Non-Gaussian Simulation: Cumulative Distribution Function Map-Based Spectral Correction
Publication: Journal of Engineering Mechanics
Volume 129, Issue 12
Abstract
Methods for stochastic simulation of sample functions have increasingly addressed the preservation of both spectral and probabilistic contents to offer an accurate description of the dynamic behavior of system input for reliability analysis. This study presents an efficient, flexible and easily applied stochastic non-Gaussian simulation method capable of reliably converging to a target power spectral density function and marginal probability density function, or a close relative thereof. Several existing spectral representation-based non-Gaussian simulation algorithms are first summarized. The new algorithm is then presented and compared with these methods to demonstrate its efficacy. The advantages and limitations of the new method are highlighted and shown to complement those of the existing algorithms.
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References
Borgman, L. E. (1990). Irregular ocean waves: Kinematics and forces, Prentice-Hall, Upper Saddle River, N.J.
Cai, G. Q., and Lin, Y. K.(1996). “Generation of non-Gaussian stationary stochastic processes.” Phys. Rev. 54(1), 299–303.
Chakrabarti, S. K.(1984). “Technical note: On the formulation of Jonswap spectrum.” Appl. Ocean. Res., 6(3), 175–176.
Deodatis, G.(1996). “Non-stationary stochastic vector processes: Seismic ground motion applications.” Probab. Eng. Mech., 11(3), 149–167.
Deodatis, G., and Micaletti, R.(2001). “Simulation of highly skewed non-Guassian stochastic processes.” J. Eng. Mech., 127(12), 1284–1295.
Elishakoff, I., Ren, Y. J., and Shinozuka, M.(1994). “Conditional simulation of non-Gaussian random fields.” Eng. Struct., 16(7), 558–563.
Grigoriu, M.(1984). “Crossing of non-Gaussian translation processes.” J. Eng. Mech., 110(4), 610–620.
Grigoriu, M.(1993). “On the spectral representation method in simulation.” Probab. Eng. Mech., 8, 17–90.
Grigoriu, M. (1995). Applied non-Gaussian processes, PTR Prentice-Hall, Englewood Cliffs, N.J.
Grigoriu, M.(1998). “Simulation of stationary non-Gaussian translation processes.” J. Eng. Mech., 124(2), 121–126.
Gurley, K., and Kareem, A.(1997). “Analysis, interpretation, modeling and simulation of unsteady wind and pressure data.” J. Wind. Eng. Ind. Aerodyn., 69–71, 657–669.
Gurley, K., and Kareem, A. (1998a). “Modelling PDFs of non-Gaussian system response.” Proc., 7th Int. Conf. on Structural Safety and Reliability (ICOSSAR), Kyoto, Japan.
Gurley, K., and Kareem, A.(1998b). “A conditional simulation of non-normal velocity/pressure fields.” J. Wind. Eng. Ind. Aerodyn., 77–78, 39–51.
Gurley, K., and Kareem, A. (1998c). “A multi-variate non-Gaussian simulation algorithm.” 4th Int. Conf. on Stochastic Structural Dynamics, Notre Dame, Ind.
Harr, M. (1987). Reliability-based design in civil engineering, Dover, Mineola, N.Y.
Hoshiya, M., Noda, S., and Inada, H.(1998). “Estimation of conditional non-Gaussian translation stochastic fields.” J. Eng. Mech., 124(4), 435–445.
Kameda, H., and Morikawa, H.(1993). “Conditioned stochastic processes for conditional random fields.” J. Eng. Mech., 120(4), 855–875.
Kumar, K., and Stathopoulos, T.(2000). “Wind loads on low building roofs: A stochastic perspective.” J. Struct. Eng., 126(8), 944–956.
Li, Y., and Kareem, A.(1997). “Simulation of multivariate nonstationary random processes: Hybrid DFT and digital filtering approach.” J. Eng. Mech., 123(12), 1302–1310.
Masters, F., and Gurley, K. “Wind load simulation: A new algorithm and comparative study.” Americas Conf. on Wind Engineering, Clemson, S.C., June, 2001.
Phoon, K. K., Huang, S. P., and Quek, S. T.(2002). “Simulation of second-order processes using Karhunen-Loeve expansion.” Comput. Struct., 80(12), 1049–1060.
Poirion, F., and Soize, C. (1999). “Monte Carlo construction of Karhunen Loeve expansion for non-Gaussian random fields.” Proc., 13th ASCE Engineering Mechanics Conf., Reston, Va.
Popescu, R., Deodatis, G., and Prevost, J. H.(1998). “Simulation of homogeneous, non-Gaussian, stochastic vector fields.” Probab. Eng. Mech., 13(1), 1–13.
Priestly, M. B.(1967). “Power spectral analysis of non-stationary random processes.” J. Sound Vib., 6(1), 86–97.
Sakamoto, S., and Ghanem, R.(2002a). “Polynomial chaos decomposition for the simulation of non-Gaussian nonstationary stochastic processes.” J. Eng. Mech., 128(2), 190–201.
Sakamoto, S., and Ghanem, R.(2002b). “Simulation of multi-dimensional non-Gaussian non-stationary random fields.” Probab. Eng. Mech., 17(2), 167–176.
Shinozuka, M. (1987). “Stochastic fields and their digital simulation.” Stochastic methods in structural dynamics, G. I. Schueller and M. Shinozuka, eds., Matinus Hijhoff, Dordrecht, 93–133.
Shinozuka, M., and Deodatis, G.(1991). “Simulation of stochastic processes by spectral representation.” Appl. Mech. Rev., 44(4), 191–204.
Shinozuka, M., and Deodatis, G.(1996). “Simulation of multi-dimensional Gaussian stochastic fields by spectral representation.” Appl. Mech. Rev., 49(1), 29–53.
Shinozuka, M., and Jan, C. M.(1972). “Digital simulation of random processes and its applications.” J. Sound Vib., 25(1), 111–128.
Vanmarcke, E. H., and Fenton, G. A.(1991). “Conditional simulation of local fields of earthquake ground motion.” Struct. Safety, 10(1–3), 247–263.
Winterstein, S.(1988). “Nonlinear vibration models for extremes and fatigue.” J. Eng. Mech., 114(10), 1772–1790.
Yamazaki, F., and Shinozuka, M.(1988). “Digital generation of non-Gaussian stochastic fields.” J. Eng. Mech., 114(7), 1183–1197.
Zerva, A.(1992). “Seismic ground motion simulations from a class of spatial variability models.” Earthquake Eng. Struct. Dyn., 21, 351–361.
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Copyright © 2003 American Society of Civil Engineers.
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Received: Aug 30, 2002
Accepted: May 28, 2003
Published online: Nov 14, 2003
Published in print: Dec 2003
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