Shannon Entropy of Binary Wavelet Packet Subbands and Its Application in Bearing Fault Extraction

The fast spectrum kurtosis (FSK) algorithm can adaptively identify and select the resonant frequency band and extract the fault feature via the envelope demodulation method. However, the FSK method has some limitations due to its susceptibility to noise and random knocks. To overcome this shortage, a new method is proposed in this paper. Firstly, we use the binary wavelet packet transform (BWPT) instead of the finite impulse response (FIR) filter bank as the frequency band segmentation method. Following this, the Shannon entropy of each frequency band is calculated. The appropriate center frequency and bandwidth are chosen for filtering by using the inverse of the Shannon entropy as the index. Finally, the envelope spectrum of the filtered signal is analyzed and the faulty feature information is obtained from the envelope spectrum. Through simulation and experimental verification, we found that Shannon entropy is—to some extent—better than kurtosis as a frequency-selective index, and that the Shannon entropy of the binary wavelet packet transform method is more accurate for fault feature extraction.