# Prediction of Self-Healing of Engineered Cementitious Composite Using Machine Learning Approaches
## 5 Results and Discussion
### Prediction Performance of the Proposed Models  
Table 5 shows the ten-fold cross-validation results (MAE, RMSE, and \(R^{2}\)) for both individual and ensemble models and their deviation with respect to the results of the LR model. Generally, most of the proposed models were able to learn and predict the empirical data with an acceptable degree of precision. Based on the results, the Stack_LR model showed the best prediction performance as it had the highest \(R^{2}\) value and the lowest MAE and RMSE values. Among the individual models, SVR performed the best in terms of the MAE (4.296), whereas BPNN had the lowest RMSE value (6.515) and the highest \(R^{2}\) of 0.899. Among the individual models boosted by either AdaBoost or bagging, Bag_CART gave the best performance in terms of the MAE (4.093), while Bag_BPNN performed better on the RMSE value (6.341). In terms of \(R^{2}\), the Bag_CART and Bag_BPNN models showed the same performance (0.901) and were better than other ensemble methods, except Stack_LR. The performances of all ML models described in Table 5 are depicted in Figure 9(a)-c in terms of the MAE, RMSE, and \(R^{2}\), respectively. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & **Models** & **MAE** & \(Dev\) (\%) & **RMSE** & \(Dev\) (\%) & \(R^{2}\) & \(Dev\) (\%) \\ \hline \multirow{3}{*}{Individual} & LR & 5.012 & - & 7.680 & - & 0.860 & - \\  & BPNN & 4.329 & \(-\)13.6 & 6.515 & \(-\)15.2 & 0.899 & 4.5 \\ \cline{1-1}  & CART & 4.305 & \(-\)14.1 & 6.811 & \(-\)11.3 & 0.887 & 3.1 \\ \cline{1-1}  & SVR & 4.296 & \(-\)14.3 & 6.826 & \(-\)11.1 & 0.883 & 2.7 \\ \hline \multirow{9}{*}{Ensemble} & Ada\_LR & 4.784 & \(-\)4.6 & 7.400 & \(-\)3.6 & 0.867 & 0.8 \\  & Ada\_BPNN & 4.226 & \(-\)15.7 & 6.435 & \(-\)16.2 & 0.900 & 4.7 \\ \cline{1-1}  & Ada\_CART & 4.207 & \(-\)16.1 & 6.455 & \(-\)15.9 & 0.898 & 4.4 \\ \cline{1-1}  & Ada\_SVR & 4.145 & \(-\)17.3 & 6.577 & \(-\)14.4 & 0.893 & 3.8 \\ \cline{1-1}  & Bag\_LR & 5.014 & 0.0 & 7.689 & 0.1 & 0.860 & 0.0 \\ \cline{1-1}  & Bag\_BPNN & 4.143 & \(-\)17.3 & 6.341 & \(-\)17.4 & 0.901 & 4.8 \\ \cline{1-1}  & Bag\_CART & 4.093 & \(-\)18.3 & 6.358 & \(-\)17.2 & 0.901 & 4.8 \\ \cline{1-1}  & Bag\_SVR & 4.302 & \(-\)14.2 & 6.820 & \(-\)11.2 & 0.883 & 2.7 \\ \cline{1-1}  & Stack\_LR & 3.934 & \(-\)21.5 & 6.118 & \(-\)20.3 & 0.904 & 5.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average performances of machine learning models for the self-healing prediction of ECC. Overall, all models could reduce the error values and increase the prediction accuracy compared with LR, except Bag_LR. Among the models boosted by AdaBoost, Ada_SVR performed the best with the lowest MAE value, whereas Ada_BPNN performed the best on the RMSE value, showing the highest \(R^{2}\) value. In the case of bagging, both Bag_CART and Bag_BPNN performed better in terms the MAE, RMSE and \(R^{2}\) than those of the corresponding models boosted by AdaBoost. However, Bag_LR showed a poor performance compared to LR on the MAE and RMSE values. For a better comparison among the ensemble methods used, the performance results between the ensemble models and their corresponding individual (or benchmark) models are indicated in Table 6. The results indicate that most ensemble methods improved the performance of individual models. For example, the MAE and RMSE values of the BPNN after bagging reduced by 4.3% and 2.7%, respectively, and its \(R^{2}\) was much higher than that of the individual BPNN model. Among all the ensemble methods studied, stacking showed the best improvement on all performance measures. However, the results showed that the effectiveness of the ensemble methods on the individual models varied. For instance, the bagging method enhanced the performance of the BPNN and CART substantially, but not for both LR and SVR models. On the other hand, the AdaBoost method brought a considerable improvement for the LR and SVR models. To  
Figure 10: Average prediction performance of 10-fold cross-validation on all ML models for predicting the self-healing ability of ECC.