When Linear RUL Labels Disagree with Vibration Degradation: A Stage-Aware Target and Dual-Scale Predictor Evaluated on XJTU-SY and IMS

Abstract

Remaining useful life (RUL) studies commonly treat the label as fixed, although clock-linear labels may decline while measured vibration remains nearly stable and then changes rapidly near failure. We separate target design from prediction. A development-only pipeline constructs an oriented vibration health indicator, identifies chronological early, middle, and late stages, and fits a continuous linear-quadratic-exponential degradation-state target. A compact CNN-LSTM and Transformer learn the target from causal feature sequences, and validation-fitted Ordered Weighted Averaging combines their outputs. In a bearing-wise XJTU-SY hold-out, all bearings ending in 5 are excluded from fitted preprocessing, training, early stopping, and fusion. The fused predictor obtains an RMSE of 0.0608, an MAE of 0.0392, and an R-squared value of 0.9617, with the Transformer providing most of the accuracy. Target shape is assessed independently on three documented IMS failed-bearing trajectories. Against the best anchored linear fit to the same vibration-derived reference, the stage-aware curve reduces RMSE by 3.6-18.2% and MAE by 3.1-31.1%; the mean reductions are 10.2% and 15.0%, respectively. Conservative BIC differences of 128.8-368.1 favor the stage-aware representation, whereas moving-block bootstrap intervals cross zero. Thus, stage-dependent targets better describe the evaluated vibration-derived degradation states, but the evidence remains descriptive because only three official IMS runs are available. The study establishes a measurement-oriented target-validity framework, not a universal nonlinear law for physical time-to-failure or robust cross-domain prediction.

28 pages, 12 figures, 13 tables

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