  This paper develops an explainable deep learning model that estimates the
remaining useful lives of rotating machinery. The model extracts high-level
features from Fourier transform using an autoencoder. The features are used as
input to a feedforward neural network to estimate the remaining useful lives.
The paper explains the model's behavior by analyzing the composition of the
features and the relationships between the features and the estimation results.
In order to make the model explainable, the paper introduces octave-band
filtering. The filtering reduces the input size of the autoencoder and
simplifies the model. A case study demonstrates the methods to explain the
model. The study also shows that the octave band-filtering in the model
imitates the functionality of low-level convolutional layers. This result
supports the validity of using the filtering to reduce the depth of the model.
