Simulation of Multivariate Random Processes: Hybrid DFT and Digital Filtering Approach
Publication: Journal of Engineering Mechanics
Volume 119, Issue 5
Abstract
A numerical simulation technique is presented that combines the advantages of the discrete Fourier transform (DFT) algorithm and a digital filtering scheme to generate continuous long‐duration multivariate random processes. This approach offers the simple convenience of conventional fast Fourier transform (FFT) based simulation schemes; however, it does not suffer from the drawback of the large computer memory requirement that, in the past, has precluded the generation of long‐duration time series utilizing FFT‐based approaches. Central to this technique is a simulation of a large number of time series segments by utilizing the FFT algorithm, which are subsequently synthesized by means of a digital filter to provide the desired duration of simulated processes. This approach offers computational efficiency, convenience, and robustness. The computer code based on the present methodology does not require users to have experience in determining optimal model parameters, unlike the procedures based on parametric models. The effectiveness of this methodology is demonstrated by means of examples concerning the simulation of a multivariate random wind field and the spatial variation of wave kinematics in a random sea with prescribed spectral descriptions. The simulated data showed excellent agreement with the target spectral characteristics. The proposed technique has immediate applications to the simulation of real‐time processes.
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References
1.
Bringham, E. O. (1974). The fast Fourier transform. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
2.
Borgman, L. E. (1969). “Ocean wave simulation for engineering design.” J. Wtrwy. Harbor Div., ASCE, 6(3), 557–583.
3.
Hasofar, A. M. (1989). “Continuous simulation of Gaussian processes with given spectrum.” Proc., 5th international conference on structural safety and reliability, ASCE, New York, N.Y.
4.
Hudspeth, R. T., and Borgman, L. E. (1979). “Efficient FFT simulation of digital time sequences.” J. Engrg. Mech. Div., ASCE, 105(2), 223–235.
5.
Iannuzzi, A., and Spinelli, P. (1987). “Artificial wind generation and structural response.” J. Struct. Engrg., ASCE, 113(12), 2382–2398.
6.
Kareem, A. (1978). “Wind excited motion of building,” PhD thesis, Colorado State University, Fort Collins, Colo.
7.
Kareem, A. (1987). “Wind effects on structures: a probabilistic viewpoint.” Probabilistic Engrg. Mech., 2(4), 166–200.
8.
Kareem, A., and Dalton, C. (1982). “Dynamic effects of wind on tension leg platforms.” Proc., ocean structural dynamics symposium '82, Dept. of Civ. Engrg., Oregon State Univ., Corvallis, Ore.
9.
Kareem, A., and Li, Y. (1988). “Stochastic response of a tension leg platform to wind and wave loads.” Technical rep. no. UHCE 88‐18, Dept. of Civ. Engrg., Univ. of Houston, Houston, Tex.
10.
Kareem, A., and Li, Y. (1991). “Continuous simulation of multi‐variate random processes.” Proc. 6th international conference on applications of statistics and probability in civil engineering, Mexico City, Mexico.
11.
Kareem, A., and Li, Y. (1992). “Digital simulation of wind load effects.” Proc., ASCE specialty conference on probabilistic mechanics and structural and geotechnical reliability, ASCE, New York, N.Y.
12.
Li, Y., and Kareem, A. (1990). “ARMA systems in wind engineering.” Probabilistic Engrg. Mech., 5(2), 50–59.
13.
Li, Y., and Kareem, A. (1989a). “On stochastic decomposition and its applications in probabilistic dynamics.” Proc., 5th international conference on structural safety and reliability (ICOSSAR), ASCE, New York, N.Y.
14.
Li, Y., and Kareem, A. (1989b). “Simulation and multivariate stationary random processes: a combination of digital filtering and DFT.” Tech. rep. no. UHCE89‐11, Dept. of Civ. Engrg., Univ. of Houston, Houston, Tex.
15.
Li, Y., and Kareem, A. (1993). “Parametric modelling of stochastic wave effects on offshore platforms.” Appl. Ocean Res., Elsevier, New York, N.Y.
16.
Mignolet, M. P., and Spanos, P‐T. D. (1987). “Recursive simulation of stationary multi‐variate random processes, parts I and II.” J. Appl. Mech., 54, 674–687.
17.
Naganuma, T., Deodatis, G., and Shinozuka, M. (1987). “ARMA model for two‐dimensional processes,” J. Engrg. Mech., ASCE, 113(2), 234–251.
18.
Reed, D. A., and Scanlan, R. H. (1984). “Autoregressive representation of longitudinal, lateral, and vertical turbulence spectra.” J. Wind Engrg. and Industrial Aerodynamics, 17, 199–214.
19.
Rice, S. O. (1954). “Mathematical analysis of random noise.” Selected papers on noise and stochastic processes, N. Wax, ed., Dover Publications, Inc., New York, N.Y.
20.
Sarpakaya, T., and Issacson, M. (1981). “Mechanics of wave forces on offshore structures.” Van Nostrand Reinhold Publication, New York, N.Y.
21.
Samaras, E., Shinozuka, M., and Tsurui, A. (1985). “ARMA representation of random vector processes.” J. Engrg. Mech., ASCE, 111(3), 449–461.
22.
Shinozuka, M. (1971). “Simulation of multivariate and multidimensional random processes (Part 2).” J. Acoustical Soc. of Am., 49(1), 357–367.
23.
Shinozuka, M., and Jan, C.‐M. (1972). “Digital simulation of random processes and its applications.” J. Sound and Vibration, 25(1), 111–128.
24.
Shinozuka, M. (1972). “Monte Carlo solution of structural dynamics.” Comp. and Struct., 2, 855–874.
25.
Shinozuka, M., and Deodais, G. (1988). “Stochastic process models for earthquake ground motion.” Probabilistic Engrg. Mech., 3, 114–123.
26.
Spanos, P‐T. D., and Mignolet, M. P. (1986). “Z‐transform modeling of P‐M wave spectrum,” J. Engrg. Mech., 112(8), 745–759.
27.
Wittig, L. E., and Sinha, A. K. (1975). “Simulation of multicorrelated random processes using the FFT algorithm.” J. Acoustical Soc. of Am., 58(3), 630–633.
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Copyright © 1993 American Society of Civil Engineers.
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Received: Dec 21, 1992
Published online: May 1, 1993
Published in print: May 1993
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