## 5 Results of Optimization  
Using the surrogate models built in Section 4, a DU21-A17 wind turbine airfoil is optimized to enhance its aerodynamic performance. The main purpose of the optimization is to figure out how the  
Figure 5: The lift-to-drag ratios of wind turbine airfoils **1**, **2** and **3** are 57.1, 98.7 and 114.5 when they are simulated at (\(\text{Re}=4.23\times 10^{5}\), \(\text{AOA}=1.01^{\circ}\)), (\(\text{Re}=5.06\times 10^{5}\), \(\text{AOA}=7.13^{\circ}\)) and (\(\text{Re}=7.35\times 10^{5}\), \(\text{AOA}=7.83^{\circ}\)), respectively. At \(\text{Re}=10^{6}\) and \(\text{AOA}=5^{\circ}\), their lift-to-drag ratios are 125.1, 121.8 and 119.3, respectively. Figure 6: The pressure coefficient graphs for the airfoils **1**, **2** and **3** presented in Figure 5. The graphs in **(a,b)** show the pressure coefficients when the airfoils are simulated at their own operating conditions (described in Figure 5’s caption) and the reference operating conditions (\(\text{Re}=10^{6}\), \(\text{AOA}=5^{\circ}\)), respectively. optimization results (in terms of magnitude of lift-to-drag ratio) are affected by the level of prediction accuracy of the surrogate models. To do this, the quantity used to evaluate the airfoil's performance should be defined first. The lift force acting on the airfoil needs to be increased while the drag force needs to be decreased to enhance the performance, which can be simply performed by maximizing the lift-to-drag ratio of the wind turbine airfoil. To avoid obtaining a very thin and unrealistic wind turbine airfoil, two airfoil's minimum thickness constraints are considered in the optimization process--first, the wind turbine airfoil at \(x=0.34c\) (where the thickness of the baseline wind turbine airfoil is at its maximum) is set to be thicker than a certain thickness to avoid finding thin optimal wind turbine airfoils. Second, at \(x=0.9c\), a minimum thickness of the optimal wind turbine airfoil is defined to reduce the risk of the trailing edge breaking, which can happen when the tip of the wind turbine airfoil is too thin. The criteria thickness values for both constraints are set based on the baseline wind turbine airfoil's thickness at the corresponding positions. For example, when the thicknesses of the baseline and optimal wind turbine airfoils at \(x=x_{0}\) are defined as \(t_{b}(x_{0})\) and \(t_{o}(x_{0})\), respectively, the airfoil thickness constraint at \(x=x_{0}\) is defined as  
\[t_{o}(x_{0})\geq kt_{b}(x_{0}), \tag{10}\]  
where \(k\) is the constant number determining the allowable thickness of the optimal wind turbine airfoil. In the current paper, the value of \(k\) is set as \(k=0.95\), producing a reasonable shape for the optimal wind turbine airfoil. The optimization process in the current study is as follows: First, \(N\) numbers of design sets are created based on the design of experiment described in Section 3.3. For each design set, the lift-to-drag ratio is computed using XFOIL. Using this calculation, the RSM-computed or ANN-computed surrogate model is constructed, allowing for the prediction of an output value at an arbitrary design set. With the constructed surrogate model, the genetic algorithm searches for the optimal input variables maximizing the lift-to-drag ratio, and then, the optimal wind turbine airfoil is created using the optimal input variables found by the genetic algorithm. Finally, the lift-to-drag ratio of the optimal wind turbine airfoil is computed using XFOIL, which is considered the performance of the optimal wind turbine airfoil. To test the influence of the surrogate model's prediction accuracy on the performance improvement of the wind turbine airfoil, optimization is performed several times with the RSM-computed and ANN-computed surrogate models constructed with G-DLB-8-3 and O-DLB-6-4.