A Time–Frequency Correlation Analysis Method of Time Series Decomposition Derived from Synchrosqueezed S Transform

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.