## 3 Rotor Blade Design Approximation with RBFNN
From the main effect results, it was found that the design performances of rotor blade were increased as the \(\rm{h_{D}}\) value was increased and the \(\rm{d_{loc}}\) value was decreased. The error analyses were carried out to evaluate the variation of performance according to the variation of learning parameters such as the SSP value, the number of training data, and the number of hidden layers. The SSP values were varied from zero to 0.1 with 0.025 step size, and the accuracy measures such as RMSE and MAX were analyzed. Their results were represented in Table 4 and Figures 13 and 14. As shown in Table 4 and Figure 13, the RMSEs of Mass, GJ, EI\({}_{22}\), and EI\({}_{33}\) were distributed in the range of 0.00590 to 0.00593, 0.00645 to 0.00647, 0.02021 to 0.02026, and 0.02375 to 0.02384, respectively, according to the variation of SSP. The MAXs of Mass, GJ, EI\({}_{22}\), and EI\({}_{33}\) were distributed in the range of 0.02473 to 0.02483, 0.01567 to 0.01589, 0.09622 to 0.09637, and 0.09031 to 0.09046, respectively, as represented in Table 4 and Figure 14. From the results of error analyses, it was clear that the variation of accuracy occurred in  
Figure 11: Meta-models for design variable—\(\rm{d_{ang}}\). the slight magnitude because the rotor blade design problem had relatively a low multimodal variation as represented in the meta-modeling results and the statistical analysis. Although the influence of SSP was not significant in the RBFNN approximation of the actual rotor blade design problem, it could be seen that the accuracy of the approximation was increased based on RMSE as the SSP was applied in the range of 0.075 to 0.1. The results of error scattering were also evaluated according to the SSP values. The results of error scattering analyses were shown in Figure 15. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Error Type** & **SSP Value** & **Mass** & **GJ** & **EI\({}_{\text{22}}\)** & **EI\({}_{\text{33}}\)** \\ \hline \multirow{4}{*}{RMSE} & 0.0 & 0.00590 & 0.00646 & 0.02023 & 0.02375 \\  & 0.025 & 0.00593 & 0.00647 & 0.02026 & 0.02384 \\  & 0.050 & 0.00592 & 0.00647 & 0.02026 & 0.02383 \\  & 0.075 & 0.00592 & 0.00645 & 0.02025 & 0.02382 \\  & 0.1 & 0.0592 & 0.00645 & 0.02021 & 0.02380 \\ \hline \multirow{4}{*}{MAX} & 0.0 & 0.02473 & 0.01567 & 0.09622 & 0.09031 \\  & 0.025 & 0.02483 & 0.01598 & 0.09641 & 0.09053 \\ \cline{1-1}  & 0.050 & 0.02482 & 0.01594 & 0.09638 & 0.09050 \\ \cline{1-1}  & 0.075 & 0.02481 & 0.01589 & 0.09636 & 0.09047 \\ \cline{1-1}  & 0.1 & 0.02483 & 0.01589 & 0.09637 & 0.09046 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of accuracy according to variation of SPP. Figure 12: Main effects on design performance functions. Figure 14: Maximum error according to variation of SPP. Figure 13: RMSE according to variation of SPP. Figure 16: RMSE according to variation of training data. Figure 17: Maximum error according to variation of training data. The results of Table 5 and Figure 16 represented that the RMSEs of Mass, GJ, El\({}_{22}\) and EI\({}_{33}\) were distributed in the range of 0.00590 to 0.00643, 0.00646 to 0.00737, 0.02023 to 0.02334, and 0.02375 to 0.02787, respectively, according to the variation of training data. It was found that the influence of the number of training data on the accuracy of the meta-model in the rotor blade design was higher than that of the SSP. RMSEs for all the design performance functions were enhanced as the number of training data was increased. The MAXs of Mass, GJ, EI\({}_{22}\) and EI\({}_{33}\) were distributed in the range of 0.02473 to 0.02509, 0.01567 to 0.01977, 0.08138 to 0.09622, and 0.08316 to 0.09031, respectively, as represented in Table 4. Among the MAX results, however, EI\({}_{22}\) and EI\({}_{33}\) were deteriorated as the number of training data was increased, as shown in Figure 17. Such result was because some larger deviation data was included in the set of training data.