A two-stage method for remaining useful life prediction of rolling bearings using an envelope-spectrum Wasserstein health indicator and ExtraTrees-guided residual correction

Accurate remaining useful life (RUL) prediction of rolling bearings is essential for predictive maintenance and the safe operation of rotating machinery. However, fault impulses are often weak during early degradation, limiting the ability of conventional statistical features to represent incipient damage. Bearings also differ in their degradation onsets and rates, making it difficult for prediction models to learn a consistent degradation-to-RUL mapping. To address these issues, this study proposes a two-stage RUL prediction method based on an envelope-spectrum Wasserstein health indicator and ExtraTrees-guided residual correction. First, envelope-spectrum energy is represented as a probability distribution over ordered frequency bands. The envelope-spectrum Wasserstein health indicator (EW-HI) measures the distributional deviation of each sample from a healthy reference state and identifies the initial prediction time (IPT). Second, IPT-referenced compact degradation features characterize post-IPT degradation while reducing the influence of redundant healthy-stage information and amplitude-scale differences. Finally, the ExtraTrees-guided residual correction (ET-RC) model combines a stable ExtraTrees prior prediction with a residual correction module that compensates for local nonlinear errors. Experiments on the PHM2012 and XJTU-SY bearing datasets show that the proposed method provides higher prediction accuracy, more reliable trend tracking, and greater prediction stability than the representative baseline models.