Time-synchronous-averaging-spectrum based on super-resolution analysis and application in bearing fault signal identification

Time-synchronous-averaging (TSA) is based on the idea of denoising by averaging, and it extracts the periodic components of a quasiperiodic signal and keeps the extracted waveform undistorted. This paper studies the mathematical properties of TSA, where three propositions are given to reveal the nature of TSA. This paper also proposes a TSA-spectrum based on super-resolution analysis and it decomposes a signal without using any base function. In contrast to discrete Fourier transform spectrum (DFT-spectrum), which is a spectrum in frequency domain, TSA-spectrum is a period-based spectrum, which can present more details of the cross effects between different periodic components of a quasiperiodic signal. Finally, a case study is carried out using bearing fault analysis to illustrate the performance of TSA-spectrum, where the rotation speed fluctuation of the shaft is estimated, which is about 0.12 ms difference. The extracted fault signals are presented and some insights are provided. We believe that this paper can provide new motivation for TSA-spectrum to be widely used in applications involving quasiperiodic signal processing (QSP).