Abstract
The method of so-called constrained stochastic simulation is introduced. This method specifies how to efficiently generate time series around some specific event in a normal process. All events which can be expressed by means of a linear condition (constraint) can be dealt with. Two examples are given in the paper: the generation of stochastic time series around local maxima and the generation of stochastic time series around a combination of a local minimum and maximum with a specified time separation. The constrained time series turn out to be a combination of the original process and several correction terms which includes the autocorrelation function and its time derivatives. For the application concerning local maxima it is shown that the presented method is in line with properties of a normal process near a local maximum as found in literature. The method can e.g. be applied to generate wind gusts in order to assess the extreme loading of wind turbines.
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References
Bierbooms, W.: Investigation of spatial gusts with extreme rise time on the extreme loads of pitchregulated wind turbines. Wind Energy 8, 17–34 (2005)
Bierbooms, W., Dragt, J.B.: A Probabilistic Method to Determine the Extreme Response of a Wind Turbine. Delft University of Technology, Delft, (2000)
Bierbooms, W., Dragt, J.B., Cleijne, H.: Verification of the mean shape of extreme gusts. Wind Energy. 2, 137–150 (1999)
Bierbooms, W., Cheng, P.W., Larsen, G., Pedersen, B.J.: Modelling of Extreme Gusts for Design Calculations—NewGust FINAL REPORT JOR3-CT98-0239. Delft University of Technology, (2001)
Cartwright, D.E., Longuet-Higgins, M.S.: The statistical distribution of the maxima of a random function. Proc. Royal Soc. London Ser. A. 237, 212–232 (1956)
Cheng, P.W.: A reliability based design methodology for extreme responses of offshore wind turbines, PhD thesis, Delft University Wind Energy Research Institute, (2002)
Database on Wind Characteristics, http://www.winddata.com/.
Dragt, J.B., Bierbooms, W.: Modeling of extreme gusts for design calculations. Proceedings European Wind Energy Conference, Göteborg, Sweden, 842–845 (1996)
Hasofer, A.M.: On the Slepian process of a random Gaussian trigonometric polynomial. IEEE Trans. Inf. Theory. 35, 868–873 (1989)
IEC 61400-1, Ed. 2, Wind Turbine generator Systems. Part 1. Safety Requirements. (1998)
Lindgren, G. Some properties of a normal process near a local maximum. Ann. Math. Stat. 41, 1870–1883 (1970)
Lindgren, G., Rychlik, I.: Slepian models and regressian approximations in crossing and extreme value theory. Int. Stat. Rev. 59, 195–225 (1991)
Mortensen, R.E.: Random Signals and Systems. Wiley, New York (1987)
Nielsen, M., Larsen, G.C., Mann, J., Ott, S., Hansen, K.S., Pedersen, B.J.: Wind simulation for extreme and fatigue loads, Risø-R-1437(EN), (2003)
Rao, C.R.: Linear Statistical Inference and its Applications. Wiley (1965)
Rice, S.O.: Mathematical analysis of random noise. Bell Syst. Techn. J. 23, 282 (1944) [Reprinted in Wax, N. (ed.), Selected papers on noise and stochastic processes, Dover, 1958]
Shinozuka, M.: Simulation of multivariate and multidimensional random processess. J. Acoust. Soc. America. 357–368 (1971)
Taylor, P.H., Jonathan, P., Harland, L.A.: Time domain simulation of jack-up dynamics with the extremes of a Gaussian process. J. Vib. Acoust. 119, 624–628 (1997)
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AMS 2000 Subject Classification
Primary—60G15, 60G70, 62G32; Secondary—62P30
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Bierbooms, W. Constrained stochastic simulation—generation of time series around some specific event in a normal process. Extremes 8, 207–224 (2005). https://doi.org/10.1007/s10687-006-7968-7
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DOI: https://doi.org/10.1007/s10687-006-7968-7