Simulation of multivariate nonstationary random processes: Hybrid stochastic wave and proper orthogonal decomposition approach

Liuliu Peng, Guoqing Huang, Xinzhong Chen, Ahsan Kareem

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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.

Original languageEnglish
Article number04017064
JournalJournal of Engineering Mechanics
Issue number9
StatePublished - Sep 1 2017


  • Fast fourier transform (FFT)
  • Multivariate
  • Nonstationary
  • Proper orthogonal decomposition (POD)
  • Random process
  • Simulation
  • Stationary
  • Stochastic wave


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