Fractional Synchrosqueezing Transformation and its Application in the Estimation of the Instantaneous Frequency of a Rolling Bearing

Xin Li,Zengqiang Ma,Suyan Liu,Feiyu Lu

doi:10.1109/access.2020.3010629

Abstract

The time-frequency energy distribution processed by a short-time Fourier transform can be compressed to the real instantaneous frequency by the synchrosqueezing transformation (SST), which improves the time-frequency energy concentration of the signal. However, there is a large error in the instantaneous frequency estimation of a multicomponent nonpure harmonic signal by the SST. Therefore, a method for determining the instantaneous frequency (IF) of a rolling bearing based on a fractional synchrosqueezing transformation (FRSST) is proposed. First, the theoretical derivation of the FRSST algorithm as a signal processing technique is given and the steps of the IF estimation are presented. Second, the main advantages of the proposed FRSST algorithm are proved. In the comparison of simulation signals, it is verified that the FRSST algorithm has a high time-frequency concentration, is non-fragile to the frequency modulation rate, has noise robustness and has nonsensitivity to the cross-frequency signal. Finally, the FRSST algorithm is applied to the IF estimation of a rolling bearing under rising speed and fluctuated speed, and is compared with the SST based on variational mode decomposition (VMD-SST), the generalized parametric SST (PSST) and polynomial chirplet transform (PCT). The test results show that the estimation error of IF based on the FRSST method is the least for a rolling bearing with the four fault types under rising speed. On average, the estimation error is 2.2180 Hz less than the corresponding error of the VMD-SST and 1.1862 Hz less than the corresponding error of the PSST method.

Highlights

The rolling bearing is the key component of rotating machinery, which is widely used
To improve the accuracy of the instantaneous frequency (IF) estimation and noise robustness, we propose the fractional synchrosqueezing transformation (FRSST) algorithm
The signal with the largest energy is extracted by the STFRFT, and its time-frequency energy distribution is obtained by the synchrosqueezing transformation (SST)

Summary

INTRODUCTION

The rolling bearing is the key component of rotating machinery, which is widely used. Considering the nonlinear, strong noise and multicomponent characteristics of the rolling bearing vibration signal, VOLUME 8, 2020 combined with the advantages of STFRFT algorithm, the FRSST combining the STFRFT and the SST is proposed to realize the instantaneous frequency estimation of a multicomponent nonpure harmonic signal. (ii) According to the characteristics of the rolling bearing signal and the advantages of the FRSST, the FRSST algorithm is introduced into the IF estimation of a rolling bearing This algorithm improves the energy concentration of the time-frequency distribution of a rolling bearing vibration signal and the estimation accuracy of the instantaneous fault frequency. In reference [45], considering the characteristics of a rolling bearing signal, the fractional Fourier transform (FRFT) is introduced into VMD to realize the adaptive decomposition of VMD and improve the noise robustness of the algorithm. Where φk is the estimated instantaneous frequency curve and ds is the integral interval

THE ERROR ANALYSIS OF THE SST

INSTANTANEOUS FREQUENCY RIDGE EXTRACTION

EXPERIMENT ANALYSIS

CONCLUSION