Stable Distribution Noise Environment Research Articles

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.

Applications of Fractional Lower Order Synchrosqueezing Transform Time Frequency Technology to Machine Fault Diagnosis

Synchrosqueezing transform (SST) is a high resolution time frequency representation technology for nonstationary signal analysis. The short time Fourier transform-based synchrosqueezing transform (FSST) and the S transform-based synchrosqueezing transform (SSST) time frequency methods are effective tools for bearing fault signal analysis. The fault signals belong to a non-Gaussian and nonstationary alpha (α) stable distribution with 1&lt;α&lt;2 and even the noises being also α stable distribution. The conventional FSST and SSST methods degenerate and even fail under α stable distribution noisy environment. Motivated by the fact that fractional low order STFT and fractional low order S-transform work better than the traditional STFT and S-transform methods under α stable distribution noise environment, we propose in this paper the fractional lower order FSST (FLOFSST) and the fractional lower order SSST (FLOSSST). In addition, we derive the corresponding inverse FLOSST and inverse FLOSSST. The simulation results show that both FLOFSST and FLOSSST perform better than the conventional FSSST and SSST under α stable distribution noise in instantaneous frequency estimation and signal reconstruction. Finally, FLOFSST and FLOSSST are applied to analyze the time frequency distribution of the outer race fault signal. Our results show that FLOFSST and FLOSSST extract the fault features well under symmetric stable (SαS) distribution noise.

A WHT Signal Detection-Based FLO-TF-UBSS Algorithm Under Impulsive Noise Environment

Linear frequency modulated (LFM) signal is used to describe radar echo signal, and Wigner–Hough transform (WHT) is a useful detection tool for LMF signals. The noise in radar echo signal has strong pulse under complex environment, which belongs to $$\alpha $$ stable distribution process. The WHT method degenerates under $$\alpha $$ stable distribution environment. Hence, fractional lower-order pseudo-Wigner–Ville distribution (FLO-PWVD) time–frequency method is introduced, and fractional lower-order pseudo-Wigner–Hough transform (FLO-PWHT) method based on the FLO-PWVD method and Hough transform is proposed for the detection of LFM signals. When the LFM signals are overlapped in time domain and generalized signal-to-noise ratio (GSNR) is relatively low, the FLO-PWHT method degenerate, even which cannot work. Therefore, fractional lower-order spacial time–frequency matrix is applied to substitute spacial time–frequency distribution matrix, and a new fractional lower-order spacial time–frequency underdetermined blind source separation (FLO-TF-UBSS) algorithm employing the time–frequency underdetermined blind source separation algorithm (TF-UBSS) is proposed in this paper. Also, we combine the FLO-PWHT method with the FLO-TF-UBSS algorithm and propose a fractional lower-order spatial time–frequency underdetermined blind source separation pseudo-Wigner–Hough transform (FLO-TF-UBSS-PWHT) method. The simulation results show that the FLO-PWHT method is obviously better than the existing PWHT algorithm under $$\alpha $$ stable distribution noise or Gaussian noise environment, which is robust. The FLO-TF-UBSS algorithm can effectively downgrade mean square error of the reconstructed LFM signals, and its performance is better than the existing TF-UBSS and minimum dispersion BSS algorithms. The FLO-TF-UBSS-PWHT algorithm can work well in the cases of time domain overlapping and relatively low GSNR; its performance is better than the FLO-PWHT algorithm, which has certain toughness. Finally, we apply the FLO-PWVD, FLO-TF-UBSS, and FLO-PWHT methods to analyze and extract fault features of the bearing outer race fault signal in DE; the experimental results illustrate their performance superiority.

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. The performance of ST-TFR method will degrade under α stable distribution noise environment, following the ST-TFF method fail. Hence, a new fractional lower order ST time frequency representation(FLOST-TFR) method employing fractional lower order moment and ST and inverse FLOST(IFLOST) are proposed in this paper. A new FLOST time frequency filtering(FLOST-TFF) algorithm based on FLOST-TFR method and IFLOST is also proposed, whose simplified method is presented in this paper. The discrete implementation of FLOST-TFF algorithm is deduced, and relevant steps are summarized. Simulation results demonstrate that FLOST-TFR algorithm is obviously better than the existing ST-TFR algorithm under α stable distribution noise, which can work better under Gaussian noise environment, and is robust. The FLOST-TFF method can effectively filter out α stable distribution noise, and restore the original signal. The performance of FLOST-TFF algorithm is better than the ST-TFF method, employing which mixed MSEs are smaller when α and generalized signal noise ratio(GSNR) change. Finally, the FLOST-TFR and FLOST-TFF methods are applied to analyze the outer race fault signal and extract their fault features under α stable distribution noise, where excellent performances can be shown.

Pseudo Cohen Time-Frequency Distributions in Infinite Variance Noise Environment

stable distribution has been suggested as a more appropriate model in impulsive noise environment.The performance of conventional time-frequency distributions (TFDs) degenerate in stable distribution noise environment. Hence, three improved methods are proposed based on Fractional Low Order statistics, Fractional Low Order Wigner-Ville Distribution (FLO-WVD), Fractional Low Order Statistic pseudo Wigner-Ville Distribution (FLO-PWVD), Fractional Low Order Statistic Cohen class distribution (FLO-Cohen). In order for real-time, on-line operation and fairly long signals processing, a new smoothed pseudo Fractional Low Order Cohen class distribution (PFLO-Cohen) is proposed.Simulations show that the methods demonstrate the advantages in this paper, are robust.