## 1 Introduction
In addition, frequency-smear problems arise when the traditional envelope analysis method is utilized for nonstationary vibration signals that emerge as a result of speed fluctuations. Figure 1: Schematic diagram of a gas turbine support structure. A large amount of research has been conducted by several experts on the noise reduction and filtering of the fault signals occurring in REBs. As a result of these efforts, wavelet de-noising and filtering based on spectral kurtosis (SK) have become known as reliable methods. Wavelet de-noising, which is suitable for nonstationary signals, was used by [PERSON] et al. [6] to de-noise bearing signals and facilitate the extraction of the features of bearing faults. A synchronous averaging method in the angular domain, based on wavelet de-noising, was proposed by [PERSON] et al. [7] to analyze the fault signals of REBs operating at variable speeds, with a huge amount of noise. This method effectively lowers the noise levels, resolving the frequency-smear problems that occur when the traditional Fourier transform is applied to analyzing nonstationary signals. How to choose filter parameters has remained a controversial issue in academic circles for a long time. Fortunately, SK was proposed to resolve this issue. This method was primarily proposed by [PERSON] [8], whose main goal was to compute the kurtosis of each spectral line and find a nonstationary signal to determine the optimal center frequency and bandwidth. [PERSON] [9; 10; 11] studied when and in what situations that SK can be applied to diagnosing equipment faults, and introduced the official definition of SK and the fast kurtogram algorithm. This method has provided significant benefits for the diagnosis of equipment faults. The utilization of SK in fault diagnosis of bearings has also been improved. The autoregressive (AR) model has been applied to processing the signal before SK is used. Meanwhile, a complex Morlet wavelet has been adopted to decompose the signal. After the optimal filter parameters are determined, the accurate fault characteristic frequency (FCF) of a bearing will be obtained in the envelope spectrum [12]. In recent years, SK has been improved and applied to the fault diagnosis for the bearings and gears used in rotating machinery. Adaptive spectral kurtosis (ASK) was proposed to identify multiple faults in bearings and successfully extracted the features of multiple faults buried by strong noise components [13]. In 2016, [PERSON] et al. [14] summarized the researches on the application of SK to fault diagnosis and prediction for rotating machinery after the method had been proposed in 1983. At the same time, experts suggested that SK had reached its full potential in areas such as operational modal analysis and fault diagnosis of electronic machinery. Therefore, SK-based filtering was adopted in this study. In addition, many other types of fault diagnosis methods for REBs have been studied. [PERSON] et al. proposed a modulation signal bi-spectrum based method in determining optimal bands for bearing diagnosis when the signal is very noisy [15]. [PERSON] et al. proposed a method of rolling bearings fault diagnosis based on variational mode decomposition (VMD). They mainly dealt with the traditional REBs used in the multistage centrifugal pump, and confirmed that the method can extract the fault feature effectively [16]. An order tracking method for rotating machinery was initially proposed in 1990 by [PERSON] [17]. Then, a computed order tracking method was proposed in 1997 by [PERSON] and [PERSON] [18] to deal with the problems that occurred when feature extraction was conducted on rolling bearings operating at variable speeds. This method can also be used to achieve a stationary signal in the angular domain rather than a nonstationary signal in the time domain. [PERSON] et al. [19] applied envelope analysis, based on order tracking, to a nonstationary signal and introduced prewhitening to improve the signal-to-noise ratio.