## 1 Introduction  
The condition monitoring of rolling bearings is very important in ensuring the safety of the mechanical system as it is one of the basic components and widely applied in various rotating machines. The measured dynamic signal of bearing has the characteristics of non-linear and non-stationary with various background noise. Moreover, the original signal is too low in energy to extract fault characteristics. As a result, some progress has been made in the research of effective health monitoring for mechanical system and key components in recent years [1; 2; 3]. The vibration signal produced by the rotating machine contains significant information related to the state of the machine; therefore, the vibration-based analysis has been widely used as an effective method to identify the machine faults [4]. However, the measured vibration signal is consisted of stationary, non-stationary, and background noise. It is necessary to select appropriate signal processing technology to obtain effective fault features for rolling bearings fault detection [5; 6; 7]. In the fault diagnosis of rolling bearings, the analysis method based on the time domain and frequency domain are commonly used for stationary signal processing, and the time-frequency domain analysis method has been widely used to analyze the non-stationary signals for fault features extraction in both the time and frequency domains. The popular time-frequency analysis methods include short time Fourier transform (STFT), empirical mode decomposition (EMD), Wigner-Ville distribution (WVD), wavelet pack transform (WPT), etc. Although these methods have been widely used in fault detection, they also have their own shortcomings. For instance, the STFT cannot satisfy the localization of time and frequency at the same time. The WVD is affected by cross-interference items. The EMD can effectively decompose amplitude modulation signals into a series of intrinsic mode functions (IMFs), but it is easily affected by modal aliasing, which makes IMFs lose their specific physical meaning. Compared with the above-mentioned method, WPT can perform orthogonal decomposition on the signal of the whole frequency band to obtain more detailed and comprehensive information. Therefore, it has been widely used in fault diagnosis of gearboxes, rolling bearings, and rotors [8; 9; 10]. On the basis of WPT, wavelet packet energy (WPE) is an improved time-frequency analysis method which can get the energy change of the signal in each frequency band and then extract the characteristic frequency band signal to reflect the impact vibration phenomenon of bearing. In recent years, WPE has become a prevalent method in the field of machinery condition monitoring and fault diagnosis [11; 12; 13; 14]. Spectra kurtosis (SK) is one of the effective approaches for transient signal enhancement. It was originally developed by [PERSON] [15] to highlight the transient components. The spectra kurtosis method uses the properties of kurtosis, is very sensitive to the transient components in a signal, and can provide an index for indicating the frequency band for transient components extraction. The definition of the \"kurtogram\" was first introduced by [PERSON] [16]. The fast kurtogram (FK) overcomes the limitation of pre-determining the parameters for the band-pass filter and can optimize the parameters adaptively according to the characteristics of the analyzed signal. Therefore, FK has been favored in the field of rotating machinery fault detection, and has been widely adopted and developed in recent years. [PERSON] et al. applied the FK to analyze the vibration signal obtained from a planetary gearbox test bench for detecting planet bearings faults [17]. He et al. proposed a new multi-faults detection method using the FK and Minimum entropy deconvolution (MED) to extract weak impulsive signal [18]. [PERSON] et al. presented an effective method for band-filter parameter optimization in rolling element bearing fault diagnosis based on the genetic algorithms and FK [19].