具有时变功率谱的非高斯随机过程的数值模拟  

Numerical simulation of non-Gaussian stochastic process with time-varying power spectrum

作　　者：李锦华[1] 李建丰[1] 陈水生[1] 余维光 李春祥[2] 

机构地区：[1]华东交通大学土木建筑学院,南昌330013 [2]上海大学土木工程系,上海200444

出　　处：《振动与冲击》2018年第2期204-209,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(11162005;51378304);江西省自然科学基金(20171BAB206051)

摘　　要：为了有效地模拟具有目标时变功率谱特征的非高斯随机过程,即非平稳非高斯随机过程。提出了基于目标时变功率谱和目标非高斯概率密度函数,通过建立非高斯与高斯随机过程之间相互转换的非线性平移关系,以及非线性平移前后高斯与非高斯随机过程的功率谱或相关函数的转换关系,将非平稳非高斯随机过程转化为非平稳高斯随机过程的模拟;而非平稳高斯随机过程可通过谱表示进行有效的模拟。为了验证该方法的有效性,进行了具有目标非平稳非高斯特征的脉动风速模拟;模拟结果表明:模拟生成的脉动风速样本的功率谱具有时变特征,且瞬时功率谱和相关函数均与目标相吻合;任意时刻脉动风速样本的概率密度函数与目标非高斯函数相互吻合;因此,模拟的随机样本不仅具有目标时变功率的非平稳特征而且还具有目标概率密度函数的非高斯特征,说明了该非平稳非高斯随机过程模拟方法的有效性。In order to simulate effectively a non-stationary non-Gaussian stochastic process possessing a given timevarying power spectrum and probability density function,a nonlinear translation relationship to achieve mutual conversion between non-Gaussian and Gaussian random processes was established, the conversion relationship between power spectrum or correlation function of a non-Gaussian stochastic process and that of a Gaussian stochastic process was also established. Then,a non-stationary non-Gaussian stochastic process was converted through these relationships into a nonstationary Gaussian stochastic process to be simulated. A non-stationary Gaussian stochastic process was effectively simulated with the spectral representation. In order to verify the effectiveness of this method,the simulation of a fluctuating wind velocity possessing target non-stationary non-gaussian characteristics was performed. The simulation results showed that the simulated fluctuating wind speed sample 's power spectrum has time-varying characteristics,meanwhile its instantaneous power spectrum and correlation function match those of the target; the probability density function( PDF) of the fluctuating wind velocity sample at any time matches the target's PDF possessing non-Gaussian characteristics; therefore,the simulated random samples not only have the non-stationary features of target time-varying power spectrum,but also have the non-Gaussian features of target probability density function,the effectiveness of the proposed method to simulate a non-stationary non-Gaussian random process is verified.

关 键 词：时变功率谱 概率密度函数 非高斯随机过程 非平稳特性 脉动风速 

分 类 号：TU311[建筑科学—结构工程]