Continuous Wavelet Transform Based Variable Projection Networks

A novel feature extraction layer using the continuous wavelet transform is developed for use with neural networks. The learned parameters (scales and shifts in time) of the proposed wavelet layer can be interpreted by humans. In addition, using the concept of adaptive orthogonal projections to approximate wavelet coefficients, a sparse representation of the input is achieved. The proposed method is applicable with any analytic mother wavelet. As a case study, the application of bearing fault detection is considered to demonstrate the efficiency of the method, using a benchmark dataset. The results clearly show that the proposed model can be used to solve fault detection problems achieving near perfect classification accuracy. Qualitative and quantitative comparisons are made to a previous wavelet based neural network architecture. It is shown that the proposed method matches or outperforms previous approaches while using significantly less parameters. This sparsity improves model performance from the point of view of interpretability as well as model complexity.