## 3 Results and Discussion  
### Slump Flow Modeling  
The performance of the proposed models for estimating S of SCC are presented in Figures 3 and 4 and Table 5. Figure 3 presents the measured slump flow and estimated values by the proposed models in the training and testing stages. Table 5 demonstrates the performance of models in the training, testing and validation stages. The scatterplot of the proposed models' results compared by measured slump flow for the validation phase is presented in Figure 4. In the training stage, the performance of MPMR model is shown better than other models with RMSE = 3.77 mm and r = 99.94%. While the worst model for modeling S is the GMDH, with a percentage of model error is 8%. The performance of ENN and ANN-PSO models are shown acceptable, with a percentage of model's errors are 4.23% and 5.77%, respectively. Meanwhile, the percentages of model's errors in the testing stage are totally changed, with values of 4.14%, 8.96%, 13.05%, and 13.54% for the ENN, ANN-PSO, GMDH and MPMR models, respectively. The correlations between measured and estimated S are 98.67%, 91.99%, 86.76%, and 82.8% for the ENN, ANN-PSO, GMDH and MPMR models, respectively. These results indicate that the number of data affects the MPMR model performance. In addition, the performance of ENN model is the best with low numbers of data for the slump of SCC. Thus, the ENN model outperforms other models and can be used for modeling the slump behavior of SCC.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistical Parameter** & **GMDH** & **MPMR** & **ENN** & **ANN-PSO** \\ \hline \hline  & Training & & & \\ \hline RMSE (mm) & 42.00 & 3.77 & 22.23 & 30.29 \\ \hline MAE (mm) & 33.61 & 1.20 & 12.97 & 20.91 \\ \hline r (\%) & 91.63 & 99.94 & 97.73 & 95.76 \\ \hline PE (\%) & 8.00 & 0.72 & 4.23 & 5.77 \\ \hline  & Testing & & & \\ \hline RMSE (mm) & 41.75 & 43.34 & 13.26 & 28.67 \\ \hline MAE (mm) & 33.87 & 31.89 & 9.53 & 21.52 \\ \hline r (\%) & 82.80 & 86.76 & 98.67 & 91.99 \\ \hline PE (\%) & 13.05 & 13.54 & 4.14 & 8.96 \\ \hline  & Overall & & & \\ \hline RMSE (mm) & 30.48 & 23.95 & 20.16 & 42.54 \\ \hline MAE (mm) & 24.55 & 10.41 & 11.09 & 31.93 \\ \hline r (\%) & 94.89 & 97.15 & 97.80 & 90.17 \\ \hline PE (\%) & 5.81 & 4.56 & 3.84 & 8.10 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance assessment of the models for S estimation.  
Figure 4: Scatterplot of proposed models with measured slump flow in the validation stage.  
For further investigation into the performance of the proposed models with a low number of data (testing phase) and a large number of data (validation stage), the Violin and Taylor diagrams are presented in Figure 5a,b, respectively. The Violin plot was used to evaluate the model's errors, and the estimated and measured data were assessed in the Taylor plot. It is obviously shown from Figure 5a that the ENN model is the best model that can be used to estimate the S of SCC. The distribution of errors is approximately normal with low outliers since the mean and median of model error is nearly same. Furthermore, summarize multiple statistical parameters were presented in Figure 5b for the models in the validation stage. The standard deviation, root mean square difference (RMSD) and r are presented in the diagram. From the figure, it can be clearly shown that the performance of ENN is better than other models for estimating the slump flow since it has a close performance model to the measured S values. From these results, it can be concluded that the ENN model can be used as a significant machine learning technique for estimating precise S values for the S data of SCC.