Error Assessment for the Coherency Matrix-Based Spectral Representation Method in Multivariate Random Processes Simulation
Publication: Journal of Engineering Mechanics
Volume 139, Issue 9
Abstract
Multivariate random processes are usually simulated by the spectral representation method (SRM). According to the matrix for decomposition, the SRM has two main types, that is, the SRM based on the decomposition of the power spectral density (PSD) matrix denoting the PSD matrix-based SRM, and the SRM based on the decomposition of the coherency matrix denoting the coherency matrix based-SRM. The stochastic errors of the PSD for the PSD matrix-based SRM have been given. This paper presents the stochastic errors of the PSD for the coherency matrix-based SRM, and makes a comparison of these errors for the PSD matrix-based SRM. For the random amplitudes formulas and random phase formula and Cholesky decomposition method, the stochastic errors of the PSDs for the PSD matrix-based SRM are the same as or the coherency matrix-based SRM, whereas for the random phases formula and eigendecomposition method and random phases formula and root decomposition method, they are different. However, the differences are slight when taking into account the sum of the PSD functions’ stochastic errors.
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Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant Nos. 51278382 and 90815020).
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 9 • September 2013
Pages: 1294 - 1299
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jan 11, 2012
Accepted: Nov 2, 2012
Published online: Nov 5, 2012
Published in print: Sep 1, 2013
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