Box-cox-sparse-measures-based blind filtering: Understanding the difference between the maximum kurtosis deconvolution and the minimum entropy deconvolution

Blind filtering is an emerging topic in various domains to recover an excitation from responses measured by sensors. In the existing literature, the minimum entropy deconvolution is often regarded as the maximum kurtosis deconvolution without providing an underlying connection between them. However, a recent progress towards sparsity measures has shown that kurtosis is actually different from negative entropy. Moreover, a generalized sparse measure, called Box-Cox sparse measures (BCSM), has been proposed to establish a connection between the kurtosis and the negative entropy. Thus, this research investigates an underlying connection between the minimum entropy deconvolution and the maximum kurtosis deconvolution by using the BCSM. After that, the BCSM is incorporated into a generalized Rayleigh quotient to form a generalized blind filter that extracts a signal with the sparsest envelope spectrum. Finally, the effectiveness of the proposed generalized filter is verified using both simulated and real experimental bearing data. Results demonstrates that the proposed method can be used to detect multiple faults using a single measurement set.