Simulation of Multivariate Nonstationary Random Processes: Hybrid Stochastic Wave and Proper Orthogonal Decomposition Approach
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
The classical spectral representation method for simulation of multivariate nonstationary Gaussian random processes may be less efficient due to difficulty in a straightforward application of the fast Fourier transform (FFT). Although several attempts have been made to invoke the FFT, there remains the need to further improve the efficiency for cases where a large number of points need to be simulated. In this paper, a stochastic wave-based simulation scheme for the multivariate nonstationary random process along a straight line is introduced in conjunction with either a direct summation of cosine functions or the application of a two-dimensional (2D) FFT. Central to the proposed schemes is the transformation of the simulation of a multivariate nonstationary random process to that of a nonstationary one-dimensional stochastic wave. The stochastic wave can be simulated based on a direct summation of cosine functions or by invocation of a 2D FFT. The latter requires that the points to be simulated are evenly distributed. To implement FFT, proper orthogonal decomposition (POD) is employed to factorize the time-dependent and space-dependent 2D decomposed evolutionary power spectral density of the converted stochastic wave. The proposed hybrid approach of a stochastic wave and POD is quite general, and can be used to simulate nonstationary multivariate random processes with complex coherence functions. Numerical examples show that the proposed hybrid approach is very efficient in comparison with existing approaches when the number of simulation locations is large, and it offers a desired level of simulation accuracy when appropriate discretization parameters are selected.
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Acknowledgments
The support by the Doctoral Innovation Fund of Southwest Jiaotong University and the National Natural Science Foundation of China (Grant Nos. 51578471 and 51478401) are greatly acknowledged. The fourth author acknowledges the support by NSF (CMMI 1301008).
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©2017 American Society of Civil Engineers.
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Received: Mar 9, 2016
Accepted: Jan 27, 2017
Published online: Apr 25, 2017
Published in print: Sep 1, 2017
Discussion open until: Sep 25, 2017
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