Summary
In this paper we describe a new method for predicting PDFs of observable quantities driven by stochastic processes with a local Markov property. The method deals with large class of nonstationarities by overembeding the vector in the conditional part of the conditional probabilities of the Markov chain which approximates the Markov process. This allows an application of a Farmer-Sidorowich-like prediction scheme [1] in the obtained vector space. Thus the conditional PDF of the investigated quantity for the next time step can be estimated and various forecasts can be performed. As an illustration the method is applied to the problem for the short-term prediction of turbulent wind gusts which are the major danger for the safe operation of wind energy turbines. Predicted gusts can be made innocent by a simple change of the pitch angle of the rotor blades. Within a prediction horizon of few seconds which is sufficient for this purpose the discussed method produces meaningful results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Farmer J. D., Sidorovich. J. J. (1987) Phys. Rev. Lett. 59: 845–848.
Takens F. (1981) Lectiture Notes in Mathematics 898: 366–381
Sauer T., Yorke J., Casdagli M. (1991) J. Stat. Phys. 65: 579–616
Kantz H., Schreiber T. (1997) Nonlinear Time Series Analysis. Cambridge University Press, Cambridge
Risken H. (1989) The Fokker-Planck Equation. Springer, Berlin
van Kampen N. G. (1992). Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam
Hegger R., Kantz H., Matassini L., Schreiber T. (2000) Phys. Rev. Lett. 84: 4092–4095
Kantz H., Ragwitz M. Int. J. Bif. Chaos (in the press).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K. (2005). Predicting Probability for Stochastic Processes with Local Markov Property. In: Peinke, J., Kittel, A., Barth, S., Oberlack, M. (eds) Progress in Turbulence. Springer Proceedings in Physics, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27401-4_20
Download citation
DOI: https://doi.org/10.1007/3-540-27401-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23216-2
Online ISBN: 978-3-540-27401-8
eBook Packages: EngineeringEngineering (R0)