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Pareto distribution for extreme loads on wind turbines
In this paper a procedure to determine extreme values for loads using methods from Extreme Value Theory (EVT) is described. Utilizing the peak-over-threshold method (POT), a computer code is designed that allows: (1) To determine a ultimate load level with a certain probability, as for example that the level is exceeded an average once within 50 years, (2) to carry out quality checks in order to guarantee that the conditions for the application of EVT are satisfied, and (3) to determine the values of the synchronous load components. As an example the tower base moment is analyzed from simulated data in the situation with 50 years wind. Analyzing tower loads, it is found that the extreme values of a given load component are described by a Pareto distribution, and non-correlated simultaneous components are normally distributed. Utilizing the peak-over-threshold method the optimal parameters of the Pareto distribution are obtained with the help of the maximum-likelihood estimation. This analysis is carried out on the basis of 80 time series. Other analyses showed that about 30 to 40 time series are sufficient in order to obtain enough statistically independent peak values to carry out the analysis with sufficient quality. The method can be viewed as a post-processing tool for load data comparable for example with the rainflow-count procedure used for fatigue calculations. It eliminates the statistical uncertainty of the naive determination of extreme values from a limited sample. As a consequence it justifies a reduction of the safety factor, as suggested also in the IEC standard. The method can be straightforwardly applied to other quantities like for example the tip-to-tower distance. It could also be used for the evaluation of measured data. Simulations are carried out with a simulation code called SIWEC, which was developed recently by the authors.
Pareto distribution for extreme loads on wind turbines
In this paper a procedure to determine extreme values for loads using methods from Extreme Value Theory (EVT) is described. Utilizing the peak-over-threshold method (POT), a computer code is designed that allows: (1) To determine a ultimate load level with a certain probability, as for example that the level is exceeded an average once within 50 years, (2) to carry out quality checks in order to guarantee that the conditions for the application of EVT are satisfied, and (3) to determine the values of the synchronous load components. As an example the tower base moment is analyzed from simulated data in the situation with 50 years wind. Analyzing tower loads, it is found that the extreme values of a given load component are described by a Pareto distribution, and non-correlated simultaneous components are normally distributed. Utilizing the peak-over-threshold method the optimal parameters of the Pareto distribution are obtained with the help of the maximum-likelihood estimation. This analysis is carried out on the basis of 80 time series. Other analyses showed that about 30 to 40 time series are sufficient in order to obtain enough statistically independent peak values to carry out the analysis with sufficient quality. The method can be viewed as a post-processing tool for load data comparable for example with the rainflow-count procedure used for fatigue calculations. It eliminates the statistical uncertainty of the naive determination of extreme values from a limited sample. As a consequence it justifies a reduction of the safety factor, as suggested also in the IEC standard. The method can be straightforwardly applied to other quantities like for example the tip-to-tower distance. It could also be used for the evaluation of measured data. Simulations are carried out with a simulation code called SIWEC, which was developed recently by the authors.
Pareto distribution for extreme loads on wind turbines
Pareto-Verteilung zur Bestimmung von extremen Belastungen bei Windturbinen
Hänler, M. (author) / Ritschel, U. (author) / Warnke, I. (author)
2006
8 Seiten, 8 Bilder, 8 Quellen
Conference paper
Storage medium
English
Aerodynamik , Bauwerk , dynamische Belastung , Extremwert , Höchstwert , IEC-Norm , Konferenzbericht , Maximum-Likelihood-Schätzung , Normalverteilung , Rechnerprogramm , Schwellenwert , Sicherheitsfaktor , Simulation , Simulationsprogramm , statistische Verteilung , Turbulenz , Turm , Unsicherheit , Wahrscheinlichkeit , Windbelastung , Windkraftwerk , Windturbine , Zeitreihe , Zeitreihenanalyse
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