## 1 Introduction
Wavelet transform (WT) is one of the common time-frequency analysis methods to extract the fault characteristics of rolling bearing vibration signals [10]. The wavelet basis function and kernel parameters need to be predefined, and the different selection of them will influence the effect of feature extraction of vibration signals. Therefore, WT cannot be used to adaptively decompose the signal according to its time-frequency characteristics, which to some extent limits the practical application of WT in rolling bearing fault diagnosis [11]. Wavelet packet transform (WPT) is also a typical time-frequency analysis method for vibration signal of rolling bearings [1]. However, it is necessary to determine the wavelet basis function and the number of decomposition layers of wavelet packet before applying WPT. Improper selection of these will directly affect the effectiveness of wavelet packet decomposition, so that the hidden essential features in the signal cannot be revealed. Empirical mode decomposition (EMD) is a self-adapting time-frequency decomposition technique that was presented by [PERSON] in 1998 [12]. EMD can adaptively decompose a nonlinear and non-stationary signal into a series of intrinsic mode functions (IMFs) containing signal characteristics of different frequencies. EMD combined with different entropy methods provides an effective method for fault feature extraction of rolling bearings [13, 14, 15, 16]. However, EMD is prone to boundary effect and mode mixing problems in the practical application process, which will lead to poor feature extraction effect. In order to avoid the above problems in EMD, ensemble empirical mode decomposition (EEMD),complete ensemble empirical mode decomposition (CEEMD) and local mean decomposition (LMD) have been proposed successively and successfully applied to rolling bearing fault diagnosis [17; 18; 19; 20; 21; 22]. Although the above methods in principle solve the boundary effect and mode mixing problem, these problems cannot be completely avoided in real-world application. The methods based on entropy theory can measure the complexity of complex time series effectively that are often used as the feature extraction methods of rolling bearing vibration signal. The decomposed signals of the above time-frequency analysis methods can be measured by different entropy theories and constitute the feature vector. Complexity of time series can be obtained through several measures such as approximate entropy, sample entropy, energy entropy, permutation entropy and so on. As the calculation result of approximate entropy (ApEn) is excessively dependent on the data length, [PERSON] and [PERSON] proposed an improved time series complexity measurement method called sample entropy (SampEn) [23]. However, ApEn and SampEn can only measure the complexity of time series from single scale. For many time series, only describing their complexity on a single scale will lose a lot of important information. To more fully describe the complexity of time series, [PERSON] et al. proposed the concept of multiscale entropy (MSE) in 2002 [24]. Firstly, spatial scale segmentation of time series is carried out, and then the SampEn at each scale is calculated, so as to obtain the complexity of time series at different scales. In recent years, combining with the characteristics of other entropy theories, multiscale permutation entropy [25] and multiscale fuzzy entropy [26] have been proposed and successfully applied in the fault feature extraction of rolling bearings. Therefore, it can be seen that the coarse-grained process of MSE to decompose the vibration signal of rolling bearings and using the entropy theory to describe the fault characteristics of the decomposed signals has become an effective way to realize the fault feature extraction of rolling bearings.