Uncertainty-Aware Bearing Remaining Useful Life Prediction Based on Conformal Prediction

Abstract

Accurate prediction of the remaining useful life of rolling element bearings is a critical task in prognostics and health management. Although deep learning methods have shown strong predictive capability, purely data-driven approaches still face two important limitations: they may produce physically inconsistent predictions that contradict the irreversible nature of bearing degradation and often fail to provide reliable uncertainty estimates. To address these issues, this paper proposes a physics-informed probabilistic framework to predict the remaining useful life. First, a health index is constructed from logarithmic envelope spectrum features using a variational autoencoder, enabling the extraction of a monotonic degradation indicator without requiring labeled fault data. Second, a Transformer-based predictor is trained with a monotonicity constraint that explicitly enforces the predicted remaining useful life to be non-increasing over time. Third, Monte Carlo dropout is used to quantify epistemic uncertainty, and a post-hoc conformal calibration strategy is applied to construct finite-sample prediction intervals with guaranteed marginal coverage by leveraging historical degradation data. Experiments on the XJTU-SY full-lifecycle bearing dataset show that the proposed framework improves point prediction accuracy relative to controlled feature and model ablations. More importantly, the uncertainty results reveal a substantial mismatch between raw Monte Carlo dropout intervals and the observed prediction errors: the average prediction interval coverage probability increases from 0.4835 before calibration to 0.9445 after conformal calibration. The resulting wider intervals should not be interpreted only as a loss of sharpness, but as a correction of the severe overconfidence of the uncalibrated model under heterogeneous degradation trajectories. Bearings with more irregular or non-stationary degradation behavior require wider calibrated intervals to maintain reliable coverage, indicating that the proposed framework can expose trajectory-dependent prediction difficulty and support risk-aware maintenance decisions.