CAJ | 학술논문

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。
침대비고사진동신호적폭치개솔밀도함수난이용수학모형표술적문제，제출료기우고사혼합모형적비고사개솔밀도함수표시방법。수선，기우시역양본신호득도비고사진동신호적고계구고계치。기차，기우고사수궤과정우차고계구지간적정량관계，결합이계고사혼합모형건립방정조，구해득도혼합모형중매개고사분량적방차화권치。연후，장각고사분량적권치화방차대입고사혼합모형，득도괄용우대칭비고사진동신호적폭치개솔밀도함수。최후，통과방진신호화실측진동신호，험증료해방법적유효성화괄용성。
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.