## 3 Application Results and Discussion
### Estimation of RCCP Mechanical Characteristics Using Classification-Based Regression Methods
#### 3.2.2 Tensile Strength  
The performance indicators of the calibration and validation capability of estimating the tensile strength of RCCP using tree-based methods are reported in Table 4. According to Table 4, the RF model presented reliable performance in the training and testing phases. The statistical assessment for the validation subset of the proposed RF, M5 rule, M5p, and CHAID techniques are (R = 0.984, NSE = 0.955 MPa, RMSE = 0.070 MPa and RSD = 0.062 MPa), (R = 0.850, NSE = 0.706 MPa, RMSE = 0.471 MPa and RSD = 0.500 MPa), (R = 0.882, NSE = 0.776 MPa, RMSE = 0.358 MPa and RSD = 0.328 MPa), and (R = 0.912, NSE = 0.817 MPa, RMSE = 0.293 MPa and RSD = 0.255 MPa), respectively. The graphical plots of subsets of the presented models are scattered in Figure 6. The presented tree-based models achieved acceptable simulation results for the TS of RCCP based on data correlated around the ideal line (1:1 line). Although a few data points developed by M5p and M5 rule around the TS of 2-5 MPa indicated some small divergence from the 1:1 line, the results revealed that all of the tree-based methods provided high accuracy to simulate of tensile strength. The time series and residual plots for tree-based simulation and actual TS are presented in Figure 7. The RF model generated the minimum RMSE and outperforms the M5 rule, M5p, and CHAID models for estimation of the TS of RCCP.  
Figure 5: Time series and residual plots of the testing phase of the classification-based regression methods for CS estimation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & **Proposed** & \multicolumn{4}{c}{**Performance Metrics**} \\ \cline{3-6}  & **Models** & **R** & **NSE** & **RMSE** & **RSD** \\ \hline \multirow{4}{*}{**Training**} & **RF** & **0.986** & **0.968** & **8.650** & **0.561** \\  & M5 rule & 0.855 & 0.731 & 74.480 & 5.460 \\  & M5p & 0.896 & 0.797 & 56.142 & 4.122 \\  & CHAID & 0.925 & 0.857 & 39.617 & 2.570 \\ \hline \multirow{4}{*}{**Testing**} & **RF** & **0.965** & **0.931** & **17.911** & **1.181** \\  & M5 rule & 0.828 & 0.680 & 83.507 & 6.499 \\  & M5p & 0.889 & 0.774 & 58.878 & 4.507 \\  & CHAID & 0.897 & 0.801 & 51.842 & 3.556 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Predictive performance of the proposed models for CS prediction.  
Figure 6: Scatter plots of the observed and simulated TS for training (light color) and testing (dark color) of the proposed models.  
Figure 7: Time series and residual plots of the testing phase of the classification-based regression methods for TS estimation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & \multirow{2}{*}{**Proposed**} & \multicolumn{4}{c}{**Performance Metrics**} \\ \cline{3-6}  & & **R** & **NSE** & **RMSE** & **RSD** \\ \hline \multirow{4}{*}{**Training**} & **RF** & **0.991** & **0.981** & **0.030** & **0.025** \\  & M5 rule & 0.892 & 0.791 & 0.338 & 0.320 \\  & M5p & 0.895 & 0.798 & 0.328 & 0.294 \\  & CHAID & 0.975 & 0.951 & 0.078 & 0.024 \\ \hline \multirow{4}{*}{**Testing**} & **RF** & **0.984** & **0.955** & **0.070** & **0.062** \\  & M5 rule & 0.850 & 0.706 & 0.471 & 0.500 \\ \cline{1-1}  & M5p & 0.882 & 0.776 & 0.358 & 0.328 \\ \cline{1-1}  & CHAID & 0.912 & 0.817 & 0.293 & 0.255 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Predictive performance of the proposed models for TS prediction.