Stochastic Extreme Wind Speed Modeling and Bayes Estimation under the Inverse Rayleigh Distribution

Abstract

Inverse Rayleigh probability distribution is shown in this paper to constitute a valid model for characterization and estimation of extreme values of wind speed, thus constituting a useful tool of wind power production evaluation and mechanical safety of installations. The first part of this paper illustrates such a model and its validity to interpret real wind speed field data. The inverse Rayleigh model is then adopted as the parent distribution for assessment of a dynamical “risk index” defined in terms of a stochastic Poisson process, based upon crossing a given value with part of the maximum value of wind speed on a certain time horizon. Then, a novel Bayes approach for the estimation of such an index under the above model is proposed. The method is based upon assessment of prior information in a novel way which should be easily feasible for a system engineer, being based upon a model quantile (e.g., the median value) or, alternatively, on the probability that the wind speed is greater than a given value. The results of a large set of numerical simulation—based upon typical values of wind-speed parameters—are reported to illustrate the efficiency and the precision of the proposed method, also with hints to its robustness. The validity of the approach is also verified with respect to the two different methods of assessing the prior information.

Keywords

• Bayes estimation
• beta distribution
• gamma distribution
• extreme values
• inverse Rayleigh distribution
• negative exponential beta distribution