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.

[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. In this paper, Wigner-Ville distribution (WVD) and pseudo Wigner-Ville distribution (PWVD) time-frequency distribution based on the fractional lower order moment are presented to be improved. We got fractional lower order WVD (FLO-WVD) and fractional lower order PWVD (FLO-PWVD) time-frequency distribution which could be suitable for a stable distribution process. We also proposed the fractional lower order spatial time-frequency distribution matrix (FLO-STFM) concept. Therefore, combining with time-frequency underdetermined blind source separation (TF-UBSS), we proposed a new fractional lower order spatial time-frequency underdetermined blind source separation (FLO-TF-UBSS) which can work in a stable distribution environment. We used the FLO-TF-UBSS algorithm to extract EPs. Simulations showed that the proposed method could effectively extract EPs in EEG noises, and the separated EPs and EEG signals based on FLO-TF-UBSS were almost the same as the original signal, but blind separation based on TF-UBSS had certain deviation. The correlation coefficient of the FLO-TF-UBSS algorithm was higher than the TF-UBSS algorithm when generalized signal-to-noise ratio (GSNR) changed from 10 dB to 30 dB and a varied from 1. 06 to 1. 94, and was approximately e- qual to 1. Hence, the proposed FLO-TF-UBSS method might be better than the TF-UBSS algorithm based on second order for extracting EP signal under an EEG noise environment.

[Blind estimation of evoked potentials based on covariations in non-gaussian noise].

Evoked potentials (EPs) have been widely used to quantify neurological system properties. Traditional EP analysis has been developed under the condition that the background noises in EP are Gaussian distributed. Recently some researches indicate that electroencephalogram (EEG) is non-guassian in some especial conditions. Alpha stable distribution can model impulsive EEG in especial experimentation such as acceleration bump and devoid oxygen. In this paper, blind signals separation based on covariations is analyzed and discussed by the nonexistence of the finite second or higher order statistic. The simulation experimental results show that the method has good performance to separate Evoked potentials (EPs) from fractional lower order alpha stable distribution noise.

[Estimation of evoked potentials based on MD criterion and Givens matrix in non-Gaussian noise environments].

Traditional EP analysis is developed under the condition that the background noises in EP are Gaussian distributed. Alpha stable distribution, a generalization of Gaussian, is better for modeling impulsive noises than Gaussian distribution in biomedical signal processing. Conventional blind separation and estimation method of evoked potentials is based on second order statistics (SOS). In this paper, we propose a new algorithm based on minimum dispersion criterion and Givens matrix. The simulation experiments show that the proposed new algorithm is more robust than the conventional algorithm.

Blind estimation of evoked potentials in alpha stable distribution environments.

Evoked potentials (EPs) have been widely used to quantify neurological system properties. Traditional EP analyses are developed under the condition that the background noise in EP analysis are Gaussian distributed. Alpha stable distribution, a generalization of Gaussian, is better for modeling impulsive noise than Gaussian distribution in biomedical signal processing. Conventional blind separation and estimation method of evoked potentials is based on second order statistics (SOS). In this paper, we modify our conventional algorithms and analyze the stability and convergence performance s of the new algorithm. The simulation experiments show that the proposed algorithm based on fractional lower order statistics is more robust than the conventional algorithm based on second order statistics.