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

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.

[1]  M. Di Paola,et al.  Digital generation of multivariate wind field processes , 2001 .

[2]  Drahomír Novák,et al.  Error assessment for wind histories generated by autoregressive method , 1995 .

[3]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .

[4]  Riccardo Rossi,et al.  Wind field simulation for structural engineering purposes , 2004 .

[5]  Mircea Grigoriu,et al.  Algorithm for Generating Samples of Homogeneous Gaussian Fields , 2003 .

[6]  George Deodatis,et al.  Simulation of Highly Skewed Non-Gaussian Stochastic Processes , 2001 .

[7]  C. Letchford,et al.  Simulation of Multivariate Stationary Gaussian Stochastic Processes: Hybrid Spectral Representation and Proper Orthogonal Decomposition Approach , 2005 .

[8]  N. Wax,et al.  Selected Papers on Noise and Stochastic Processes , 1955 .

[9]  J. Kaimal,et al.  Spectral Characteristics of Surface-Layer Turbulence , 1972 .

[10]  Mircea Grigoriu,et al.  On the spectral representation method in simulation , 1993 .

[11]  Qiusheng Li,et al.  Prediction of wind-induced pressures on a large gymnasium roof using artificial neural networks , 2007 .

[12]  Ahsan Kareem,et al.  ON THE APPLICATION OF STOCHASTIC DECOMPOSITION IN THE ANALYSIS OF WIND EFFECTS , 2000 .

[13]  L. E. Wittig,et al.  Simulation of Multicorrelated Random Processes Using the FFT Algorithm , 1973 .

[14]  L. Borgman,et al.  Ocean wave simulation for engineering design , 1967 .

[15]  L. Carassale,et al.  Modal transformation tools in structural dynamics and wind engineering , 2000 .

[16]  M. Shinozuka,et al.  Simulation of Seismic Ground Motion Using Stochastic Waves , 1989 .

[17]  F. Kozin,et al.  Autoregressive moving average models of earthquake records , 1988 .

[18]  L. Carassale,et al.  Monte Carlo simulation of wind velocity fields on complex structures , 2006 .

[19]  J.-N. Yang,et al.  Simulation of random envelope processes. , 1972 .

[20]  Muruhan Rathinam,et al.  A New Look at Proper Orthogonal Decomposition , 2003, SIAM J. Numer. Anal..

[21]  M. Shinozuka,et al.  Auto‐Regressive Model for Nonstationary Stochastic Processes , 1988 .

[22]  Ahsan Kareem,et al.  Proper Orthogonal Decomposition-Based Modeling, Analysis, and Simulation of Dynamic Wind Load Effects on Structures , 2005 .

[23]  C. Scruton,et al.  Wind Effects on Structures , 1970 .

[24]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .

[25]  Masanobu Shinozuka,et al.  Monte Carlo solution of structural dynamics , 1972 .

[26]  Haifan Xiang,et al.  Simulation of stationary Gaussian stochastic wind velocity field , 2006 .

[27]  Ahsan Kareem,et al.  Simulation of Multivariate Nonstationary Random Processes by FFT , 1991 .

[28]  S. Rice.  Mathematical analysis of random noise , 1944 .

[29]  N. Jensen,et al.  Lateral coherence in isotropic turbulence and in the natural wind , 1979 .

[30]  Ahsan Kareem,et al.  Digital Simulation of Wind Load Effects , 1992 .

[31]  Jinkyu Yang,et al.  On the normality and accuracy of simulated random processes , 1973 .

[32]  Ahsan Kareem,et al.  Simulation of Multivariate Random Processes: Hybrid DFT and Digital Filtering Approach , 1993 .

[33]  W. Gersch,et al.  Synthesis of multivariate random vibration systems: A two-stage least squares AR-MA model approach☆ , 1977 .

[34]  G. Deodatis.  Simulation of Ergodic Multivariate Stochastic Processes , 1996 .

[35]  Kenny C. S Kwok,et al.  Eigenvector modes of fluctuating pressures on low-rise building models , 1997 .

[36]  Paolo Spinelli,et al.  Artificial Wind Generation and Structural Response , 1987 .

[37]  Jorge Daniel Riera,et al.  A comparison of proper orthogonal decomposition and Monte Carlo simulation of wind pressure data , 2000 .

[38]  M. D. Paola,et al.  Digital simulation of wind field velocity , 1998 .

[39]  Masanobu Shinozuka,et al.  Simulation of Multivariate and Multidimensional Random Processes , 1971 .