## 1 Introduction  
As an important part of rotating machinery, monitoring the health condition of bearings is very necessary during the industrial productions. Once a local fault occurs on the surface of a bearing, a series of impacts are aroused by the strikes between the rolling elements and the local fault on the outer or inner race [1]. However, the impacts caused by the local fault may be submerged in the noise as the severe environment. Therefore, effectively highlighting the impact components of the signal is beneficial to improving the recognition results of bearing fault severity. Recently, the importance of bearing fault severity recognition has been paid more and more attention [2; 3]. In general, the damage severity of bearings is usually measured from the aspect of signal complexity [4]. Currently, as the effective method for fault severity recognition, the Lempel-Ziv indicator (LZ indicator) is frequently used for the recognition of bearing fault severity. The LZ indicator can effectively reflect the change in frequency component in signals, and the different fault severities of the inner and outer race of the bearing will cause the change in the frequency component [4]. Thus, The LZ indicator can be effectively used for the recognition of bearing fault severity. However, although the LZ indicator can effectively recognize the fault severity of the inner and outer race of the bearing,the recognition results are often affected by the environmental noise. Therefore, based on Lempel-Ziv complexity, various methods of noise reduction have been used to improve the recognition results of bearing fault severity. To date, continuous wavelet transform [5], Empirical Mode Decomposition [6], local mean decomposition [7; 8], intrinsic time-scale decomposition [9], double-dictionary matching pursuit [10], and sparsogram [11] have been used in combination with the Lempel-Ziv complexity to reduce the noise and improve the recognition results of fault severity. Therefore, reducing noise and improving signal-to-noise ratio are helpful for improving the fault severity recognition results of the LZ indicator. Recently, the frequency band selection methods have been widely used to improve the signal-to-noise ratio and to highlight the impact components of signal. As a common time-frequency method, wavelet transform is used to decompose and extract the effective frequency components of the signals. For examples, [PERSON] et al. [12] combined the Hilbert and wavelet transforms to improve the results of bearing fault identification. In order to extract the effective information of the signal effectively, spectral kurtosis was first used to select that of the signal. For example, [PERSON] et al. [13] applied the K-Nearest Neighbor (KNN) distance measurement to bearing fault detection based on the multiple features which, extracted by cross-correlation, improve spectral kurtosis. [PERSON] et al. [14] applied support vector regression to estimate the residual useful life (RUL) of the high-speed shaft bearings based on the time indicators derived from spectral kurtosis. Based on the high potential of spectral kurtosis in detecting and characterizing non-stationary signals, [PERSON] et al. [15] proposed a new method called Kurtogram, which improved spectral kurtosis using short-time Fourier transform, depending on a series of different window lengths. In addition, Kurtogram has been continuously improved to improve the ability to select the effective fault information. For example, [PERSON] et al. [16] applied manifold learning to overcome the drawbacks of Kurtogram, in which the in-band noise was left unprocessed. [PERSON] et al. [17] improved Kurtogram based on a meshing frequency modulation index which utilized the particular gearbox related phenomenon to extract the bearing fault-induced impact components under the background noise of the planetary gearbox. Besides this, other new methods have been used in combination with the original methods to improve the extraction results. [PERSON] et al.