  Remaining useful life (RUL) refers to the expected remaining lifespan of a
component or system. Accurate RUL prediction is critical for prognostic and
health management and for maintenance planning. In this work, we address three
prevalent challenges in data-driven RUL prediction, namely the handling of high
dimensional input features, the robustness to noise in sensor data and
prognostic datasets, and the capturing of the time-dependency between system
degradation and RUL prediction. We devise a highly accurate RUL prediction
model with uncertainty quantification, which integrates and leverages the
advantages of deep learning and nonstationary Gaussian process regression
(DL-NSGPR). We examine and benchmark our model against other advanced
data-driven RUL prediction models using the turbofan engine dataset from the
NASA prognostic repository. Our computational experiments show that the
DL-NSGPR predictions are highly accurate with root mean square error 1.7 to 6.2
times smaller than those of competing RUL models. Furthermore, the results
demonstrate that RUL uncertainty bounds with the proposed DL-NSGPR are both
valid and significantly tighter than other stochastic RUL prediction models. We
unpack and discuss the reasons for this excellent performance of the DL-NSGPR.
