Theory,Methodology Of Synchro Transform And Its Application In Engineering Signal Processing

The traditional time-frequency analysis method is a powerful tool for dealing with non-stationary signals.It can describe both the time-domain and frequency-domain characteristics of the signal.Due to the influence of Heisenberg’s uncertainty principle,the time-frequency representation of the short-time Fourier transform(STFT)and the wavelet transform is poor,and cross-term interference makes it difficult to analyze multi-component signals based on the Wigner-Ville distribution.Therefore,this thesis mainly studies a kind of time-frequency post-processing method based on the STFT,namely the synchro transform method.Synchro transform method uses the instantaneous frequency or group delay information of the signal to synchronously compress or extract the time-frequency coefficients of the STFT,thereby improving the energy aggregation of the time-frequency representation without introducing a cross term.The content of this thesis overall involves three aspects: the theory,methodology of the synchro transform and its application in engineering signal processing.The thesis studies the basic theory of the synchrosqueezing transform.Synchrosqueezing transform is the most typical method of the synchro transform,and it is also the basis of the entire synchro transform theoretical framework.Therefore,the thesis first introduces the basic concepts of synchrosqueezing transform.Secondly,according to the different compression direction of time-frequency coefficients,the synchrosqueezing transform is subdivided into the frequency-reassigned synchrosqueezing transform and the time-reassigned synchrosqueezing transform.By comparing the differences between their STFT forms,a new explanation of the working principle of the synchrosqueezing transform is proposed.In this thesis,the time-domain and frequency-domain models of signals are studied,and three specific synchro transform methods are proposed on the basis of these signal models,which enriches the existing theoretical framework of synchro transform.First,the thesis reviews the definition and properties of the Gaussian-modulated linear chirp signal model.Combined with the concept of synchronous extraction,the second-order frequency synchroextracting transform(FSET2)is proposed.This method is suitable for processing strong time-varying signals.Secondly,this thesis further extends the above-mentioned time-domain signal model into the frequency domain,and gives the definition and properties of the Gaussian-modulated linear group delay signal model.Then the second-order time-reassigned synchrosqueezing transform(TRST2)and the second-order time synchroextracting transform(TSET2)are proposed,which are suitable for processing transient signals.The thesis discusses the application of synchro transform in fault diagnosis of rotating machinery and in transient signal analysis.Signals in different situations should be described by different signal models.For nonstationary signals in rotating machinery,the instantaneous frequency function is a single-valued function of time,so it is suitable to be described by the time-domain signal model.For transient signals,the group delay function is a single-valued function of frequency,so it is suitable to be described by the frequency domain signal model.Relying on the above conclusions,this paper respectively uses the FSET2 and the TSET2 to complete the fault diagnosis of rotary machinery and the analysis of transient signal,which proves the engineering application value of the synchro transform.