Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 842183, 24 pages
Research Article

Spline-Interpolation-Based FFT Approach to Fast Simulation of Multivariate Stochastic Processes

1Department of Civil Engineering, Shanghai University, No. 149 Yanchang Road, Shanghai 200072, China
2Department of Civil Engineering, East China Jiaotong University, No. 808 Shuanggang Street, Nanchang 330013, China

Received 2 June 2011; Revised 17 August 2011; Accepted 19 August 2011

Academic Editor: Wei-Chiang Hong

Copyright © 2011 Jinhua Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The spline-interpolation-based fast Fourier transform (FFT) algorithm, designated as the SFFT algorithm, is proposed in the present paper to further enhance the computational speed of simulating the multivariate stochastic processes. The proposed SFFT algorithm first introduces the spline interpolation technique to reduce the number of the Cholesky decomposition of a spectral density matrix and subsequently uses the FFT algorithm to further enhance the computational speed. In order to highlight the superiority of the SFFT algorithm, the simulations of the multivariate stationary longitudinal wind velocity fluctuations have been carried out, respectively, with resorting to the SFFT-based and FFT-based spectral representation SR methods, taking into consideration that the elements of cross-power spectral density matrix are the complex values. The numerical simulation results show that though introducing the spline interpolation approximation in decomposing the cross-power spectral density matrix, the SFFT algorithm can achieve the results without a loss of precision with reference to the FFT algorithm. In comparison with the FFT algorithm, the SFFT algorithm provides much higher computational efficiency. Likewise, the superiority of the SFFT algorithm is becoming more remarkable with the dividing number of frequency, the number of samples, and the time length of samples going up.