Abstract
Traditional correlation analysis is analyzed separately in the time domain or the frequency domain, which cannot reflect the time-varying and frequency-varying characteristics of non-stationary signals. Therefore, a time–frequency (TF) correlation analysis method of time series decomposition (TD) derived from synchrosqueezed S transform (SSST) is proposed in this paper. First, the two-dimensional time–frequency matrices of the signals is obtained by synchrosqueezed S transform. Second, time series decomposition is used to transform the matrices into the two-dimensional time–time matrices. Third, a correlation analysis of the local time characteristics is carried out, thus attaining the time–frequency correlation between the signals. Finally, the proposed method is validated by stationary and non-stationary signals simulation and is compared with the traditional correlation analysis method. The simulation results show that the traditional method can obtain the overall correlation between the signals but cannot reflect the local time and frequency correlations. In particular, the correlations of non-stationary signals cannot be accurately identified. The proposed method not only obtains the overall correlations between the signals, but can also accurately identifies the correlations between non-stationary signals, thus showing the time-varying and frequency-varying correlation characteristics. The proposed method is applied to the acoustic signal processing of an engine–gearbox test bench. The results show that the proposed method can effectively identify the time–frequency correlation between the signals.
Highlights
When analyzing multi-input and multi-output vibration systems, most of the inputs are thought to be independent and to have no influence on each other
Considering that the synchrosqueezed S transform (SSST)-time series decomposition (TD) TF correlation changes with time, the phase change must be Considering that the changes with time, the phase must be Considering that the SSST-TD
A time series decomposition algorithm derived from time-varying features
Summary
When analyzing multi-input and multi-output vibration systems, most of the inputs are thought to be independent and to have no influence on each other. Compared with the Fourier transform (FT), which can only obtain the frequency components in general, the time–frequency (TF) analysis can better uncover the local characteristics and simultaneously provide insight on the time and frequency information of the signal [6]. TF representations provide a powerful tool for analyzing non-stationary time signals and can be used in correlation analysis. The advantages of the SSST can be summarized as follows: (a) the results are directly in the TF domain and not the time–scale domain; (b) the frequency axis presents a linear and uniform distribution, which meets the basic requirements of the inverse Fourier transform; (c) the algorithm is reversible and reconfigurable; (d) the TF resolution is improved; and (e) the SSST can be used to compute complex valued time signals.
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