偏斜非高斯随机振动信号幅值概率密度函数研究

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (12) : 121-125.

论文

偏斜非高斯随机振动信号幅值概率密度函数研究

程红伟1,2，陶俊勇1,2，陈循1,2，蒋瑜1,2

作者信息 +

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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文章历史 +

摘要

偏斜非高斯振动信号幅值概率密度没有明确、简洁的解析表达式。研究概率密度的解析表达式，对于非高斯振动理论研究具有重要意义。针对以上需求，提出了一种基于高斯混合模型的概率密度函数表示方法。首先，通过时间样本序列得到偏斜非高斯振动信号前五阶矩的估计值。其次，根据平稳高斯随机过程各阶矩之间的定量关系，结合二阶高斯混合模型的数学表达式建立方程组，求解得到混合模型中每个高斯分量的均值、标准差和权重系数。然后，将每个高斯分量的参数代入高斯混合模型，得到偏斜非高斯振动信号的幅值概率密度的解析表达式。最后，将所提出的方法应用于仿真非高斯加速度信号和实测非高斯振动应力信号，充分验证了该方法的有效性和适用性。

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.

导出引用

程红伟;陶俊勇;陈循;蒋瑜;. 偏斜非高斯随机振动信号幅值概率密度函数研究[J]. 振动与冲击, 2014, 33(12): 121-125

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