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High-Frequency (HF) signals are ubiquitous in the industrial world and are ofgreat use for monitoring of industrial assets. Most deep learning tools aredesigned for inputs of fixed and/or very limited size and many successfulapplications of deep learning to the industrial context use as inputs extractedfeatures, which is a manually and often arduously obtained compactrepresentation of the original signal. In this paper, we propose a fullyunsupervised deep learning framework that is able to extract a meaningful andsparse representation of raw HF signals. We embed in our architecture importantproperties of the fast discrete wavelet transformation (FDWT) such as (1) thecascade algorithm, (2) the conjugate quadrature filter property that linkstogether the wavelet, the scaling and transposed filter functions, and (3) thecoefficient denoising. Using deep learning, we make this architecture fullylearnable: both the wavelet bases and the wavelet coefficient denoising arelearnable. To achieve this objective, we propose a new activation function thatperforms a learnable hard-thresholding of the wavelet coefficients. With ourframework, the denoising FDWT becomes a fully learnable unsupervised tool thatdoes neither require any type of pre- nor post-processing, nor any priorknowledge on wavelet transform. We demonstrate the benefits of embedding allthese properties on three machine-learning tasks performed on open source sounddatasets. We perform an ablation study of the impact of each property on theperformance of the architecture, achieve results well above baseline andoutperform other state-of-the-art methods.

Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series