## 4 Results of Prediction Accuracy Tests
This corresponds to the claim presented in the current paper, which is the ANN-computed surrogate model works better than the RSM-computed \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Types** & \(E\) **(RMS)** & \(E\) **(ANN)** & \(\gamma\) \\ \hline O-FCCD-4 & \(2.994\times 10^{-1}\) & \(2.434\times 10^{-1}\) & \(1.230\) \\ O-FCCD-6 & \(3.922\times 10^{-1}\) & \(1.428\times 10^{-1}\) & \(2.746\) \\ \hline O-DLB-4-3 & \(3.193\times 10^{-1}\) & \(2.250\times 10^{-1}\) & \(1.419\) \\ O-DLB-4-4 & \(2.577\times 10^{-1}\) & \(1.454\times 10^{-1}\) & \(1.772\) \\ O-DLB-4-5 & \(2.415\times 10^{-1}\) & \(4.873\times 10^{-2}\) & \(4.956\) \\ O-DLB-6-3 & \(2.778\times 10^{-1}\) & \(1.036\times 10^{-1}\) & \(2.682\) \\ O-DLB-6-4 & \(2.240\times 10^{-1}\) & \(6.568\times 10^{-2}\) & \(3.411\) \\ O-DLB-6-5 & \(2.071\times 10^{-1}\) & \(5.492\times 10^{-2}\) & \(3.772\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The same as Table 3, but for the surrogate models using the datasets whose parameters are the wind turbine airfoil’s geometric and operational variables. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Types** & \(E\) **(RMS)** & \(E\) **(ANN)** & \(\gamma\) \\ \hline G-FCCD-2 & \(1.687\times 10^{-3}\) & \(3.299\times 10^{-3}\) & \(0.511\) \\ G-FCCD-4 & \(5.779\times 10^{-3}\) & \(1.184\times 10^{-2}\) & \(0.488\) \\ G-FCCD-6 & \(7.379\times 10^{-3}\) & \(1.766\times 10^{-2}\) & \(0.418\) \\ G-FCCD-8 & \(4.648\times 10^{-2}\) & \(2.505\times 10^{-2}\) & \(1.855\) \\ \hline G-DLB-2-3 & \(1.749\times 10^{-3}\) & \(2.582\times 10^{-3}\) & \(0.677\) \\ G-DLB-4-3 & \(4.949\times 10^{-3}\) & \(1.027\times 10^{-2}\) & \(0.482\) \\ G-DLB-6-3 & \(5.768\times 10^{-3}\) & \(9.717\times 10^{-3}\) & \(0.594\) \\ G-DLB-8-3 & \(3.201\times 10^{-2}\) & \(1.472\times 10^{-2}\) & \(2.174\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The values of the normalized root-mean-square deviation of the surrogate models constructed from an RSM and ANN using the various datasets whose parameters are the wind turbine airfoil’s geometric variables. Here, the RSM-computed and ANN-computed surrogate models are constructed with exactly the same sample data. surrogate model when the datasets have high complexity. This observation is supported by the findings in the previous studies of [PERSON] et al. [49] and [PERSON] et al. [50], which concluded that the ANN-computed surrogate model is better than the RSM-computed one for predicting the behavior of a nonlinear system. The design of experiment's type in creating the datasets does not appear to be a significant factor which it comes to causing accuracy differences between RSM-computed and ANN-computed surrogate models. Rather, the number of datasets tends to affect the prediction accuracy more. To quantitatively measure it, the variable \(\alpha_{n}\)  
\[\alpha_{n}=\frac{E_{n,3}}{E_{n,5}}, \tag{9}\]  
is defined for a \(n\)-degree of freedom prediction test where \(E_{n,m}\) is the normalized root-mean-square deviation of the surrogate model constructed by using the datasets of the O-DLB-\(n\)-\(m\). If this value is high, the prediction accuracy is highly improved because the value of \(m\) of the discrete \(m\)-level based method increases from 3 to 5, resulting in an increase of the number of datasets. Figure 3 shows the values of \(\alpha_{4}\) and \(\alpha_{6}\) of the surrogate models obtained from the RSM and ANN. Because these values for the RSM-computed surrogate models are greater than unity, the prediction accuracy of the corresponding surrogate models are improved when a large amount of datasets are offered. However, the ANN's values of \(\alpha_{n}\) are higher than the RSM's values, showing that the ANN-computed surrogate models are more highly improved than the RSM's when the number of datasets increases. The prediction values for the lift-to-drag ratio using RSM-computed and ANN-computed surrogate models for the 50 test samples are plotted in Figure 4 with their exact (computed from XPOIL) values.