Research on bearing fault feature extraction based on singular value decomposition and optimized frequency band entropy

Singular value decomposition (SVD) is widely used in condition monitoring of modern machine for its unique advantages. A novel relative change rate of singular value kurtosis (SVK) is proposed in order to determine the reconstructed order of singular values effectively. Since the bandwidth parameter of the band-pass filter designed by FBE need to be determined based on experience, obviously, there are significant deficiencies. Then, a optimized frequency band entropy (OFBE) method based on the principle of maximum kurtosis is proposed to optimize the bandwidth parameters. In addition, because the fault signal of the rolling bearing at the initial stage is very weak and submerged by ambient noise, SVD cannot extract fault features clearly, a new method for fault feature extraction of rolling bearing based on SVD and OFBE, named SVD-SVK-OFBE, is proposed. Firstly, the Hankel matrix is reconstructed from the original vibration signal in the phase space and the noise reduction is performed using SVD. Here, the relative change rate of singular value kurtosis is performed on the Hankel matrix to determine the reconstructed order. Secondly, the OFBE analysis is performed on the reconstructed signal to determine the center frequency and the bandwidth of the band-pass filter adaptively. The bandwidth of the designed band-pass filter is optimized by the kurtosis maximum principle. Thirdly, the reconstructed signal of SVD is filtered by the optimized filter, and the envelope demodulation analysis is performed on the filtered signal. Finally, the fault feature frequency is extracted and compared with the theoretical fault feature frequency to identify the fault type of the rolling bearing. The effectiveness and advantages of the method described in this paper are verified by the simulation analysis and experimental data analysis of the rolling bearing.