Investigation on the kurtosis filter and the derivation of convolutional sparse filter for impulsive signature enhancement

Minimum Entropy Deconvolution (MED) filter, which is a non-parametric approach for impulsive signature detection, has been widely studied recently. Although the merits of the MED filter are manifold, this method tends to over highlight the dominant peaks and its performance becomes less stable when strong noise exists. In order to better understand the behavior of the MED filter, this study first investigated the mathematical fundamentals of the MED filter and then explained the reason why the MED filter tends to over highlight the dominant peaks. In order to pursue finer solutions for weak impulsive signature enhancement, the Convolutional Sparse Filter (CSF) is originally proposed in this work and the derivation of the CSF is presented in details. The superiority of the proposed CSF over the MED filter is validated by both simulated data and experimental data. The results demonstrate that CSF is an effective method for impulsive signature enhancement that could be applied in rotating machines for incipient fault detection.