Fractional lower order linear chirplet transform and its application to bearing fault analysis

The amplitude and frequency of the mechanical bearing fault vibration signals vary with time, and which are non-stationary and non-Gaussian process. The fault signals belong to α stable distribution, and the characteristic index 1 < α < 2, even the noises are α stable distribution in extreme cases. The existing linear chirplet transform (LCT) degenerates, even fails under α stable distribution environment. A fractional low order linear chirplet transform (FLOLCT) which takes advantage of fractional p order moment is presented for α stable distribution noise environment, and the corresponding FLOLCT time-frequency representation (FLOLCTTFR) is developed in this paper. By employing a series of polynomial chirp rate parameters instead of a single chirp rate of the FLOLCT method, a fractional low order polynomial linear chirplet transform (FLOPLCT) is developed to improve time frequency concentration of the signals. The improved FLOLCT and FLOPLCT methods are used to compare with the existing LCT and PLCT methods based on second order statistics, the results reveal performance advantages of the proposed methods. Finally, the FLOLCT and FLOPLCT methods are applied to analyze the fault signature of the bearing ball fault data in the position of DE (Drive end accelerometer) and extract their fault signature, the result illustrates their performances.