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Simulation of multivariate Stationary Guassian Stochastic Processes: Hybrid Spectral Representation and POD approach

Citation

Chen, L and Letchford, CW, Simulation of multivariate Stationary Guassian Stochastic Processes: Hybrid Spectral Representation and POD approach, Journal of Engineering Mechanics, 131, (8) pp. 801-808. ISSN 0733-9399 (2005) [Refereed Article]

DOI: doi:10.1061/(ASCE)0733-9399(2005)131:8(801)

Abstract

By observing that the optimal basis for the proper orthogonal decomposition (POD) can be obtained from the cross power spectral density (XPSD) matrix of a multivariate stationary Gaussian stochastic process, the computational efficiency, in both time and memory consumption, of simulations of this process is improved by using a hybrid spectral representation and POD approach with negligible loss of accuracy. This hybrid approach actually simulates another multivariate process with many fewer variables in an optimal subspace obtained by the POD. This approach is straightforward, effective, and does not place any conditions on the XPSD matrices. Furthermore, the error induced by the reduction of variables is predictable and controllable prior to the simulation procedure. The spectral representation method (SRM) is discussed in a heuristic way. In this paper, a specific POD theorem is formally stated, proved, and related to XPSD matrices. A numerical example is given to demonstrate the effectiveness of this hybrid approach. This approach may also have potential applications for simulations of nonstationary non-Gaussian processes. Journal of Engineering Mechanics © ASCE.

Item Details

Item Type:Refereed Article
Research Division:Engineering
Research Group:Interdisciplinary Engineering
Research Field:Turbulent Flows
Objective Division:Construction
Objective Group:Construction Planning
Objective Field:Civil Construction Planning
Author:Letchford, CW (Professor Chris Letchford)
ID Code:47865
Year Published:2005
Web of Science® Times Cited:22
Deposited By:Engineering
Deposited On:2007-09-22
Last Modified:2007-09-22
Downloads:0

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