Simulation and Prediction of Wind Speeds: A Neural Network for Weibull

Wind as a resource of renewable energy has obtained an important share of the energy market already. Therefore simulation and prediction of wind speeds is essential for both, for engineers and energy traders. In this paper we analyze the surface wind speed data from three prototypic locations: coastal region (Rotterdam), undulating forest landscape few 100 m above sea level(Kassel), and alpine mountains about 3000 m above sea level (Zugspitze). Rather than matching the conventional Weibull distribution to the wind speed data, we investigate two alternative models for wind speed prediction, both being refinements of a log-normal model, but with very different approaches and capability for capturing the extremal events. In both models deterministic effects such as trend and seasonality are separated. The first (structural stochastic) model predicts wind speeds exponentially from a linear combination of separate mean-reverting jump processes for the high and low wind speed regimes, and the regular (diffusive) wind speed regime. The second (neuro-stochastic) model is a prediction with volatility-enhanced trend, with parameters dynamically learned by the middle-layer neurons of an MLP-type neural network operating on dynamically updated and re-weighted history. The numerical results suggest that, for a coastal region (e.g. Rotterdam) the R-2-determination is higher, while for the undulating forest regions (e.g. Kassel) and even more the higher mountain regions (e. g.Zugspitze) the structural stochastic model yields higher determination. The neuro-stochastic algorithm opens a new path within statistical learning: feature space and kernel functions are completely defined by the parameters of the stochastic process.