# Diagnosis Method for Mechanical Faults Based on Rotation Synchrotexting Chirplet Transform
###### Abstract  
The problems of the synchrotexting transform method being unable to handle FM signals and being prone to time-frequency feature discontinuity in a strong noise environment are addressed by the construction of a novel rotation synchrotexting chirplet transform under the framework of the synchrotexting transform. The method retains the advantage of the generalized linear chirplet transform that can fit the time-frequency characteristics of the original signal and retains the high precision time-frequency analysis ability of the syn  
signal more perfectly. In order to overcome these problems in the traditional SET, some revised SET methods are proposed. The basic idea of these improved SET is to apply signal decomposition methods, such as: two-level adaptive FM modal decomposition [10], Empirical mode decomposition [11], primary kernel regression residual decomposition [12], nonlinear FM modal decomposition [13], and time-frequency coefficient modal great [14], decompose multi-component signals before SET processing. [PERSON] et al. [14] proposed a method to identify the instantaneous frequency of time-varying structural response signals by combining SET with modal maxima of time-frequency coefficients. [PERSON] [15] proposed a method combining SET and empirical wavelet transform method and applied this method to analyze the time-frequency of seismic signals at high-resolution. [PERSON] et al. [16] proposed a method combining primary kernel regression residual decomposition with SET and applied it successfully to defect mechanical faults. [PERSON] et al. [17] proposed a method combining variational nonlinear frequency modulation modal decomposition with SET to diagnose the fault characteristic frequency of bearings. Although the above methods have solved the problem of frequency aliasing to some extent, the complexity and processing time increase. It is obvious that sacrificing the processing speed and computational complexity to eliminate frequency aliasing is a trade-off. In addition, this treatment often does not yield the ideal results because it does not fundamentally improve the shortcomings of SET. Therefore, some scholars continue to explore new SET methods. [PERSON] et al. [18] improved the results of SET for stressed FM signal by local frequency approximation and verified the noise robustness performance and signal reconstruction capability of the method. [PERSON] et al. [19] proposed a method of synchroextracting generalized S transform considering the advantages of the generalized S transform and successfully applied it to process seismic signals. [PERSON] et al. [20] proposed the second-order SET and high-order SET methods to address the deficiencies of SET in processing emphasized FM-AM signals. The proposed second-order SET method has higher time-frequency accuracy, and the proposed high-order SET method has the clearest description of low-frequency components and high-frequency components. [PERSON] [21] proposed a TF analysis method for recursive mapping demodulation high-order SET, which focuses on solving the demodulation of cross-aliasing signal components of external interference and the accurate estimation of local instantaneous frequencies in high-order. However, although the above methods improve the TF accuracy and anti-interference performance of the SET to a certain level, they fail to improve the adaptive performance. To overcome the above problems, we replace the STFT in the SET framework with the generalized linear chirplet transform (GLCT) and propose a rotating synchroextracting chirplet transform (RSECT) method. The proposed method is characterized by retaining the advantages of the GLCT in fitting the TF ridge energy of signal, and also retaining the advantages of the SET in terms of high-precision TF. Therefore, the method has a strong TF resolution and can effectively characterize the time-frequency features of the fault signal. Simulation and experimental results verify the effectiveness of the proposed method. The remainder of the paper is organized as follows.