Simulation of Non-Gaussian Stochastic Process with Target Power Spectral Density and Lower-Order Moments
Publication: Journal of Engineering Mechanics
Volume 138, Issue 5
Abstract
In this paper, a direct simulation algorithm is presented for the generation of a class of non-Gaussian stochastic processes according to target lower-order moments and prescribed power spectral density (PSD) function. The proposed algorithm is to expand the autoregressive (AR) model and the autoregressive moving average (ARMA) model, which are available to generate Gaussian random process, to simulate directly non-Gaussian stochastic process. The coefficients of the AR or ARMA model are determined based on the prescribed PSD function. It is well known that outputting stochastic process is also non-Gaussian if inputting white noise is non-Gaussian. But the skewness and kurtosis of the outputting non-Gaussian random process are not identical to these of inputting non-Gaussian white noise. In this paper, the relationships of lower-order moments such as skewness and kurtosis between output and input are analyzed and close to linear transformations. To corroborate the feasibility and correctness of the present methodology, numerical examples involving simulation of fluctuating wind pressures are taken into consideration. Numerical results indicate that the skewness and kurtosis of generated wind pressures based on the AR or ARMA model closely match their targets. In addition, the PSD and correlation functions of simulated samples also show considerably good agreement with prescribed functions. Therefore, the proposed algorithm is effective to simulate directly the class of non-Gaussian stochastic process.
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Acknowledgments
The authors acknowledge the financial contributions received from the National Science Foundation of China with Grant Nos. 50578092 and 11162005. The authors thank the reviewers for their careful, unbiased, and constructive suggestions that significantly improved the quality of this paper.
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© 2012. American Society of Civil Engineers.
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Received: Jun 24, 2010
Accepted: Nov 2, 2011
Published online: Nov 4, 2011
Published in print: May 1, 2012
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