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

ABSTRACT: 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(?) stable distribution process(1 < ? < 2) in this paper, even the noise also is ? stable distribution in some special cases. The performance of ST-TFR method will degrade under ? 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 ? stable distribution noise, which can work better under Gaussian noise environment, and is robust. The FLOST-TFF method can effectively filter out ? 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 ? 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 ? stable distribution noise, where excellent performances can be shown.

SUBMITTER: Long J

PROVIDER: S-EPMC5391006 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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

Long Junbo J Wang Haibin H Zha Daifeng D Li Peng P Xie Huicheng H Mao Lili L

PloS one 20170413 4

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 beari ...[more]

PMID: 28406916

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Project description:Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Dataset Information

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

Publications

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

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