Applications of an Improved Time‐Frequency Filtering Algorithm to Signal Reconstruction

Abstract

The short time Fourier transform time-frequency representation (STFT-TFR) method degenerates, and the corresponding short time Fourier transform time-frequency filtering (STFT-TFF) method fails under α stable distribution noise environment. A fractional low order short time Fourier transform (FLOSTFT) which takes advantage of fractional p order moment is proposed for α stable distribution noise environment, and the corresponding FLOSTFT time-frequency representation (FLOSTFT-TFR) algorithm is presented in this paper. We study vector formulation of the FLOSTFT and inverse FLOSTFT (IFLOSTFT) methods and propose a FLOSTFT time-frequency filtering (FLOSTFT-TFF) method which takes advantage of time-frequency localized spectra of the signal in time-frequency domain. The simulation results show that, employing the FLOSTFT-TFR method and the FLOSTFT-TFF method with an adaptive weight function, time-frequency distribution of the signals can be better gotten and time-frequency localized region of the signal can be effectively extracted from α stable distribution noise, and also the original signal can be restored employing the IFLOSTFT method. Their performances are better than the STFT-TFR and STFT-TFF methods, and MSEs are smaller in different α and GSNR cases. Finally, we apply the FLOSTFT-TFR and FLOSTFT-TFF methods to extract fault features of the bearing outer race fault signal and restore the original fault signal from α stable distribution noise; the experimental results illustrate their performances.

Applications of Fractional Lower Order Frequency Spectrum Technologies to Bearing Fault Analysis

“…The conventional frequency spectrum estimation methods mentioned above are suitable for rotating machine condition monitoring and performance evaluation in general. However, probability density functions (PDFs) of the bearing fault signals have heavy trails in some special cases, even the same with the noise in the signals, which belong to stable distribution [20][21][22][23][24][25]. Because stable distribution has no finite second moment, the existing methods based on Gaussian hypothesis and second-order statistics degenerate under stable distribution environment.…”