## 4 Results
### Developing Predictive Models  
Cross-plots comparing the measured and the predicted FV values for the standalone ML (RBFNN, MELM) and optimized HML (MELM-GO, RBFNN-GO) models constructed with training data are illustrated in Figure 8.  
Figure 8: Comparative cross-plots evaluating accuracy of measured and predicted FV values utilizing (**a**) MELM, (**b**) MELM-GO, (**c**) RBFNN, and (**d**) RBFNN-GO models on training data. Figure 7: The iterative reduction of RMSE within various iterations of the GO algorithm is employed to ascertain the optimal structure of the MELM algorithm in the prediction of the FV. Predictions generated by the RBFNN-GO model (Figure 8) are in closest proximity to the y = x line, indicating the most accurate trained-model outcomes. RBFNN predictions, on the other hand, exhibit marginally greater variation and deviate more from actual values than RBFNN-GO, indicating less precise estimates. The MELM models generated the most imprecise forecasts, especially the standalone MELM model, which indicates a diminished capacity to accurately quantify the FV. Figure 9 displays the evolution of the training subset RMSE for sequences of GO iterations. The hybridized RBFNN-GO architecture showed the highest degree of performance consistency, with negligible error fluctuations throughout subsequent optimizations. The RBFNN-GO model converged more slowly than the MELM-GO model but reached an improved solution. The HML models are clearly more effective learners than the standalone models. The prediction performance metrics applied to the training subset (Table 3) rank the models RBFNN-GO (best) > MELM-GO > RBFNN > MELM (worst). Figure 10 presents cross-plots contrasting measured and estimated FV values for the trained standalone ML algorithms (MELM, RBFNN) and optimized HML designs (MELM-GO, RBFNN-GO) applied to the testing data subset. The RBFNN and RBFNN-GO models achieved the most precise FV predictions of the four models evaluated, as seen by the tight alignment with the ideal y = x line. In comparison, the MELM architectures generated more diffuse estimations with numerous points deviating further from the y = x line. \begin{table}
\begin{tabular}{l l l l l l l} \hline
**Type** & **Models** & **ARE** & **RMSE (mL)** & **RRMSE** & \(\mathbf{R^{2}}\) & **PI** & **a20-Index** \\ \hline \multirow{2}{*}{Simple} & MELM & 0.0483 & 1.6583 & 0.2064 & 0.9213 & 0.1053 & 0.9497 \\  & RBFNN & 0.0081 & 0.8122 & 0.1011 & 0.9809 & 0.0508 & 0.9065 \\ \hline \multirow{2}{*}{Hybrid} & MELM-GO & 0.0081 & 0.6687 & 0.0832 & 0.9870 & 0.0418 & 0.9638 \\  & RBFNN-GO & 0.0055 & 0.5919 & 0.0737 & 0.9898 & 0.0369 & 0.9682 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of prediction performance for standalone and HML models applied to the FV training subset. Figure 9: Assessment of the error convergence of GO algorithm iteration sequences for the two HML models configured to predict the FV. Table 4 contrasts the statistical accuracy metrics achieved by the ML and the HML trained models applied to forecast FV values for the testing data subset. Collectively, the metrics rank the models RBFNN-GO (best) > RBFNN > MELM-GO > MELM (worst). These results suggest that the trained RBFNN-GO and RBFNN models are more generalizable than either of the MELM models when applied FV dataset studied. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Type** & **Models** & **ARE** & **RMSE (mL)** & **RRMSE** & **R\({}^{2}\)** & **PI** & **a20-Index** \\ \hline \multirow{2}{*}{Simple} & MELM & \(-\)0.0083 & 2.4417 & 0.1221 & 0.9875 & 0.0612 & 1 \\  & RBFNN & 0.0024 & 0.9690 & 0.0485 & 0.9961 & 0.0242 & 1 \\ \hline \multirow{2}{*}{Hybrid} & MELM-GO & \(-\)0.0059 & 0.9753 & 0.0488 & 0.9968 & 0.0244 & 0.9921 \\  & RBFNN-GO & \(-\)0.0072 & 0.6396 & 0.0320 & 0.9994 & 0.0160 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of prediction performance for standalone and HML models applied to the FV testing subset.