Robust Optimization of Wind Turbine Blade Profiles under Several Sources of Uncertainty

Abstract

The aerodynamic shape optimization of the turbine blade is a crucial aspect of maximizing the performance of the wind turbine. The design of airfoils specially developed for wind turbine blades has a significant impact on wind turbine performance. Traditionally, the airfoil shape optimization is carried out in a deterministic fashion, where a fixed value for operational conditions is taken into account. The airfoil shape tailored in a deterministic manner could lead to serious performance loss while accounting for the uncertainty in the operational conditions. Hence, to encounter these aleatoric uncertainties in operational conditions, such as wind speed and direction, a robust optimization of an airfoil shape is considered. In robust optimization of an airfoil, the objective function is modified as a statistic of a quantity of interest. Monte-Carlo sampling is not feasible to determine such statistics of the quantity of interest, especially while dealing with aerodynamically shape optimization problems, where each evaluation of Computational Fluid Dynamics (CFD) is very expensive. Therefore, in this work, a surrogate-based uncertainty quantification approach is considered to determine the statistic of the quantity of interest. As a choice of surrogate model, Kriging process is used to approximate the full order model. The surrogate model is constructed based on initial low discrepancy sampling. The number of sample points required to build an accurate surrogate model is reduced by using infill sampling criteria such as the probability of misclassification. The inverse design methodologies for shape optimization not only lead to sub-optimal configurations but also restrict robust objective functions or constraints from being explicitly considered. The direct design approach can cope with these limitations and allows well exploration of design space, and provides global solutions. In this work, the surrogate-based optimization method as a direct design approach is taken into account for robust optimization. The Kriging surrogate model for the same is constructed by initial samples and infill samples. For infill sampling, maximum expected improvement as exploration criteria and trust region method as exploitation criteria are used, which aids in reducing the overall CFD evaluations to build an accurate surrogate model. In this approach, for statistics of the quantity of interest, the quantile is used instead of an integral statistical moment such as mean or standards deviation. The 95% quantile is considered to account for extreme events. Therefore, the robust optimization framework follows a bi-level surrogate approach, where the surrogate-based optimization is formulated to minimize the given quantile, and this quantile is determined by surrogate-based uncertainty quantification. The feasibility of a robust optimum for an airfoil shape optimization compared to a deterministic optimum is demonstrated. Two different considerations of uncertainty in operational conditions are outlined: robust optimization under uncertainty in wind speed, and robust optimization under uncertainty in wind speed and direction.