# Prediction of Self-Healing of Engineered Cementitious Composite Using Machine Learning Approaches
## 5 Results and Discussion
### Prediction Performance Comparison  
#### 5.2.1 Comparison of the MAE  
To reveal the accuracy of the proposed ML models in self-healing prediction, the comparison of the observed crack widths of ECC after self-healing with predicted crack widths are shown in Figures 11-14. Figure 11a shows the observed crack widths compared with the crack widths predicted by different individual ML models. Figure 11b-e shows the variations between the observed and the crack widths predicted by each individual ML model corresponding to their initial crack widths before self-healing. In other words, the prediction performance of the models in a particular range of crack widths can be revealed. It should be noted that the horizontal line located at the vertical coordinate of zero (\(y=0\)) is considered as the target line [25; 31]. Generally, the smaller the variation (i.e., closer to the target line), the better the self-healing prediction was, which means smaller or even no variation between the observed and the predicted crack widths after self-healing. As shown in Figure 11, the SVR model generally exhibited better prediction results than other individual models, while the LR model was the worst, showing substantial deviation from the target line (denoting relatively large differences between the observed and the predicted crack widths). For the initial crack widths less than 20 \(\upmu\)m and over 100 \(\upmu\)m before self-healing, the variations between the observed and the ones predicted by the SVR model were smaller than other individual ML models. The corresponding MAE values were 1.358 and 2.724. However, for the crack widths between 20 \(\upmu\)m and 60 \(\upmu\)m, the CART model performed the best with the lowest MAE of 5.045, while the BPNN model had the lowest MAE of 9.565 for the crack widths between 60 \(\upmu\)m and 100 \(\upmu\)m. It seems that the choice of ML models may depend on the initial crack widths. However, in terms of overall accuracy among the individual models, SVR performed the best, followed by CART, the BPNN, and LR. This is consistent with the results shown in Table 5.  
The performance of ensemble methods using AdaBoost and bagging is shown in Figures 12 and 13. In general, the ensemble models Ada_CART and bag_CART exhibited lower variations in the self-healing results compared to the other ensemble models. In particular, the MAE values of Ada_CART and bag_CART for crack widths between 20 self heal and 60 \(\upmu\)m were 5.037 and 5.000, respectively. These values were smaller than that of CART (5.045), as shown in Figure 11e. However, the variations among the BPNN, Ada_BPNN, and bag_BPNN were not significant. Similar variations can be found when comparing SVR with Ada_SVR and bag_SVR. After stacking, the error variations shown in Figure 14 were much reduced when compared to those shown in Figures 11-13. More specifically, the MAE of stack_LR for crack widths less than 20 \(\upmu\)m, between 20 \(\upmu\)m and 60 \(\upmu\)m, between 60 \(\upmu\)m and 100 \(\upmu\)m, and over 100 \(\upmu\)m were 1.361, 4.931, 9.789, and 3.177, respectively. These MAE values were the lowest among all the ML models studied. Based on the results, it can be concluded that the stack_LR model performed the best.