基于高斯混合模型的非高斯随机振动幅值概率密度函数  

Amplitude probability density functions for non-Gaussian random vibrations based on a Gaussian mixture model

作　　者：程红伟[1,2] 陶俊勇[1,2] 蒋瑜[1,2] 陈循[1,2] 

机构地区：[1]国防科技大学装备综合保障技术重点实验室,长沙410073 [2]国防科技大学机电工程与自动化学院,长沙410073

出　　处：《振动与冲击》2014年第5期115-119,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(50905181)

摘　　要：针对非高斯振动信号的幅值概率密度函数难以用数学模型表述的问题,提出了基于高斯混合模型的非高斯概率密度函数表示方法。首先,基于时域样本信号得到非高斯振动信号的高阶矩估计值。其次,基于高斯随机过程偶次高阶矩之间的定量关系,结合二阶高斯混合模型建立方程组,求解得到混合模型中每个高斯分量的方差和权值。然后,将各高斯分量的权值和方差代入高斯混合模型,得到适用于对称非高斯振动信号的幅值概率密度函数。最后,通过仿真信号和实测振动信号,验证了该方法的有效性和适用性。Aiming at the difficulty in deriving mathematical expressions of amplitude probability density functions of non-Gaussian vibrations,a Gaussian mixture model-based probability density function （PDF ） was proposed for non-Gaussian vibration signals.The estimation of higher-order moments of a non-Gaussian vibration process was obtained with sample time histories.Based on the quantitative relations between the even order moments of a given Gaussian process, combining with a secorld order Gaussian mixture model,an equation set for achieving the parameters of each Gaussian component in the Gaussian mixture model was established.Based on the obtained weighting factors and variances of Gaussian components,the mathematical model of non-Gaussian probability density function was then achieved.The examples of simulated signals and measured signals verified the validity of the presented method.

关 键 词：非高斯随机振动 高斯混合模型 概率密度函数(PDF) 高阶矩 PROBABILITY DENSITY function (PDF) 

分 类 号：TB123[理学—工程力学]