistency compared with representative baselines.