Simulation of Multivariate Nonstationary Random Processes by FFT
Publication: Journal of Engineering Mechanics
Volume 117, Issue 5
Abstract
The fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description. A stochastic decomposition technique facilitates utilization of the FFT algorithm. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time‐dependent weights that are simulated by the FFT algorithm. The desired evolutionary spectral characteristics of the multivariate unidimensional process may be prescribed in a closed form or a set of numerical values at discrete frequencies. The effectiveness of the proposed technique is demonstrated by means of three examples with different evolutionary spectral characteristics derived from past earthquake events. The closeness between the target and the corresponding estimated correlation structure suggests that the simulated time series reflect the prescribed probabilistic characteristics extremely well. The simulation approach is computationally efficient, particularly for simulating large numbers of multiple‐correlated nonstationary random processes.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Borino, G., Paola, M. DI, and Muscilina, G. (1988). “Non‐stationary spectral moments of base excited MDOF systems.” Earthquake Engrg. and Struct. Dynamics, 16, 745–756.
2.
Cakmak, A. S., Sherit, R. I., and Ellis, G. (1985). “Modeling earthquake ground motions in California using parametric time series methods.” Soil Dynamics and Earthquake Engrg., 4(3), 124–131.
3.
Deodatis, G., and Shinozuka, M. (1988). “Auto‐regressive model for nonstationary stochastic processes.” J. Engrg. Mech., ASCE, 114(12), 1995–2012.
4.
Gersch, W., and Kitagawa, G. (1985). “A time varying AR coefficient model for modeling and simulating earthquake ground motion.” Earthquake Engrg. and Struct. Dynamics, 13(2), 124–131.
5.
Gersch, W., and Yonemoto, J. (1972). “Synthesis of multivariate random vibration systems: A two‐stage least squares ARMA model approach.” J. Sound and Vibration, 52(4), 553–565.
6.
Harichandran, R. S., and Wang, W. (1988). “Response of simple beam to spatially varying earthquake excitation.” J. Engrg. Mech., 114(9), 1526–1541.
7.
Harichandran, R. S., and Vanmarcke, E. (1986). “Stochastic variation of earthquake ground motion in space and time.” J. Engrg. Mech., ASCE, 112(2), 154–174.
8.
Hoshiya, M., Ishii, K., and Nagata, S. (1984). “Recursive covariance of structural response.” J. Engrg. Mech., ASCE, 110(12), 1743–1755.
9.
Kareem, A., and Dalton, C. (1982). “Dynamic effects of wind on tension leg platforms.” Proc. of Offshore Technology Conference, Houston, Tex.
10.
Kozin, R., and Nakajima, F. (1980). “The order determination problem for linear time‐varying AR models.” IEEE Trans. Auto Control, IEEE, (2), 250–251.
11.
Li, Y. (1988). “Stochastic response of a tension leg platform to wind and wave fields,” Dissertation presented to the University of Houston, at Houston, Texas, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
12.
Li, Yousun, and Kareem, A. (1988). “Recursive modeling of dynamic systems.” J. Engrg. Mech., ASCE.
13.
Li, Yousun, and Kareem, A. (1989a). “ARMA systems in wind engineering.” Proc. of the Sixth U.S. National Conference on Wind Engineering, Mar. 8–10, Houston, Tex.
14.
Li, Yousun, and Kareem, A. (1989b). “Continuous simulation of multi‐variate random processes by FFT.” Tech. Report No. UHCE89‐11, Dept. of Civ. Engrg.
15.
Li, Y., and Kareem, A. K. (1989c). “On stochastic decomposition and its application in probabilistic dynamics.” Proc. of the 5th International Conference on Structural Safety and Reliability (ICOSSAR '89), ASCE, 1311–1318.
16.
Lin, Y. K., and Yong, Y. (1985). “On modeling earthquakes as nonstationary random processes.” Structural Safety and Reliability, Vol. II, ICOSSAR '85, Konishi, Ang, and Shinozuka, eds.
17.
Liu, S. C. (1970). “Evolutionary power spectral density of strong motion earthquakes.” Bull. Seism. Soc. Am., 60(3), 891–900.
18.
Madsen, P., and Krenk, S. (1982). “Stationary and transient response statistics.” J. Engrg. Mech. Div., ASCE, 108(8), 622–635.
19.
Mark, W. D. (1986). “Power spectrum representation for nonstationary random vibration.” Random vibration—Status and recent developments, Elsevier, 211–240.
20.
Naganuma, T., Deodatis, G., and Shinozuka, M. (1987). “An ARMA model for two‐dimensional processes.” J. Engrg. Mech., ASCE, 113(2), 234–251.
21.
Priestly, M. B. (1967). “Power spectral analysis of non‐stationary random processes.” J. Sound Vib., 6, 86–97.
22.
Samaras, E., Shinozuka, M., and Tsurui, A. (1985). “ARMA representation of random processes.” J. Engrg. Mech., ASCE, 111(3), 449–461.
23.
Shinozuka, M. (1971). “Simulation of multivariate and multidimensional random processes.” J. Acoustical Soc. of America, 49, 357–367.
24.
Shinozuka, M. (1972). “Monte Carlo solution of structural dynamics.” Computer and Struct., 2, 855–874.
25.
Shinozuka, M., and Deodatis, G. (1988). “Stochastic process models for earthquake ground motion.” Probabilistic Engrg. Mech., 3(3), 114–123.
26.
Shinozuka, M., and Jan, C.‐M. (1972). “Digital simulation of random processes and its application.” J. Sound and Vibration, 25(1), 111–128.
27.
Shinozuka, M., Vaicaitis, R., and Asada, H. (1976). “Digital generation of random forces for large‐scale experiments.” J. Aircraft, 13(6), 425–431.
28.
Shinozuka, M., Yun, C.‐B., and Sey, H. (1989). “Stochastic methods in wind engineering.” Proc. of the Sixth U.S. National Conference on Wind Engineering, Mar. 8–10.
29.
Spanos P. D., and Mignolet, M. P. (1987). “Recursive simulation of stationary multivariate random processes—Part I and part II.” Trans. of the ASME, American Society of Mechanical Engineers, 54, 674–680 and 681–687.
30.
Spanos, P. D., and Solomos, G. P. (1983). “Markov approximation to nonstationary random vibration.” J. Engrg. Mech., ASCE, 109(4), 1134–1150.
31.
Sun, Wei‐Joe, and Kareem, A. (1989). “Response of MDOF systems to nonstationary random excitation,” Engrg. Struct., 11 (Apr.).
32.
Wittig, L. E., and Sinha, A. K. (1975). “Simulation of multicorrelated random processes using FFT algorithm.” J. Acoustic Soc. of America, 58(3), 630–633.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 117 • Issue 5 • May 1991
Pages: 1037 - 1058
Copyright
Copyright © 1991 ASCE.
History
Published online: May 1, 1991
Published in print: May 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.