## 3 Results and Discussion
### Compressive Strength Modeling  
The four models with the eight input variables were used to estimate the compressive strength of SCC. The model's performance in training and testing stage are compared in Figure 6. A high correlation between measured and estimated CS is observed with MPMR and ENN models in both stages. While maximum error can be observed with models GMDH and MPMR at training and testing stages, respectively. Table 6 summarizes the performance of proposed models at training, testing and validation stages, and Figure 7 presents the performance of the four models in the validation stage. Figure 5: Performance of models for slump modeling based on the number of data. (**a**) Violin diagram for the testing stage; (**b**) Taylor diagram for the validation stage. The performance of MPMR model is also seen the best in the training stage, as presented in Table 6. The percentage error of the model is 4.21%; followed by the ENN model within 6.02% percentage error. In contrast, the best model in the testing and validation stages is ENN model within 8.08% and 6.26% percentage errors, respectively (see Table 6 and Figures 6 and 7); while, the worst models' performance in the testing and validation stages are the MPMR and GMDH models, respectively. Thus, the MPMR model is also influenced by the data number when used to estimate the CS of SCC. Here, the ENN model outperforms other models with RMSE = 2.59 MPa and r = 96.07% for the overall data. The MAE of ENN model for predicting CS of SCC is 1.77 MPa (a lower value compared by other models). These results reveal that the ENN model can be used as a soft computing model for detecting accurate CS of SCC with the eight inputs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistical Parameter** & **GMDH** & **MPMR** & **ENN** & **ANN-PSO** \\ \hline \multicolumn{5}{c}{Training} \\ \hline RMSE (MPa) & 3.41 & 1.74 & 2.49 & 3.20 \\ \hline MAE (MPa) & 2.62 & 1.25 & 1.64 & 2.12 \\ \hline r (\%) & 93.76 & 98.40 & 96.70 & 94.56 \\ \hline PE (\%) & 8.24 & 4.21 & 6.02 & 7.73 \\ \hline \multicolumn{5}{c}{Testing} \\ \hline RMSE (MPa) & 3.65 & 4.08 & 2.78 & 2.88 \\ \hline MAE (MPa) & 2.85 & 3.11 & 2.04 & 2.09 \\ \hline r (\%) & 89.79 & 86.97 & 94.36 & 93.54 \\ \hline PE (\%) & 10.62 & 11.86 & 8.08 & 8.37 \\ \hline \multicolumn{5}{c}{Overall} \\ \hline RMSE (MPa) & 3.47 & 2.67 & 2.59 & 3.09 \\ \hline MAE (MPa) & 2.66 & 1.81 & 1.77 & 2.43 \\ \hline r (\%) & 92.78 & 95.84 & 96.07 & 94.47 \\ \hline PE (\%) & 8.39 & 6.45 & 6.26 & 7.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance assessment of the models for CS estimation. Figure 6: The performance of the models compared by compressive strength measured values in the training and testing stages. For more investigation, the performance of the proposed models in testing and validation phases were assessed. The Violin and Taylor diagrams for the testing and validation phases are presented in Figure 8a,b, respectively. The Violin plot for CS estimation also assessed the model's errors, and the estimated and measured CS values were used in the Taylor plot. It is obviously shown from Figure 8a that the ENN model is the best model that can be used to estimate the CS of SCC. The distribution of errors is approximately normal with low outliers compared by other models, the average of maximum variation of model's errors are about \(\pm\)12.88 MPa, \(\pm\)15.49 MPa, \(\pm\)10.62 MPa, \(\pm\)11.27 MPa. Some shift changes can be observed in the quartiles of Violin plot of ENN model, but it is still the best distribution among the four models. In addition, a summary of multiple statistical parameters was presented in Figure 8b for the proposed models in the validation stage. From the figure, it can be clearly shown that the performance of ENN is better than other models for estimating the compressive strength of SCC since it possesses the close performance model to the measured CS values.