Horizontal rearrangement frequency domain chirplet transform: Algorithm and Applications

Abstract Based on the idea of optimal time-frequency analysis (TFA) theory, a time-frequency post-processing method called horizontal rearrangement frequency domain chirplet transform (HRFCT) is proposed. The proposed method is designed to analyze non-stationary transient signals with nonlinear group delay (GD), aiming at obtaining energy-concentrated and accurate time-frequency representation (TFR). First, based on the image characteristics of the constructed amplitude function, the selection criteria of GD are defined, that is, the local maximum of amplitude function and the local minimum of absolute value of derivative of amplitude function are calculated. Next, according to the calculated GD, the coefficients on the GD trajectory are adaptively extracted, and the coefficients that cause the TFR to be blurred are discarded. Finally, the analysis result of a two-component simulation signal demonstrates the satisfactory performance of the HRFCT, and compared with four advanced TFA methods, the competitiveness of the HRFCT is verified. Additionally, the application of the HRFCT in the processing of constant and variable speed bearing signals highlights its prospects in transient signal analysis and rotating machinery condition monitoring.