# Estimation of the Ultimate Strength of FRP Strips-to-Masonry Substrates Bond
## 4 Results  
Here, the efficiency and performance of the proposed model are investigated by comparing them with the existing models (see Table 1). Table 4 presents the values of \(R^{2}\) and RMSE for various models.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model’s Name** & **References** & \(\boldsymbol{R^{2}}\) & **RMSE** \\ \hline [PERSON] & [54] & 0.2833 * & 1.103 \\ \hline [PERSON] & [55] & 0.2168 * & 1.087 \\ \hline [PERSON] & [5] & 0.1088 * & 1.319 \\ \hline [PERSON] et al. & [6] & 0.1624 * & 1.159 \\ \hline [PERSON] & [56] & 0.3837 * & 0.953 \\ \hline [PERSON] & [57; 58] & 0.6723 * & 4.040 \\ \hline [PERSON] & [57] & 0.1179 * & 1.714 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Values of \(R^{2}\) and RMSE for different studied models.  
Based on Table 4, the \(R^{2}\) values for the considered models (i.e., ANN, KFCV, MARS, and M5 MT) are 0.9877, 0.9871, 0.9839, and 0.9802, respectively. The best value for this parameter is 0.9646 in the other existing models (i.e., model from [19]). Based on Table 4, the proposed models have fewer RMSE values than other empirical models. As described in Section 3, the mentioned configuration for the input/output parameters also utilized the well-known soft computing techniques, leading to high accuracy, low computational cost, and more feasibility for practical engineering applications.  
Moreover, the RMSE (root mean-squared error), MAE (mean absolute error), MAPE (mean absolute percentage error), and correlation coefficient values for the considered models (i.e., KFCV, MARS, and M5 MT) in comparison to the best existing model are proposed in Table 5. The best values for these parameters are shown in bold form. These results mean that the simulated results were consistent with the experimental results. It also shows that the considered models accurately forecast the ultimate strength of FRP strips applied on masonry substrates. Based on Table 4, the model suggested in [19] has more precision than the models available in the literature. Therefore, this model is chosen to compare with the considered models. Figure 11 shows the comparison between these models. From Figure 11 and Table 5, it can be inferred that the considered model (i.e., the KFCV technique) has more accuracy than the model presented in [19]. It should be noted that percentage values in Figure 11 show the underestimated and overestimated bounds as error zones.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Model’s Name** & **References** & \(\mathbf{R^{2}}\) & **RMSE** \\ \hline [PERSON] et al. & [57; 59] & 0.2124 * & 1.148 \\ \hline [PERSON] et al. & [52] & 0.4898 * & 0.987 \\ \hline [PERSON] et al. & [5] & 0.8841 * & 0.475 \\ \hline [PERSON] and [PERSON] & [60; 61] & 0.3190 * & 1.027 \\ \hline [PERSON] & [60; 62] & 0.1204 * & 1.226 \\ \hline [PERSON] et al. & [19] & 0.9646 & 0.240 \\ \hline [PERSON] and [PERSON] & [3] & 0.5425 & 1.869 \\ \hline [PERSON] and [PERSON] & [4] & 0.478 & 0.96 \\ \hline [PERSON] and [PERSON] & [63] & 0.62 & 0.87 \\ \hline \multirow{4}{*}{Present study} & ANN & **-** & **0.9877** & **0.157** \\ \cline{2-4}  & ANN-KFCV & **-** & **0.9871** & **0.159** \\ \cline{1-1} \cline{2-4}  & MARS & **-** & **0.9839** & **0.176** \\ \cline{1-1} \cline{2-4}  & M5 MT & **-** & **0.9802** & **0.193** \\ \hline \end{tabular}  
* shows that these data are extracted from [19].  
\end{table}
Table 4: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Method Error** & **ANN-KFCV** & **MARS** & **M5 MT** & **[PERSON] et al. [19]** \\ \hline MAPE (\%) & **19.08** & 21.02 & 27.10 & 19.31 \\ \hline RMSE & **0.159** & 0.176 & 0.193 & 0.24 \\ \hline AAE & **0.0778** & 0.0917 & 0.1036 & 0.1144 \\ \hline Correlation coefficient & **0.9935** & 0.9919 & 0.9900 & 0.9853 \\ \hline \end{tabular}
\end{table}
Table 5: A comparison between the considered models and best existing model.