Monte Carlo Methods for Estimating the Extreme Response of Dynamical Systems
Publication: Journal of Engineering Mechanics
Volume 134, Issue 8
Abstract
The development of simple accurate, and efficient methods for estimation of the extreme response of dynamical systems subjected to random excitations is discussed in the present paper. The key quantity for calculating the statistical distribution of extreme response is the mean level upcrossing rate function. By exploiting the regularity of the tail behavior of this function, an efficient simulation based methodology for estimating the extreme response distribution function is developed. This makes it possible to avoid the commonly adopted assumption that the extreme value data follow an appropriate asymptotic extreme value distribution, which would be a Gumbel distribution for the models considered in this paper. It is demonstrated that the commonly quoted obstacle against using the standard Monte Carlo method for estimating extreme responses, i.e., excessive CPU time, can be circumvented, bringing the computational efforts down to quite acceptable levels.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support from the Research Council of Norway (NFR) through the Centre for Ships and Ocean Structures (CeSOS) at the Norwegian University of Science and Technology is gratefully acknowledged.
References
Au, S. K., and Beck, J. L. (2003). “Importance sampling in high dimensions.” Struct. Safety, 25, 139–163.
Castillo, E. (1988). Extreme value theory in engineering, Academic, San Diego.
IfM, University of Innsbruck. (2004). “Benchmark study on reliability estimation in higher dimensions of structural systems.” ⟨http://www.uibk.ac.at/mechanik/Benchmark-Reliability⟩.
Iman, R. L., and Helton, J. C. (1988). “An investigation of uncertainty and sensitivity analysis techniques for computer models.” Risk Anal., 8(l), 71–90.
Leadbetter, R. M., Lindgren, G., and Rootzen, H. (1983). Extremes and related properties of random sequences and processes, Springer, New York.
Macke, M., and Bucher, C. (2003). “Importance sampling for randomly excited dynamical systems.” J. Sound Vib., 268, 269–290.
Mckay, M. D., Beckman, R. J., and Conover, W. J. (1979). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 21(2), 239–245.
Naess, A. (1984). “On the long-term statistics of extremes.” Appl. Ocean. Res., 6(4), 227–228.
Naess, A. (1990). “Approximate first-passage and extremes of narrow-band Gaussian and non-Gaussian random vibrations.” J. Sound Vib., 138(3), 365–380.
Naess, A. (1998). “Estimation of long return period design values for wind speeds.” J. Eng. Mech., 124(3), 252–259.
Naess, A., and Gaidai, O. (2007). “Clustering effects on the extreme response statistics for dynamical systems.” Proc., 5th Int. Conf. on Mathematical Methods of Reliability, Univ. of Strathclyde, Glasgow, U.K., Paper No. 148.
Naess, A., and Skaug, C. (1999). “Importance sampling for dynamical systems.” Proc., ICASP8 Conf., R. E. Melchers and M. G. Stewart, eds., Balkema, Rotterdam, The Netherlands.
Olsen, A. I., and Naess, A. (2007). “An importance sampling procedure for estimating failure probabilities of nonlinear dynamic systems subjected to random noise.” Int. J. Non-Linear Mech., 42, 848–863.
Proppe, C., Pradlwarter, H. J., and Schuëller, G. I. (2003). “Equivalent linearization and Monte Carlo simulation in stochastic dynamics.” Probab. Eng. Mech., 18(1), 1–15.
Rice, S. O. (1954). “Mathematical analysis of random noise.” Selected papers on noise and stochastic processes, N. Wax, ed., Dover, New York, 133–294.
Shinozuka, M. (1972). “Monte Carlo solution of structural dynamics.” Comput. Struct., 2, 855–874.
Shinozuka, M., and Wen, Y.-K. (1972). “Monte Carlo solution of nonlinear vibrations.” AIAA J. 10(1), 37–40.
Tanaka, H. (1998). “Application of an importance sampling method to time-dependent system reliabilility analyses using the girsanov transformation.” Proc., ICOS-SAR’97—7th Int. Conf. on Structural Safety and Reliability, Vol. 1, N. Shiraishi, M. Shinozuka, and Y. K. Wen, eds., Balkema, Rotterdam, The Netherlands, 411–418.
Wen, Y. K. (1980). “Equivalent linearization for hysteretic systems under random excitation.” Trans. ASME, J. Appl. Mech., 47, 150–154.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 8 • August 2008
Pages: 628 - 636
Copyright
© 2008 ASCE.
History
Received: Nov 13, 2006
Accepted: Aug 8, 2007
Published online: Aug 1, 2008
Published in print: Aug 2008
Notes
Note. Associate Editor: Erik A. Johnson
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.