Monte–Carlo Based Method for Predicting Extreme Value Statistics of Uncertain Structures
Publication: Journal of Engineering Mechanics
Volume 136, Issue 12
Abstract
In the present paper, a simple method is proposed for predicting the extreme response of uncertain structures subjected to stochastic excitation. Many of the currently used approaches to extreme response predictions are based on the asymptotic generalized extreme value distribution, whose parameters are estimated from the observed data. However, in most practical situations, it is not easy to ascertain whether the given response time series contain data above a high level that are truly asymptotic, and hence the obtained parameter values by the adopted estimation methods, which points to the appropriate extreme value distribution, may become inconsequential. In this paper, the extreme value statistics are predicted taking advantage of the regularity of the tail region of the mean upcrossing rate function. This method is instrumental in handling combined uncertainties associated with nonergodic processes (system uncertainties) as well as ergodic ones (stochastic loading). For the specific applications considered, it can be assumed that the considered time series has an extreme value distribution that has the Gumbel distribution as its asymptotic limit. The present method is numerically illustrated through applications to a beam with spatially varying random properties and wind turbines subjected to stochastic loading.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The 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. The writers thank the anonymous reviewers for insightful comments leading to a substantial revision of the manuscript.
References
Agarwal, P., and Manuel, L. (2008). “Extreme loads for an offshore wind turbine using statistical extrapolation from limited field data.” Wind Energy, 11(6), 673–684.
Coles, S. (2001). An introduction to statistical modeling of extreme values, Springer, London.
Dunne, J. F., and Ghanbari, M. (2001). “Efficient extreme value prediction for nonlinear beam vibrations using measured random response histories.” Nonlinear Dyn., 24(1), 71–101.
Dunne, L., and Dunne, J. (2009). “An FRF bounding method for randomly uncertain structures with or without coupling to an acoustic cavity.” J. Sound Vib., 322(1–2), 98–134.
Fishman, G. S. (1996). Monte Carlo: Concepts, algorithms, and applications, Springer, New York.
Ghanem, R. G., and Spanos, P. D. (1991). Stochastic finite elements: A spectral approach, Springer, New York.
Gill, P., Murray, W., and Wright, M. H. (1981). Practical optimization, Academic Press, London.
Gupta, S., and Manohar, C. S. (2002). “Dynamic stiffness method for circular stochastic Timoshenko beams: Response variability and reliability analyses.” J. Sound Vib., 253(5), 1051–1085.
Henriques, A. (2008). “Efficient analysis of structural uncertainty using perturbation techniques.” Eng. Struct., 30(4), 990–1001.
Igusa, T., and Kiureghian, A. D. (1988). “Response of uncertain systems to stochastic excitation.” J. Eng. Mech., 114(5), 812–832.
International Electrotechnical Commission. (2009). “Wind turbines—Part 3: Design requirements for offshore wind turbines.” IEC 61400–3.
Jensen, H., and Iwan, W. D. (1992). “Response of systems with uncertain parameters to stochastic excitation.” J. Eng. Mech., 118(5), 1012–1025.
Jonkman, B. J. (2009). “TurbSim user’s guide for version 1.50.” Technical Rep. No. NREL/TP-500–46198, National Renewable Energy Laboratory, Golden, Colo.
Jonkman, J. M., and Buhl, M. L., Jr. (2005). “Fast user’s guide.” Technical Rep. No. NREL/EL-500-38230, National Renewable Energy Laboratory, Golden, Colo.
Kleiber, M., and Tran, H. T. (1992). The stochastic finite element method: basic perturbation technique and computer implementation, Wiley, New York.
Leadbetter, R. M., Lindgren, G., and Rootzen, H. (1983). Extremes and related properties of random sequences and processes, Springer, New York.
Li, J., and Chen, J. -B. (2005). “Dynamic response and reliability analysis of structures with uncertain parameters.” Int. J. Numer. Methods Eng., 62(2), 289–315.
Malcolm, D. J., and Hansen, A. C. (2002). “Windpact turbine rotor design study.” Technical Rep. NREL/SR-500-32495, National Renewable Energy Laboratory, Golden, Colo.
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.
Melchers, R. E. (1999). Structural reliability analysis and prediction, Wiley, New York.
Meyer, S. L. (1975). Data analysis for scientists and engineers, Wiley, New York.
Naess, A. (1984a). “On a rational approach to extreme value analysis.” Appl. Ocean. Res., 6(3), 173–174.
Naess, A. (1984b). “On the long-term statistics of extremes.” Appl. Ocean. Res., 6(4), 227–228.
Naess, A., and Gaidai, O. (2008). “Monte Carlo methods for estimating the extreme response of dynamical systems.” J. Eng. Mech., 134(8), 628–636.
Naess, A., and Gaidai, O. (2009). “Estimation of extreme values from sampled time series.” Struct. Safety, 31(4), 325–334.
Naess, A., Gaidai, O., and Batsevych, O. (2009). “Extreme value statistics of combined load effect processes.” Struct. Safety, 31(4), 298–305.
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(6), 848–863.
Papadrakakis, M., and Kotsopulos, A. (1999). “Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation.” Comput. Methods Appl. Mech. Eng., 168(1–4), 305–320.
Rubinstein, R. Y., and Kroese, D. P. (2008). Simulation and the Monte Carlo method, Wiley, New York.
Saha, N., and Roy, D. (2007). “Variance-reduced weak Monte Carlo simulations of stochastically driven oscillators of engineering interest.” J. Sound Vib., 305(1–2), 50–84.
Schall, G., Faber, M. H., and Rackwitz, R. (1991). “The ergodicity assumption for sea states in the reliability estimation of offshore structures.” J. Offshore Mech. Arct. Eng., 113(3), 241–246.
Schuëller, G. I., and Pradlwarter, H. (2009). “Uncertainty analysis of complex structural systems.” Int. J. Numer. Methods Eng., 80(6–7), 881–913.
Socha, L. (2005). “Linearization in analysis of nonlinear stochastic systems: Recent results. Part I: Theory.” Appl. Mech. Rev., 58(3), 178–205.
Soize, C. (2003). “Random matrix theory and non-parametric model of random uncertainties in vibration analysis.” J. Sound Vib., 263(4), 893–916.
Stefanou, G. (2009). “The stochastic finite-element method: Past, present and future.” Comput. Methods Appl. Mech. Eng., 198(9–12), 1031–1051.
Vanmarcke, E. H., and Grigoriu, M. (1983). “Stochastic finite-element analysis of simple beams.” J. Eng. Mech., 109(5), 1203–1214.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 12 • December 2010
Pages: 1491 - 1501
Copyright
© 2010 ASCE.
History
Received: Jun 4, 2009
Accepted: May 27, 2010
Published online: May 29, 2010
Published in print: Dec 2010
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.