Amplitude Probability Density Function for Skewed Non-Gaussian Vibrations Based on Gaussian-Mixture Model

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Journal of Vibration and Shock ›› 2014, Vol. 33 ›› Issue (12) : 121-125.

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Amplitude Probability Density Function for Skewed Non-Gaussian Vibrations Based on Gaussian-Mixture Model

Cheng Hongwei1,2, Tao Junyong1,2, Chen Xun1,2, Jiang Yu1,2

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Abstract

There are no explicit expressions for the probability densities of skewed non-Gaussian vibration signals. But the explicit expression is fundamental to the research of non-Gaussian vibrations. An approach based on Gaussian mixture model for the skewed non-Gaussian vibration is presented to fill the gap said before. First of all, the first five original moments of the non-Gaussian vibration signal can be estimated from the same time history. The quantitative relationships among the differently ordered moments of the Gaussian signal are studied. Based on these relationships and the mathematical expression of the Gaussian mixture model, an equation set about the parameters of the Gaussian mixture model is established. The parameters are the mean, standard deviation and weighting factor of each Gaussian element. Then the parameters are derived by solving the equation set. The expression for skewed non-Gaussian vibration is obtained by substituting the parameters into the Gaussian mixture model established before. Finally, the examples of simulated signals and measured signals have verified the validity of the presented method.

Key words

non-Gaussian / Gaussian mixture model / probability density function / skewness / kurtosis

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Cheng Hongwei;Tao Junyong;Chen Xun;Jiang Yu;. Amplitude Probability Density Function for Skewed Non-Gaussian Vibrations Based on Gaussian-Mixture Model[J]. Journal of Vibration and Shock, 2014, 33(12): 121-125