Quadrature methods for wind turbine load calculations

Two sources of uncertainty can be distinguished in models for wind turbine calculations. Firstly, the environment the wind turbine has to withstand is uncertain and has a direct impact on the life time of the turbine. Secondly, the models used to predict the forces acting on the turbine contain an unknown error, which can also be modeled as a random variable. This thesis discusses numerical methods based on polynomial approximation to study these two types of uncertainty. In essence the computationally costly model is replaced by a polynomial, which is cheap to evaluate using a computer. The first part of the thesis is mainly focused on computing the loads acting on a wind turbine. The key uncertainties in this case originate from the variability in the environmental conditions (such as the weather). For load cases, the main interest is on integral quantities of the computationally expensive model. For the purpose of computing integral quantities, polynomial approximation is equivalent to smartly constructing interpolatory quadrature rules. Various algorithms are proposed to construct such quadrature rules. Their efficiency is demonstrated by computing loads acting on a turbine using measurement data obtained at the Dutch North Sea. Modeling the uncertainty arising from model error is significantly less trivial. Two different approaches, either based on interpolation using Leja nodes or integration based on quadrature rules, are discussed. Which approach is best in a certain computational test case depends on the specific quantity of interest. Examples of the applicability of all proposed methods are discussed throughout the thesis. A common theme in all results is that high convergence rates are obtained for models that can be approximated well using polynomials, which is usually the case for models arising in the field of wind energy.

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