Abstract: Due to the non-stationarity of the gear vibration signals measured under the speed-up and speed-down process, a novel fault diagnosis approach based on the combined application of the chirplet path pursuit algorithm and the Fractional Fourier transform (FrFT) method is proposed. With the chirplet path pursuit algorithm, the instantaneous frequency of the signal component whose energy is maximal among all the components in the gear vibration signal is estimated. And then according to the time-frequency curve of the estimated instantaneous frequency, the vibration signal segment whose instantaneous frequency curve approximates as an ascending or descending linear straight line can be intercepted from the original gear vibration signal. By means of the FrFT analysis on the extracted vibration signal segment, the fault of the gear can be detected from the modulation phenomenon which displayed on the FrFT spectrum of the extracted vibration signal segment. In the foregoing process, according to the chirp rate of the instantaneous frequency, the best order of the FrFT method can be figured out. Because of the low correlations between the noise and the chirplet atoms, the chirplet path pursuit algorithm is immune to noise. Furthermore, by selecting a proper fractional order, the good signal-noise separation capability of the FrFT can be achieved. Therefore，the proposed method can be used to process the gear vibration signals with the low signal-to noise ratio which being measured under the speed-up and speed-down process. The validity and the good anti-noise ability of the proposed method are demonstrated by both simulation and practical experiment.

Key words: Chirplet atoms, Fault diagnosis, Fractional Fourier transform(FrFT), Instantaneous frequency, Signal-to noise ratio