一种非高斯随机振动过程数值模拟方法  

A Numerical Simulation Method for Non-Gaussian Random Vibration Process

作　　者：杨喆[1] 朱大鹏[1] 高全福[1] YANG Zhe;ZHU Da-peng;GAO Quan-fu(Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学

出　　处：《包装工程》2019年第15期48-53,共6页Packaging Engineering

基　　金：国家自然科学基金(51765028)

摘　　要：目的考虑真实随机振动的非高斯特性,提出一种根据已知信息生成与其相符的非高斯随机振动过程的数值模拟方法。方法基于均值、方差、偏斜度、峭度及功率谱密度函数(或自相关函数)等约束条件,对非高斯随机振动进行模拟。根据功率谱获取非高斯过程的自相关矩阵;通过Hermite多项式的正交性质和多项式混沌展开方法推导出的公式,构造满足标准正态分布随机过程的协方差矩阵,并对其进行谱分解和主成分分析;最后,利用Karhunen-Loeve展开和多项式混沌展开来表示所模拟的非高斯振动过程。结果随着采样点个数的增加,实测数据与模拟数据之间的误差越来越小,该方法具有较好的模拟精度。结论应用多项式混沌展开、Karhunen-Loeve展开以及蒙特卡洛等方法,可生成非高斯随机振动过程,并得到准确有效的各项统计参数模拟值。The work aims to propose an appropriate numerical simulation method for non-Gaussian random vibration processes generated according to the known information when considering non-Gaussian property of the actual random vibration.Based on such constraint conditions as mean,variance,skewness,kurtosis and PSD function (or autocorrelation function),the non-Gaussian random vibration was simulated.The autocorrelation matrix of the non-Gaussian process was obtained from the PSD.Through the formula derived from Hermite polynomial orthogonal property and polynomial chaos expansion,the covariance matrix of the standard normal distribution random process was constructed,and the spectral decomposition and principal component analysis were also performed.Finally,the simulated non-Gaussian vibration process was represented by Karhunen-Loeve expansion and polynomial chaos expansion.As the number of sampling points increased,the error between measured data and simulated data became smaller and smaller,besides,the proposed method had good simulation accuracy.Combined with polynomial chaos expansion,Karhunen-Loeve expansion and Monte Carlo method,the non-Gaussian random vibration process can be generated and accurate and effective simulation values of various statistical parameters can be obtained.

关 键 词：非高斯随机振动 多项式混沌展开 Karhunen-Loeve展开 蒙特卡洛方法 

分 类 号：TB123[理学—工程力学]