Adaptive continuous wavelet transform based model driven neural networks for fault detection

In this paper we develop a novel fault detection methodology and demonstrate its effectiveness by recognizing so-called acoustic overload events (AOLs) in audio signals captured by MEMS microphones. In particular, we propose a model-driven neural network (NN) architecture, whose first layer implements a continuous wavelet transform realized by recently introduced rational Gaussian wavelets. The output of this layer is then channeled into a usual NN. Learnable parameters of the proposed wavelet layer include parameters defining wavelet coefficients (such as scales) and parameters which govern the morphology of the analyzing wavelet. The latter is possible due to the favorable properties of rational Gaussian wavelets. Unlike other deep learning approaches, the learned signal representation has physical meaning which is crucial in safety critical fault detection applications. Importantly, the parameters of the wavelet transformation layer are optimized together with the weights of the underlying NN, leading to ideal signal representations.