# Collaborative Optimization of Aerodynamics and Wind Turbine Blades
## 4 MDO of the Wind Turbine Blade
### Surrogate Model  
Numerical simulation has been widely applied in many engineering areas since it can provide accurate calculation results. However, the calculation might be lengthy, especially for complicated systems. Directly incorporating a numerical simulation module into an optimization farmwork degrades the efficiency. The use of surrogate models provides an  
Figure 21: Effects of design variables on the performance indices of disciplines. (**a**) Design variable effects on the torque of blade; (**b**) design variable effects on the mass of blade. effective way to perform discipline analysis in an MDO application since the use of an accurate surrogate model can significantly improve optimization efficiency. In this study, two surrogate models are constructed to replace the CFD calculation in the aerodynamic analysis and the FEA calculation in the structural analysis. A typical process of surrogate model construction is shown in Figure 22. Starting from data sampling, one might select a type of surrogate model and then generate the model by using the samples. Afterward, by performing an error analysis, one can confirm if the generated surrogate model satisfies accuracy requirements and can be applied to the optimization. In the step of data sampling, a design of experiment (DOE) method, optimal Latin hypercube design (Opt LHD) is employed. In the step of model selection, the classical Kriging model is selected. To verify the Kriging surrogate model, determination coefficients are calculated. As stated above, torque is selected as the performance index for the aerodynamic discipline while mass is selected as the performance under the stress and deflection constraints. The torque can be calculated by the CFD technique. The mass, stress, and deflection can be determined by FEA. In the study, Kriging surrogate models are constructed with respect to these indices/constraints. Table 6 lists the determination coefficients for the surrogate models. In the table, \(R^{2}\) denotes the determination coefficient, denotes the maximal deflection of the blade, and denotes the maximal stress. As can be seen from the table, the surrogate models have high accuracy, which implies that they can replace the numerical simulation modules in an optimization project. \begin{table}
\begin{tabular}{c c c c c} \hline \(\mathbf{D}\) & \(\mathbf{M}\) & \(\mathbf{w_{\text{max}}}\) & \(\sigma_{\text{max}}\) \\ \hline \(R^{2}\) & 0.93107 & 0.97377 & 0.9183 & 0.96663 \\ \hline \end{tabular}
\end{table} 
Table 6: Determination coefficients. Figure 22: Construction process of a surrogate model. The CO framework on the Isight platform combined with the surrogate models is shown in Figure 23.  
By running the two-level optimizers shown in Figure 23, one can obtain the optimization results, as shown in Table 7, in which the design variables and the optimization objectives, i.e., the torque and the mass of the blade, are listed. As can be seen, the torque is increased by 10.1%, which implies that the power coefficient of the wind turbine can be improved. Similarly, the mass is decreased by 5%, which implies that the cost of the wind turbine can be reduced. The optimized chord and twist angle of the wind turbine blade are shown in Figure 24. As can be seen, the chord length of the blade increases to some extent. The twist angle becomes smaller around the root and larger around the tip, which contributes to the improvement in the torque. In terms of contributions to the reduction in mass, although the chord length and the twist angle do not change sharply, the thickness of the blade noticeably decreases, as can be seen in Table 7. It is noted that in this study, the optimized design is not a completely different design but an improvement on the original NACA 4412 airfoil.