Robust post-processing time frequency technology and its application to mechanical fault diagnosis.

Post-processing synchrosqueezing transform and synchroextracting transform methods can improve TFR resolution for fault diagnosis. The normal and fault signal can be described by infinite variance process, and 1 < α ≤ 2, even the background noise belongs to the process under complex conditions. The effect of traditional SST and SET methods is greatly reduced and even lost in infinite variance process environment.

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.

Applications of fractional lower order S transform time frequency filtering algorithm to machine fault diagnosis.

Stockwell transform(ST) time-frequency representation(ST-TFR) is a time frequency analysis method which combines short time Fourier transform with wavelet transform, and ST time frequency filtering(ST-TFF) method which takes advantage of time-frequency localized spectra can separate the signals from Gaussian noise. The ST-TFR and ST-TFF methods are used to analyze the fault signals, which is reasonable and effective in general Gaussian noise cases. However, it is proved that the mechanical bearing fault signal belongs to Alpha(α) stable distribution process(1 < α < 2) in this paper, even the noise also is α stable distribution in some special cases.

[Evoked Potential Blind Extraction Based on Fractional Lower Order Spatial Time-Frequency Matrix].

The impulsive electroencephalograph (EEG) noises in evoked potential (EP) signals is very strong, usually with a heavy tail and infinite variance characteristics like the acceleration noise impact, hypoxia and etc., as shown in other special tests. The noises can be described by a stable distribution model.