Slope synchronous chirplet transform and its application to tacho-less order tracking of rotating machineries

Chirplet transform (CT) has been widely used in time-frequency analysis (TFA) of rotating ma-chinery vibration signals. However, due to the smear effect and time-frequency resolution lim-itation, CT and most of its improved algorithms cannot achieve sufficient refined time-frequency representation (TFR) for the instantaneous frequency (IF) close-spaced and IF trajectory slope mutation signals. Aiming at the aforementioned shortcomings, a novel TFA method named slope synchronous chirplet transform (SSCT) is proposed to address this problem. The proposed SSCT algorithm can adaptively adjust the window lengths according to the slope variation of the IF trajectory, thereby higher time-frequency resolution can be obtained for the IF close-spaced components. Besides, the proposed method utilizes a high-order phase operator to accurately capture the trend of IF trajectory slope, so that the time-frequency (TF) energy of the IF trajectory can be better concentrated, thereby the weak TF energy of the IF trajectory can be uncovered. The effectiveness of the proposed method is verified by simulated signals and an aero-engine vibration signal measured under a transient operating mode, the validation results indicate the proposed method outperforms some latest reported TFA algorithms and is available for accurate estimation of instantaneous angular speed for tacho-less order tracking of rotating machineries.