基于时变AR模型的非平稳非高斯随机过程的数值模拟  

Simulation of non-stationary non-Gaussian stochastic process based on a time-varying AR model

作　　者：李锦华[1,2] 陈水生[2] 吴春鹏[2] 李建丰[2] 

机构地区：[1]华东交通大学铁路环境振动与噪声教育部研究工程中心,南昌330013 [2]华东交通大学土木建筑学院,南昌330013

出　　处：《振动与冲击》2015年第17期142-146,160,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11162005);江西省自然科学基金项目(20132BAB216003)

摘　　要：为了有效地模拟具有目标非平稳、非高斯特征的随机过程,提出了基于时变AR模型的非平稳非高斯随机过程的模拟方法。该方法首先需要建立实现非高斯与高斯随机过程之间相互转换的非线性平移关系,然而该非线性平移也会导致平移前后高斯与非高斯随机过程的功率谱发生变化。因此该方法还需要进一步建立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。然后,通过已建立的非线性平移,以及功率谱或相关函数的转换关系,可将非平稳非高斯随机过程的模拟转化成对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建立的时变AR模型进行有效的模拟。最后将具有目标非平稳、非高斯特征的脉动风速模拟作为数值算例,验证了该方法模拟非平稳非高斯随机过程的有效性。In order to simulate effectively a stochastic process possessing given non-stationary non-Gaussian features,a method to simulate a non-stationary non-Gaussian stochastic process based on a time-varying AR model was proposed here.Firstly,it was necessary to establish a nonlinear translation relationship to realize mutual conversion between a non-Gaussian and a Gaussian one.Meanwhile,the power spectra both the non-Gaussian and the Gaussian random processes were different due to the nonlinear translation.Furthermore,the transformation relationship between their power spectra or correlation functions was established.Then,the simulation of a non-stationary non-Gaussian stochastic process was converted into a simulation of a non-stationary Gaussian random process by utilizing the nonlinear translation relationship and the transformation relationship of their power spectra or correlation functions constructed above.The non-stationary Gaussian random process was effectively simulated with a presented time-varying AR model.Finally,taking the simulation of a fluctuating wind velocity possessing target non-stationary non-Gaussian characteristics as a numerical example,the effectiveness of the method to simulate a non-stationary non-Gaussian random process was verified.

关 键 词：时变AR模型 数值模拟 非平稳随机过程 非高斯 脉动风速 

分 类 号：TU311[建筑科学—结构工程]