偏斜非高斯随机振动信号幅值概率密度函数研究  

Amplitude probability density function for skewed non-gaussian random vibration signals based on gaussian-mixture model

作　　者：程红伟[1,2] 陶俊勇[1,2] 陈循[1,2] 蒋瑜[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12期121-125,144,共6页Journal of Vibration and Shock

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。There are no explicit expressions for the probability densities of skewed non-Gaussian random vibration signals.But to study these explicit expressions is meaningful for studying non-Gaussian vibrations.An approach based on Gaussian mixture model for skewed non-Gaussian random vibration was presented here.First of all,the first five order moments of non-Gaussian vibration signals were estimated with time history sample sequences.The quantitative relationships among different order moments of a stationary Gaussian signal were derived.Based on these relationships and the mathematical expression of Gaussian mixture model,an equation-set for the parameters of Gaussian mixture model was established.The parameters were mean,standard deviation and weighted factor of each Gaussian component.Then the parameters were obtained by solving the equation set.The analytical expression for skewed non-Gaussian vibration was achieved by substituting the parameters into Gaussian mixture model established before.Finally,the examples of simulated signals and measured signals verified the validity of the presented method.

关 键 词：非高斯 高斯混合模型 概率密度函数 偏度 峭度 

分 类 号：TB123[理学—工程力学]