Wind speed modelling using Weierstrass function fitted by a genetic algorithm

In this paper a wind speed model as a time series is presented. The main goal is to use it as a model of the load of wind turbine gears for simulation of real, varying operational conditions for wind turbine vibration modelling. Several wind characteristics for evaluation of the wind model accuracy in the context of a wind turbine gears load simulation are proposed. Verification of the hypothesis that wind speed as a time series has a fractal character is another aim of this paper. The Weierstrass functions family, whose graphs are fractal sets, in combination with medium-term trends, is used as the basis of the model. The function with a fractal component is fitted to the past observation data. A genetic algorithm is used as the fitting procedure. Fractal dimension is utilized as a parameter in a fitness function. The results have shown that the proposed approach yielded very good fit for the observation data. The hypothesis about fractal character of the wind speed is positively verified.