Structural instantaneous frequency identification based on synchrosqueezing fractional Fourier transform

Abstract

The fractional Fourier transform can transform the signal or function into any intermediate domain between time and frequency domains called fractional Fourier domain, in which the non-stationary signals can be processed. To be a time-frequency analysis tool, the fractional Fourier transform may face the same ridge line blurred problem for noisy signals as other time-frequency analysis methods. To improve the instantaneous frequency identification accuracy of fractional Fourier transform, this paper proposes the synchrosqueezing fractional Fourier transform by using the mechanism that can rearrange the energy in the time-frequency plane and make the frequencies more concentrated on the real frequency of the signal. The synchrosqueezing fractional Fourier transform and its corresponding inverse transformation are theoretically derived. Then the corresponding instantaneous frequency identification based on synchrosqueezing fractional Fourier transform is formulated. The accuracy and effectiveness of proposed instantaneous frequency method is verified by a numerical example of three-degree-of-freedom damped time-varying structural system and experiments of moving vehicle-beam system with simply supported and continuously supported beam tested in the laboratory. Compared with the fractional Fourier transform without synchrosqueezing transform, synchrosqueezing wavelet transform and Fourier synchrosqueezing transform, it is demonstrated that the synchrosqueezing fractional Fourier transform can effectively improve the time-frequency distribution divergence and enhance the accuracy of the instantaneous frequency identification. The method has a certain anti-noise performance. Due to quick calculation by means of traditional fast Fourier transform and superior orthogonal transform feature, the proposed synchrosqueezing fractional Fourier transform can be used as an effective time-frequency signal processing tool for multi-component non-stationary signals.