A Degradation-Stage-Aware Transformer-GRU Method for Offline Cross-Condition Bearing Remaining Useful Life Prediction

Cross-condition remaining useful life (RUL) prediction of rolling bearings is affected by distribution shifts between operating conditions, limited labeled target-domain degradation samples, and interference from long stationary healthy stages. Under an offline full-life retrospective analysis protocol, this paper proposes a Degradation-Stage-Aware Transformer-GRU (DSA-TGRU) method. First, a health indicator is constructed from selected multidimensional degradation features by principal component analysis (PCA-HI), and an adaptive threshold moving rate of change (ATMROC) criterion is used to identify the transition from the healthy stage to the degradation stage, defined as the first prognostic time (FPT), i.e., the degradation-start time. Only post-FPT windows are then used to construct RUL labels for model training and evaluation. The prediction model combines a Transformer encoder for long-range sequence dependencies with gated recurrent units for temporal degradation evolution. The model is pretrained on source-domain bearings and then fine-tuned using a small number of labeled target-domain degradation samples available under the offline protocol. Stage-binned sampling and late-stage linear weighting are treated as auxiliary training strategies rather than universally effective modules. Experiments on the XJTU-SY and PHM2012 datasets show that post-FPT degradation modeling and target-domain fine-tuning play major roles in reducing cross-condition errors. The proposed method achieves average normalized MAE values of 0.0492 and 0.0738 and average normalized RMSE values of 0.0626 and 0.0928 on the two datasets, respectively, and generally outperforms several transfer-learning baselines in normalized error metrics. Ablation results further indicate that the benefits of stage-binned sampling and late-stage weighting are dataset- and task-dependent. The current version is not designed for online RUL prediction from incomplete target-bearing trajectories.