## 3 Results
### Scour Depth Prediction by Optimized ANN Models
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Performance Metrics**} \\ \cline{2-5}  & **MAE** & **RMSE** & **CC** & **WI** & **MAPE** **(\%)** \\ \hline \multicolumn{5}{c}{**Training period**} \\ \hline ANN-HHO & 0.1791 & 0.2626 & 0.9557 & 0.9769 & 43.0994 \\ ANN-PSO & 0.1887 & 0.2845 & 0.9491 & 0.9737 & 41.6057 \\ ANN-GA & 0.2228 & 0.3268 & 0.9308 & 0.9618 & 54.2987 \\ ANN & 0.2657 & 0.3537 & 0.9197 & 0.9554 & 80.9093 \\ \hline \multicolumn{5}{c}{**Testing period**} \\ \hline ANN-HHO & 0.1760 & 0.2538 & 0.7765 & 0.8030 & 30.5081 \\ ANN-PSO & 0.2094 & 0.2891 & 0.7755 & 0.7323 & 32.7147 \\ ANN-GA & 0.2178 & 0.2981 & 0.7733 & 0.6544 & 37.3840 \\ ANN & 0.2494 & 0.3152 & 0.7708 & 0.4597 & 51.3543 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance metrics of hybrid and simple ANN models during training and testing. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Parameters** \\ \hline ANN-HHO & \begin{tabular}{c} IW\({}_{1}\) = [1.2702; \(-\)4.5789; \(-\)2.3216] \\ b\({}_{1}\) = 4.2473; 4.2087; \(-\)3.5027] \\ LW\({}_{2}\) = [\(-\)4.9710; \(-\)0.8578; \(-\)4.6376] \\ b2 = [\(-\)1.0285] \\ \end{tabular} \\ \hline ANN-PSO & \
\begin{tabular}{c} IW\({}_{1}\) = [0.3307; \(-\)2.3738; 0.4136] \\ b\({}_{1}\) = [2.1814; \(-\)2.9212; 0.4245] \\ LW\({}_{2}\) = [0.6612; \(-\)0.8655; 2.2048] \\ b\({}_{2}\) = [\(-\)2.0182] \\ \end{tabular} \\ \hline ANN-GA &
\begin{tabular}{c} IW\({}_{1}\) = [1.5678; \(-\)2.4749; \(-\)0.5116] \\ b\({}_{1}\) = [1.6005; \(-\)2.9850; 1.7257] \\ LW\({}_{2}\) = [\(-\)1.9123; 0.7718; \(-\)1.7505] \\ b\({}_{2}\) = [1.1099] \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal ANN parameters using HHO, PSO and GA algorithms. of modeled (predicted) scour depth values by the ANN-HHO, ANN-PSO, ANN-GA, and ANN models over the observed values during training and testing periods through the box plot. It can be seen from Figure 6a-b that the distributional variations among predicted vs. observed scour depth values are relatively minor. Therefore, the verdict based on performance measures (MAE, RMSE, CC, WL, and MAPE) and graphical inspection (coefficients of determination of regression line, scatter, and box plots) show a better scour depth prediction accuracy of ANN-HHO model than ANN-PSO, ANN-GA, and ANN models. Figure 4: Line and scatter plots of (**a**) ANN-HHO, (**b**) ANN-PSO, (**c**) ANN-GA, and (**d**) ANN models during the training period. Figure 5: Line and scatter plots of (**a**) ANN-HHO, (**b**) ANN-PSO, (**c**) ANN-GA, and (**d**) ANN models during the testing period. Besides, the Taylor diagram [66], which is a consortium of standard deviation, RMSE, and the correlation coefficient, was employed to display the spatial variation of predicted scour depth by the ANN-HHO, ANN-PSO, ANN-GA, and ANN models over the observed one in single topology, as illustrated in Figure 7a,b. It can be seen from Figure 7a,b that the outcomes obtained by the ANN-HHO model are close to the observed one for SD prediction, showing superior performance of this model as discussed earlier in Table 4 and Figure 4a-d to Figure 5a-d.  
Figure 6: Box plots of observed and predicted scour depth by ANN-HHO, ANN-PSO, ANN-GA, ANN models during (**a**) training, and (**b**) testing periods.