Fast implementation of synchrosqueezing transform based on downsampling for large-scale vibration signal analysis

Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In this paper, some fast implementation methods of SST based on downsampled short-time Fourier transform (STFT) are proposed. By controlling the downsampling factor both in time and frequency, combined with the proposed selective reassignment and frequency subdivision scheme, one can keep a balance between efficiency and accuracy according to practical needs. Moreover, the reconstruction property is available, accomplished by an approximate but direct inverse formula under downsampling. The effects of parameters on the concentration, computing efficiency, and reconstruction accuracy are also investigated quantitatively, followed by a mathematic model of reassignment behavior with decimate factors. Experimental results on an aero-engine and a spindle show that the fast implementation of SST can effectively characterize the non-stationary characteristics of the large-scale vibration signal to reveal the mechanism of mechanical systems.