A multi-scale progressive fusion method for predicting the remaining useful life of gears guided by a control-equation-compatible a priori cascade

Gears are core transmission components of high-end equipment in aerospace, rail transit and other key fields. Accurate remaining useful life (RUL) prediction of gears is critical for equipment prognostics and health management (PHM), to ensure operational safety and reduce maintenance costs. Aiming at key limitations of existing data-driven gear RUL prediction methods, including strong data dependency, insufficient physical interpretability, low mapping accuracy and weak cross-condition generalization, this paper proposes a novel progressive multi-level feature fusion RUL prediction framework guided by cascaded control equation compatibility priors. Taking gear vibration time-domain signals as the sole input, the framework sequentially adopts three customized modules: Governing Equations Auto-Encoder (GEAE) to extract physically consistent robust degradation features, Multi-scale Fusion Network (MsNet) to construct health indicators for degradation characterization, and Dual Temporal Constraints Network (DTCNet) to achieve accurate RUL mapping. Systematic validation on two heterogeneous datasets demonstrates that the framework reduces RMSE by up to 40.6% and improves R 2 by 25.0% over end-to-end methods, while significantly enhancing HI monotonicity and trendability. Cross-seed statistical tests confirm its robustness (coefficient of variation ≤ 1.9%). The method consistently outperforms state-of-the-art approaches and exhibits strong cross-scenario generalization.