## 5 Results and Discussion
### Driving Physical Meaning of AI Results
#### 5.3.2 Effects of \(e/D\) and \(Kc\) on \(V_{R}^{*}\)  
Figure 9a-d shows the variations of \(V_{R}^{*}\) against \(e/D\) at given values of \(Kc\) and for \(\alpha=0^{\circ}\), according to AI models. All AI models exhibit a downward trend when interpreting the variations of \(V_{R}^{*}\) with \(e/D\) increasing from 0.1 to 0.4. For example, M5 MT simulates that \(V_{R}^{*}\) decreases linearly with increasing \(e/D\), as shown in Figure 9a. In addition, for a constant value of \(e/D\), \(V_{R}^{*}\) increases with increasing \(Kc\), with a tendency towards an asymptotic value. For example, \(V_{R}^{*}\) increases sharply from 2.94 for \(Kc\) = 8.7 to 4.56 for \(Kc\) = 18, at \(e/D\) = 0.1 as shown in Figure 10a. This trend was generally repeated in Figure 9b-d.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**KC and \(\alpha\) Values**} & \multicolumn{4}{c}{**SSE Values for AI Models**} \\ \cline{2-5}  & **M5 MT** & **GEP** & **EPR** & **MARS** \\ \hline \(KC=8.7\) and \(\alpha=0^{\circ}\) & 0.300 & 0.435 & 0.843 & 0.161 \\ \(KC=15.8\) and \(\alpha=0^{\circ}\) & 0.018 & 0.040 & 0.081 & 0.078 \\ \(KC=18.0\) and \(\alpha=0^{\circ}\) & 0.147 & 0.276 & 0.018 & 0.142 \\ \(KC=18.0\) and \(\alpha=15^{\circ}\) & 0.049 & 0.018 & 0.040 & 0.010 \\ \(KC=15.8\) and \(\alpha=30^{\circ}\) & 0.011 & 0.047 & 0.003 & 0.063 \\ \(KC=18.0\) and \(\alpha=30^{\circ}\) & 0.031 & 0.054 & 0.028 & 0.040 \\ \(KC=15.8\) and \(\alpha=45^{\circ}\) & 0.005 & 0.035 & 0.006 & 0.054 \\ \hline \hline \end{tabular}
\end{table}
Table 5: SSE values for the considered AI models when predicting \(V_{H}^{*}\) at various \(e/D\) ratios.  
Analogously, Figure 10a-d shows the variations of \(V_{R}^{*}\) against \(K\)C at given values of \(e/D\), according to AI models. All AI models exhibit an upward trend when interpreting the variations of \(V_{R}^{*}\) with \(K\)C increasing from 8.7 to 18. For example, M5 MT simulates that \(V_{R}^{*}\) increases from 2.4 for \(K\)C = 8.7 to 4.56 for \(K\)C = 18, at \(e/D\) = 0.2. However, in general, the trend is not linear but approximately asymptotic. In addition, for a constant value of \(K\)C, \(V_{R}^{*}\) decreases as \(e/D\) increasing. For example, \(V_{R}^{*}\) values decline from 4.344 for \(e/D\) = 0.1 to 2.927 for \(e/D\) = 0.4, at \(K\)C = 15.8, as shown in Figure 10d.  
Moreover, statistical performance of AI techniques for the prediction of \(V_{R}^{*}\) with consideration of \(e/D\) and \(K\)C variations at \(\alpha\) = 0\({}^{\circ}\) is presented in Table 6. It was found that all the AI techniques had the best performance for better understanding the general pattern of \(V_{R}^{*}\) versus \(e/D\) at \(K\)C = 8.7. For instance, the GEP model indicated the most satisfying efficiency at \(K\)C = 8.7 with an SSE of 0.0622 than results predicted at \(K\)C = 15.8 (SSE = 0.2602) and \(K\)C = 18 (SSE = 0.0827). For \(K\)C = 8.7, EPR was found more compromisingly for the assessment of \(V_{R}^{*}\) with SSE = 0.0168 in comparison with M5 MT (SSE = 0.0388), MARS (SSE = 0.0483), and GEP (SSE = 0.0622). In the case of \(K\)C = 15.8, EPR had the most successful efficiency while for \(K\)C = 18, the M5 MT technique stood at the highest level of accuracy for simulation of \(V_{R}^{*}\) variations versus \(e/D\) ratios. In Table 6, it was inferred that AI models indicated the best performance to perceive variations of \(V_{R}^{*}\) versus \(K\)C values for different \(e/D\) ratios. MARS (SSE = 0.0544), M5 MT (SSE = 0.0244), and EPR (SSE = 0.0035) had the most accurate efficiency at \(e/D\) = 0.3 while for \(e/D\) = 0.1, the GEP technique had the most prosperous performance (SSE = 0.0349). GEP showed variations of \(V_{R}^{*}\) versus at \(e/D\) = 0.1, with the highest level of accuracy (SSE = 0.0349) whereas for \(e/D\) = 0.2, EPR was determined as the most precise model. On the other hand, EPR (SSE = 0.0035) and MARS (SSE = 0.0920) stood at the highest level of accuracy at \(e/D\) = 0.3 and \(e/D\) = 0.4, respectively.