TECHNICAL PAPERS
Oct 1, 1999

Simulation of Homogeneous and Partially Isotropic Random Fields

Publication: Journal of Engineering Mechanics
Volume 125, Issue 10

Abstract

A rigorous methodology for the simulation of homogeneous and partially isotropic multidimensional random fields is introduced. The property of partial isotropy of the random field is explicitly incorporated in the derivation of the algorithm. This consideration reduces significantly the computational effort associated with the generation of sample functions, as compared with the case when only the homogeneity in the field is taken into account. The approach is based on the spectral representation method, utilizes the fast Fourier transform, and generates simulations with random variability in both their amplitudes and phases, or in their phases only. Spatially variable seismic ground motions experiencing loss of coherence are generated as an example application of the developed approach.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Abrahamson, N. A. (1992). “Generation of spatially incoherent strong motion time histories.” Proc., 10th World Conf. on Earthquake Engrg.
2.
Conte, J. P., Pister, K. S., and Mahin, S. A. (1992). “Non-stationary ARMA modeling of seismic ground motions.” Soil Dyn. and Earthquake Engrg., 11, 411–426.
3.
Ditlevsen, O. (1992). “Discussion of “Simulation of improved Gaussian time history,' by Loren D. Lutes and Jin Wang.”J. Engrg. Mech., ASCE, 118(6), 1276.
4.
Ellis, G. W., and Cakmak, A. S. (1991). “Time series modeling of strong ground motion from multiple event earthquakes.” Soil. Dyn. and Earthquake Engrg., 10, 42–54.
5.
Fenton, G. A. (1994). “Error evaluation of three random-field generators.”J. Engrg. Mech., ASCE, 120(12), 2478–2497.
6.
Fenton, G. A., and Vanmarcke, E. H. (1990). “Simulations of random fields via local average subdivision.”J. Engrg. Mech., ASCE, 116(8), 1733–1749.
7.
Grigoriu, M. (1993a). “On the spectral representation method in simulation.” Probabilistic Engrg. Mech., England, 8, 75–90.
8.
Grigoriu, M. (1993b). “Simulation of non-stationary Gaussian processes by random trigonometric polynomials.”J. Engrg. Mech., ASCE, 119(2), 328–343.
9.
Grigoriu, M., and Balopoulou, S. (1993). “A simulation method for stationary random functions based on the sampling theorem.” Probabilistic Engrg. Mech., 8, 239–254.
10.
Gurley, K., and Kareem, A. (1994). “On the analysis and simulation of random processes utilizing higher order spectra and wavelet transforms.” Proc., 2nd Int. Conf. on Computational Stochastic Mech.
11.
Hao, H., Olivera, C. S., and Penzien, J. (1989). “Multiple-station ground motion processing and simulation based on smart-1 data.” Nuclear Engrg. and Design, 111, 293–310.
12.
Ivanov, A. K., and Leonenko, N. N. (1989). Statistical analysis of random fields. Kluwer, Dordrecht, The Netherlands.
13.
Jin, S., Lutes, L. D., and Sarkani, S. (1997). “Efficient simulation of multidimensional random fields.”J. Engrg. Mech., ASCE, 123(10), 1082–1089.
14.
Kahrunen, K. (1946). “Zur spektraltheorie stochastisher prozesse.” Ann. Acad. Sci. Fennicae, Ser. A, I(34), 3–7.
15.
Kiureghian, A. D., and Crempien, J. (1989). “An evolutionary model for earthquake ground motion.” Struct. Safety, Amsterdam, 6, 235–246.
16.
Kozin, F. (1988). “Auto-regressive moving-average models of earthquake records.” Probabilistic Engrg. Mech., England, 3, 58–63.
17.
Li, Y., and Kareem, A. (1993). “Simulation of multivariate random processes: Hybrid DFT and digital filtering approach.”J. Engrg. Mech., ASCE, 119(5), 1078–1098.
18.
Li, Y., and Kareem, A. (1997). “Simulation of multivariate nonstationary random processes: Hybrid DFT and digital filtering approach.”J. Engrg. Mech., ASCE, 123(12), 1302–1310.
19.
Loh, C. H., and Lin, S. G. (1990). “Directionality and simulation in spatial variation of seismic waves.” Engrg. Struct., 12, 134–143.
20.
Luco, J. E., and Wong, H. L. (1986). “Response of a rigid foundation to a spatially random ground motion.” Earthquake Engrg. and Struct. Dynamics, 14, 891–908.
21.
Lutes, L. D., and Wang, J. (1991). “Simulation of improved Gaussian time history.”J. Engrg. Mech., ASCE, 117(1), 218–224.
22.
Mantoglou, A., and Wilson, J. L. (1981). “Simulation of random fields with the turning bands method.” Tech. Rep. No. 264, Dept. of Civ. Engrg., Massachusetts Institute of Technology, Cambridge, Mass.
23.
Mignolet, M. P., and Harish M. V. (1996). “Comparison of some simulation algorithms on basis of distribution.”J. Engrg. Mech., ASCE, 122(2), 172–176.
24.
