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.

中文翻译：

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结合不确定性量化和校准的 RUL 预测贝叶斯深度学习框架

在本文中，深度学习 (DL) 在剩余使用寿命 (RUL) 预测方面引起了越来越多的关注。然而，大多数基于 DL 的预测方法仅提供确定性的 RUL 值，而忽略了相关的认知和任意不确定性。在实践中，重要的是要知道模型预测的准确置信度以进行决策。在本文中，提出了一种结合不确定性量化和校准的用于 RUL 预测的贝叶斯深度学习 (BDL) 框架。首先，认知不确定性和任意不确定性分别解释了对模型的无知和观察中固有的噪声，其特征在于将两种类型的不确定性整合到 BDL 框架中。其次，为了避免过度自信的预测，提出了一种新的迭代校准方法，通过将等渗回归与标准偏差缩放相结合，联合校准认知、任意和预测不确定性。涡扇发动机和锂离子电池数据集的案例研究证明了所提出方法的有效性。