基于时变AR模型的非平稳非高斯随机过程的数值模拟

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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，本文提出了基于时变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。本文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。

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	李锦华1
	2 陈水生2 吴春鹏2 李建丰2

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

Abstract：In order to simulate effectively the stochastic process possessing the given non-stationary non-Gaussian features, a method for simulating the non-stationary non-Gaussian stochastic process based on time-varying AR model is proposed in this paper. Firstly, it needs to establish a nonlinear translation relationship to achieve mutual conversion between non-Gaussian and Gaussian random processes. Meanwhile, it is certain that the power spectrums both non-Gaussian and Gaussian random processes are different due to the nonlinear translation. So, it must further find the transformation relationship between the power spectrums or correlation functions of the non-Gaussian and Gaussian stochastic processes. Then, the simulation of a non-stationary non-Gaussian stochastic process can be converted into the simulation of the non-stationary Gaussian random process through utilizing the nonlinear translation relationship of the random process and the transformation relationship of the power spectrum or correlation function. And the non-stationary Gaussian random process can be effectively simulated by the presented time-varying AR model. Finally, taking the simulation of the fluctuating wind velocity possessing the target non-stationary non-Gaussian characteristics as a numerical example, verifies the effectiveness of the method for generating non-stationary non-Gaussian random process.

Key words： Time-varying AR model Numerical simulation Non-stationary stochastic process Non-Gaussian Fluctuating wind velocity.

收稿日期: 2015-01-07 出版日期: 2015-09-15

引用本文:

李锦华1, 2 陈水生2 吴春鹏2 李建丰2. 基于时变AR模型的非平稳非高斯随机过程的数值模拟[J]. 振动与冲击, 2015, 34(17): 142-146.
Li Jin-hua1, 2 Chen Shui-sheng2 Wu Chun-peng2 Li Jian-feng2. Simulation of Non-stationary Non-Gaussian Stochastic Process Based on Time-varying AR Model. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(17): 142-146.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2015/V34/I17/142

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