多变量随机过程的模拟方法研究
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摘要
在对自然风或地震等随机过程的模拟中,具有随机振幅、频率含量和相位角的随机过程模拟模型能更加真实地反映其随机性。该文推导一种可以描述上述随机特性的单变量和多变量随机过程的模型,并从理论上证实所模拟的样本具有平稳性,各态历经性以及高斯性等统计特性。经过数值算例分析证明模型的准确性以及有效性。
According to the spectral representation theorem, a weakly stationary stochastic process, such as the stochastic wind velocity fluctuations, can be simulated as a summation of a series of harmonic functions with random properties. In the present paper, a new model based on the spectral representation technique is proposed to simulate the random processes. The harmonic functions have random amplitudes, random phase angles and random frequencies that can represent the natural stochastic process properly. For the univariate case, probabilistic characteristics of the simulated sample, including the stationarity, ergodicity and Gaussianness, are firstly verified. Then a multivariate stationary model is proposed and formulated. At last, an example involving simulation of turbulent wind velocity is given to show the capability and accuracy of the proposed model.
According to the spectral representation theorem, a weakly stationary stochastic process, such as the stochastic wind velocity fluctuations, can be simulated as a summation of a series of harmonic functions with random properties. In the present paper, a new model based on the spectral representation technique is proposed to simulate the random processes. The harmonic functions have random amplitudes, random phase angles and random frequencies that can represent the natural stochastic process properly. For the univariate case, probabilistic characteristics of the simulated sample, including the stationarity, ergodicity and Gaussianness, are firstly verified. Then a multivariate stationary model is proposed and formulated. At last, an example involving simulation of turbulent wind velocity is given to show the capability and accuracy of the proposed model.
引文
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[7]程纬,刘光栋,易伟建.平稳地震动过程功率谱拟合及收敛性分析[J].世界地震工程,2002,18(2):43-47(Cheng Wei,Liu Guangdong,Yi Weijian.PSD simulation and covergence analysis of stationary ground motion process[J].World Earthquake Engineering,2002,18(2):43-47(in Chinese))
[8]Hu Dihe.Analysis probabilistic theorem[M].Beijing:Science Press,1984
[9]罗俊杰.大跨度屋盖风荷载模拟方法研究及张拉式索-膜结构风振响应分析[D].广州:华南理工大学,2008:33-37(Luo Junjie.A study on simulation method of wind loads for large-space roofs and the wind-induced response analysis of a tensile cable-membrane structure[D].Guangzhou:South China University of Technology,2008:33-37(in Chinese))
[10]Simiu E,Scanlan R H.Wind effects on structures[M].2nd edition.New York:John Wiley & Sons,1986
[2]Shinozuka M,Deodatis D.Simulation of stochastic processes by spectral representation[J].Applied Mechanics Reviews,1991,44(4):191-204
[3]Wittig L E,Sinha A K.Simulation of multicorrelated random processes using FFT algorithm[J].Journal of Acoustical Society of America,1975,58(3):630-634
[4]Shinozuka M,Jan C M.Digital simulation of random processes and its applications[J].Journal of Sound and Vibration,1972,25(1):111-128
[5]Goto H,Toki K.Structural response to nonstationary random excitation[C]//Proceedings of the 4th World Conference on Earthquake Engineering.Santiago,Chile,1969
[6]Shinozuka M.Simulation of multivariate and multidimensional random processes[J].Journal of Acoustical Society of America,1971,49:357-368
[7]程纬,刘光栋,易伟建.平稳地震动过程功率谱拟合及收敛性分析[J].世界地震工程,2002,18(2):43-47(Cheng Wei,Liu Guangdong,Yi Weijian.PSD simulation and covergence analysis of stationary ground motion process[J].World Earthquake Engineering,2002,18(2):43-47(in Chinese))
[8]Hu Dihe.Analysis probabilistic theorem[M].Beijing:Science Press,1984
[9]罗俊杰.大跨度屋盖风荷载模拟方法研究及张拉式索-膜结构风振响应分析[D].广州:华南理工大学,2008:33-37(Luo Junjie.A study on simulation method of wind loads for large-space roofs and the wind-induced response analysis of a tensile cable-membrane structure[D].Guangzhou:South China University of Technology,2008:33-37(in Chinese))
[10]Simiu E,Scanlan R H.Wind effects on structures[M].2nd edition.New York:John Wiley & Sons,1986
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