Three-dimension extracting scaling Chirplet transform

Abstract Planetary gearboxes and bearings serve as key components for the stable operation of mechanical equipment, their vibration signals often containing strong frequency variations and non-proportional frequency components that pose challenges for existing time-frequency analysis (TFA) techniques. Therefore, the three-dimension extracting scaling chirplet transform (TESCT) is proposed. In the TESCT, the first-order chirprate parameter, which has small computational complexity, low noise sensitivity, and can accurately capture instantaneous frequency (IF) trend, is utilized to construct the three-dimensional space of time-frequency-first-order chirprate, and scaling-basis CT (SBCT) results are mapped to the three-dimensional space to separate frequency components, especially non-proportional frequencies. Then, the three-dimensional synchroextracting operator (TDSEO) is designed in the time-frequency-chirprate domain based on the estimated local frequency and local chirprate, and based on the TDSEO, amplitude coefficients at frequency points are computed within the time-frequency-first-order chirprate space. Finally, the calculated three-dimensional result is transformed back into the time-frequency domain, which yields a time-frequency representation (TFR) with more concentrated energy. The effectiveness of the TESCT is validated through a comparative analysis of a signal with cross frequencies (as a non-proportional frequency special case) using various TFA techniques. Additionally, experimental results demonstrate that the TESCT can provide a clearer result for bearing and gearbox condition monitoring.