Deep learning (DL) has shown great potential for remaining useful life (RUL) prediction, yet most existing methods focus on point estimates and lack reliable uncertainty quantification and calibration, which are crucial for risk-aware decision-making in prognostic applications. This paper proposes a unified uncertainty-aware framework for RUL prediction that integrates Bayesian deep learning (BDL)–based uncertainty quantification with principled uncertainty calibration. Deep Bayesian neural networks trained via Gaussian dropout are employed to jointly model epistemic and aleatoric uncertainties, and ensemble predictive distributions are obtained through stochastic forward passes. A key insight of this work is that, for a well-calibrated model, prediction residuals should be positively correlated with predictive variance. Based on this principle, isotonic regression is introduced as a monotonic structural constraint to actively calibrate heteroscedastic predictive uncertainty. The calibrated uncertainty is further incorporated into a split conformal prediction (SCP) framework to construct prediction intervals with finite-sample marginal coverage guarantees when standard conformal prediction assumptions (e.g., exchangeability) hold. Extensive experiments on the C-MAPSS and lithium-ion battery datasets demonstrate improved prediction accuracy, effective uncertainty quantification, and reliable uncertainty calibration under approximate exchangeability, while maintaining strong empirical performance under practical distribution shifts. • A Bayesian deep learning (BDL) framework for remaining useful life (RUL) prediction is proposed to effectively account for both epistemic and aleatoric uncertainties. • Gaussian dropout has been shown to outperform Monte Carlo (MC) dropout in approximating the variational posterior distribution for variational inference (VI). • Isotonic regression is utilized to calibrate the standard deviation of predicted results in BDL models. • Split conformal prediction (SCP) is applied to construct prediction intervals with coverage guarantees under standard assumptions. • Isotonic regression bridges the BDL and SCP to integrate uncertainty quantification and calibration of RUL prediction.
Xu et al. (Wed,) studied this question.