A Bayesian Deep Learning Framework for RUL Prediction Incorporating Uncertainty Quantification and Calibration

In this article, deep learning (DL) has attracted increasing attention for remaining useful life (RUL) prediction. However, most DL-based prognostics methods only provide deterministic RUL values while ignoring the associated epistemic and aleatoric uncertainties. In practice, it is important to know the exact confidence in model predictions for decision making. In this article, a Bayesian deep learning (BDL) framework for RUL prediction incorporating uncertainty quantification and calibration is proposed. First, the epistemic and aleatoric uncertainties, which account for the ignorance about the model and the noise inherent in the observations, respectively, are characterized by integrating both types of uncertainties into a BDL framework. Second, to avoid under- and over-confident predictions, a novel iterative calibration method is proposed to jointly calibrate epistemic, aleatoric, and predictive uncertainties by combining isotonic regression with standard deviation scaling. The effectiveness of the proposed method is demonstrated by the case study of turbofan engines and lithium-ion batteries datasets.