Mignolet, M. P., and Spanos, P. D. (1992). “Simulation of homogeneous two-dimensional random fields: Part I—AR and ARMA models.” J. Appl. Mech., 59, 260–269.
25.
Prudnikov, A. P., Brychkov, Y. A., and Marichev, O. I. (1988). Integrals and series. Vol. 1, Gordon and Breach, New York.
26.
Ramadan, O., and Novak, M. (1993a). “Coherency functions for spatially correlated seismic ground motions.” Tech. Rep. No. GEOT-9-93, Geotech. Res. Ctr., University of Western Ontario, London, Canada.
27.
Ramadan, O., and Novak, M. (1993b). “Simulation of multidimensional anisotropic ground motions.”J. Engrg. Mech., ASCE, 120(8), 1773–1785.
28.
Ramadan, O., and Novak, M. (1993c). “Simulation of spatially incoherent random ground motions.”J. Engrg. Mech., ASCE, 119(5), 997–1016.
29.
Rice, S. O. (1944a). “Mathematical analysis of random noise.” Bell Sys. Tech. J., 23(3), 282–332.
30.
Rice, S. O. (1944b). “Mathematical analysis of random noise.” Bell Sys. Tech. J., 24(1), 46–156.
31.
Rice, S. O. ( 1954). “Mathematical analysis of random noise.” Selected papers on noise and stochastic processes. N. Wax, ed., 133–294.
32.
Shinozuka, M. (1971). “Simulation of multivariate and multidimensional random processes.” J. Acoustical Soc. of Am., 49, 357–367.
33.
Shinozuka, M. (1972). “Monte Carlo solution of structural dynamics.” Comp. and Struct., 2, 855–874.
34.
Shinozuka, M. (1974). “Digital simulation of random processes in engineering mechanics with the aid of FFT technique.” Stochastic problems in mech., S. T. Ariaratnam and H. H. E. Leipholz, eds., University of Waterloo Press.
35.
Shinozuka, M. (1987). “Stochastic fields and their digital simulation.” Stochastic methods in structural dynamics, G. I. Schuëller and M. Shinozuka, eds., Martinus Niijhoff, Dordrecht, The Netherlands.
36.
Shinozuka, M., and Deodatis, G. (1991). “Simulation of stochastic processes by spectral representation.” Appl. Mech. Rev., 44, 191–203.
37.
Shinozuka, M., and Deodatis, G. (1996). “Simulation of multidimensional Gaussian stochastic fields by spectral representation.” Appl. Mech. Rev., 49, 29–53.
38.
Shinozuka, M., and Jan, C.-M. (1972). “Digital simulation of random processes and its applications. J. Sound and Vibration, 25, 111–128.
39.
Spanos, P. D., and Mignolet, M. P. (1992). “Simulation of homogeneous two-dimensional random fields: Part II—MA and ARMA models.” J. Appl. Mech., 59, 270–277.
40.
Spanos, P. D., and Zeldin, B. A. (1996). “Efficient iterative ARMA approximation of multivariate random processes for structural dynamics applications.” Earthquake Engrg. and Struct. Dynamics, 25, 497–507.
41.
Vanmarcke, E. H., Heredia-Zavoni, E., and Fenton, G. A. (1993). “Conditional simulation of spatially correlated earthquake ground motion.”J. Engrg. Mech., ASCE 119(11), 2333–2352.
42.
Vilenkin, N. J. (1968). Special functions and the theory of group representations. American Mathematical Society, Providence, R.I.
43.
Watson, G. N. (1966). A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge, England.
44.
Yang, J. N. (1972). “Simulations of random envelope processes.” J. Sound Vib., 25, 73–85.
45.
Yeh, C. H., and Wen, Y. K. (1990). “Modeling of nonstationary ground motion and analysis of inelastic structural response.” Struct. Safety, Amsterdam, 8, 281–298.
46.
Zeldin, B. A., and Spanos, P. D. (1996). “Random field representation and synthesis using wavelet bases.” J. Appl. Mech., 63, 946–952.
47.
Zerva, A. (1992). “Seismic ground motion simulations from a class of spatial variability models.” Earthquake Engrg. and Struct. Dynamics, 21, 351–361.
48.
Zerva, A. (1994). “On the spatial variation of seismic ground motions and its effects on lifelines. Engrg. Structures, 16, 534–546.
49.
Zerva, A. (1998). “Spatial variability of seismic ground motions over extended ground surface areas.” Wave problems in earthquake engineering, E. Kausel and G. D. Manolis, eds., Wessex Institute of Technology Press, U.K.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 125Issue 10October 1999
Pages: 1180 - 1189

History

Received: Feb 3, 1999
Published online: Oct 1, 1999
Published in print: Oct 1999

Permissions

Request permissions for this article.

Authors

Affiliations

Dept. of Civ. Engrg., Hong Kong Univ. of Sci. and Technol., Clear Water Bay, Kowloon, Hong Kong. E-mail: [email protected]
Dept. of Civ. and Arch. Engrg., Drexel Univ., Philadelphia, PA 19104. E-mail:[email protected]
Int. Math. Ctr., 3 Tereshchenkivs'ka str., 252601 Kiev, Ukraine. E-mail: [email protected]

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share