Block-wise recursive APES aided with frequency-squeezing postprocessing and the application in online analysis of vibration monitoring signals

Abstract The amplitude and phase estimation of a sinusoid (APES) method, receiving superior results to conventional Fourier transform (FT) featured as narrower spectral peaks and lower side-lobe levels, has been widely applied in the fields of medical imaging, remote sensing, synthetic aperture radar, etc. Both FT and APES suppose the signal collected is stationary. When handing with non-stationary signals, we have to resort to the adaptive extension of FT, i.e., the short time Fourier transform (STFT). Likewise, we also need to extend APES to adapt to changing signal spectrum while maintaining the advantage of high-resolution. To this end, this paper proposes a block-wise recursive APES (BRAPES) method for online spectral estimation of time-varying signals, in which the size of the updating block is adjustable to accommodate the real-time requirement of online computing. Additionally, inspired by recent developments in reassignment method (RM) and synchrosqueezing transform (SST) against the Heisenberg uncertainty principle, we construct a frequency-squeezing postprocessing (FSP) technique aiming at improving the concentration of time–frequency (TF) representation by BRAPES, which essence is to move the spectral lines towards the nearest natural frequency rather than changing the amplitude. The numerical examples demonstrate that the proposed approach, BRAPES aided with FSP (BRAPES-FSP), not only has high accuracy in processing nonstationary signals, but also can adopt a much shorter data sequence for analysis than Fourier class methods, which greatly guarantee the real-time performance of computation in online environment. Furthermore, we employ BRAPES-FSP to process the acceleration responses of cables of a real cable-stayed bridge and a experimental cable in workshop, proving its capability and potential of dealing with vibration monitoring signals in such fields as structural health monitoring.