  In the last decade, deep learning (DL) has outperformed model-based and
statistical approaches in predicting the remaining useful life (RUL) of
machinery in the context of condition-based maintenance. One of the major
drawbacks of DL is that it heavily depends on a large amount of labeled data,
which are typically expensive and time-consuming to obtain, especially in
industrial applications. Scarce training data lead to uncertain estimates of
the model's parameters, which in turn result in poor prognostic performance.
Quantifying this parameter uncertainty is important in order to determine how
reliable the prediction is. Traditional DL techniques such as neural networks
are incapable of capturing the uncertainty in the training data, thus they are
overconfident about their estimates. On the contrary, Bayesian deep learning
has recently emerged as a promising solution to account for uncertainty in the
training process, achieving state-of-the-art performance in many classification
and regression tasks. In this work Bayesian DL techniques such as Bayesian
dense neural networks and Bayesian convolutional neural networks are applied to
RUL estimation and compared to their frequentist counterparts from the
literature. The effectiveness of the proposed models is verified on the popular
C-MAPSS dataset. Furthermore, parameter uncertainty is quantified and used to
gain additional insight into the data.
