## 1 Introduction  
The condition monitoring of railway infrastructure and vehicles is very important to ensure the safe operation of trains, which has gradually attracted considerable attention in recent years [1, 2, 3]. Among them, the wheelset bearing, as one of the key rotating elements in the bogie frame of high-speed or heavy-duty locomotives, working status has a significant impact on the safety of the vehicle [4, 5, 6]. Hence, it is essential to the diagnosis of the wheelset bearing's damage in its initial stages for preventing potential accidents [7, 8]. For the fault feature extraction of bearings, vibration-based analysis has developed into an effective approach after the development of recent years [9, 10]. However, influencedby the complex wheel/rail excitation and the severe operating condition, the fault-related repetitive impulses are usually submerged by strong background noise and complex harmonic interferences, which bring some difficulties for the early fault detection of the wheelset bearing. When a local defect occurs on the contact surfaces of the bearing, a typical feature is that the fault-induced repetitive transients are modulated in a high-frequency resonance band related to the machine structure [11]. Therefore, a valid strategy for the extraction of fault-induced repetitive transients is to determine an IFB to filter the vibration signal [12; 13; 14]. However, how to choose the IFB adaptively is still a difficult problem. In order to determine the IFB adaptively, [PERSON] proposed the spectral kurtosis (SK)-based method [15] and fast kurtogram (FK) [16], in which the kurtosis of the filtered time signal is taken to extract the impulse-like characteristics from bearing fault signal. Up to now, SK-based kurtogram and FK have been widely used in the fault diagnosis of rotating machinery, such as railway locomotives, wind turbines, excavating machinery, and so on. Afterwards, several research works have been made to improve the validity and stability of the kurtogram. On one hand, more accurate bandpass filters have been developed to improve the effect of decomposition (e.g., multiwavelets [17], wavelet packet transform (WPT) [18; 19], dual-tree wavelets [20; 21], maximal overlap discrete WPT (MODWPT) [22], dynamic Bayesian wavelet transform [23], tunable Q-factor wavelet transform [24; 25], etc.). On the other hand, more robust indicators are adopted to estimate the impulse-like characteristics of the filtered time signal. [PERSON] proposed a novel smoothness index-based method to select the wavelet parameter to de-noise, and its performance is verified by bearing experimental signal [26]. [PERSON] used the Gini index to generate kurtograms for bearing fault feature extraction [27]. [PERSON] utilized a peak energy to choose the appropriate market wavelet parameters for the demodulation of bearing vibration signal [28]. [PERSON] proposed spectral L2/L1 norm for characterizing non-stationary signals, and then some extensions of spectral L2/L1 norm are also generalized to bearing fault diagnosis [29; 30]. [PERSON] extended the applicability of the kurtogram by negentropy, which inspired by idea derived from the field of thermodynamics [31]. Although the validity of these methods have been extensively verified, one of the most severe limitations of the kurtogram is still unsolved, that is, it is powerless to determine whether a sequence of transients is periodic or not [31; 32]. Recently, [PERSON] [30] demonstrated that all of the L2/L1 norm, SK, Gini, and the reciprocal of smoothness can be regarded as a monotonically incremental functions of the maximum squared envelope by a strict mathematical derivation, which implies that the above indicators are easily disturbed by the large impulse interference. Therefore, when the faulty bearing signal contains large impulse interference, the stability of the above methods based on the impulse-like characteristics will be greatly reduced.