## 4 Application and Results
### Performance of Standalone Models  
A statistical summary of the DO concentration performance using the standalone models (MLP and CCNN) is given in Table 3. Results of the MLP model with higher (NSE, WI, and R\({}^{2}\)) and lower (RMSE and MAE) values indicated that the first (MLP-I) and third (MLP-III) input combinations acted better than the others for the training and testing phases, respectively. Since, however, choosing the best model is always based on the performance of the testing phase, the MLP model with the third combination topology (MLP-III) was selected as the best model. Similar interpretation can be done for the CCNN models. While the second combination (CCNN-II) provided the best performance for the training phase, the third input combination (CCNN-III) gave the best results for the testing phase. All the statistics were enriched in the CCNN-III model in comparison to the MLP-III model. A general comparison of the MLP-III and CCNN-III models revealed that the CCNN-III model yielded the better predictions than the MLP-III model. The RMSE, NSE, WI, R\({}^{2}\), and MAE criteria for the testing phase of the CCNN-III model were improved by 129%, 8%, 2%, 3%, and 434% compared with the MLP-III model, respectively.  
The variations of the observed versus predicted DO concentration values are depicted in Figure 6a,b. Visual analysis confirmed the better results of the CCNN-III model compared to those of the MLP-III model with he observed values. Figure 7a,b provides scatter plots of the testing dataset between the observed and predicted values using the MLP-III and CCNN-III models. From visual interpretation of Figure 7a,b, it can be understood that the dots in the MLP-III plot were a bit more sporadic than those in the CCNN-III plot. In addition, based on the coefficient of determination and the slope of the trend lines to the unity, it can be concluded that the CCNN-III model acted better in predicting the DO concentration.  
Figure 6: \(Cont\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**VMD**} & \multirow{2}{*}{**Topology**} & \multicolumn{6}{c}{**Training Phase**} & \multicolumn{6}{c}{**Testing Phase**} \\ \cline{3-13}  & & & **RMSE** & **NSE** & **WI** & **R\({}^{2}\)** & **MAE** & **RMSE** & **WSI** & **R\({}^{2}\)** & **MAE** & **MAE** & **MAE** \\  & & & **mg/L** & **NSE** & **WI** & **R\({}^{2}\)** & **(mg/L)** & **(mg/L)** & **NSE** & **WI** & **R\({}^{2}\)** & **(mg/L)** \\ \hline \multirow{3}{*}{MLP-III} & \(K=3,\alpha=5\) & 9-22-1 & 0.354 & 0.981 & 0.995 & 0.981 & 0.270 & 0.339 & 0.979 & 0.995 & 0.979 & 0.280 \\  & \(K=4,\alpha=5\) & 12-25-1 & 0.335 & 0.983 & 0.996 & 0.983 & 0.240 & 0.146 & 0.986 & 0.996 & 0.986 & 0.054 \\  & \(K=4,\alpha=10\) & 12-19-1 & 0.257 & 0.990 & 0.997 & 0.990 & 0.191 & 0.107 & 0.992 & 0.998 & 0.993 & 0.034 \\ \hline \multirow{3}{*}{CCNN-III} & \(K=3,\alpha=5\) & 9-01 & 1.312 & 0.729 & 0.920 & 0.744 & 1.003 & 1.307 & 0.717 & 0.916 & 0.762 & 0.965 \\  & \(K=4,\alpha=5\) & 12-01 & 1.322 & 0.735 & 0.921 & 0.737 & 1.026 & 0.611 & 0.750 & 0.926 & 0.792 & 0.228 \\  & \(K=4,\alpha=10\) & 12-01 & 1.327 & 0.733 & 0.921 & 0.738 & 1.036 & 0.597 & 0.761 & 0.929 & 0.791 & 0.218 \\ \hline \end{tabular}
\end{table}
Table 5: Performance statistics using VMD-MLP-III and VMD-CCNN-III models.  
Figure 6: Comparison of observed and predicted DO values using standalone models for the testing phase.  
Figure 7: Scatter plots of observed and predicted DO values using standalone models for the testing phase.  
Figure 8 displays the error residual in mg/L over the testing phases of the MLP-III and CCNN-III modeling. It explained that the residuals of local peaks were relatively insignificant for the CCNN-III model, and tended to overestimate the DO concentration values; whereas the MLP-III model had larger residuals, and tended to underestimate the DO concentration values.