*3.2. Model Construction and Evaluation*

The data used for model construction were 128 sets of PE debonding and 101 sets of IC debonding, as listed in Table 1. The model's input parameters are identified in Section 2 of this paper, shown in Figure 5. For PE debonding, the input parameters are FRP stiffness (*Eftf*), concrete strength (*f'c*), the ratio of sheet width to beam width (*bf*/*b*), stirrup reinforcement ratio (*ρsv*), tensile strength of tensile reinforcement (*fy*), shear span ratio (*λ*), and location of FRP cut-off point (*Lu/a*). For IC debonding, the input parameters are concrete strength (*f'c*), FRP stiffness (*Eftf*), shear span ratio (*λ*), stirrup reinforcement ratio (*ρsv*), the ratio of sheet width to beam width (*bf*/*b*), tensile strength of tensile reinforcement (*fy*), tensile reinforcement ratio (*ρs*), location of FRP cut-off point (*Lu/a*). The training set, validation set, and test set of the model are 60%, 20%, and 20%, respectively.

In the paper, *MAE* and *R*<sup>2</sup> are used to evaluate the performance of the model, where *MAE* indicates the mean of the absolute error between the predicted value of the model and the actual value of the sample, and *R*<sup>2</sup> indicates the degree of fit between the predicted value of the model and the actual value of the sample, and their equation are shown in Equation (5).

$$\begin{aligned} MAE &= \frac{1}{n} \sum\_{i=1}^{n} |y\_i - p\_i| \\ R^2 &= 1 - \frac{\sum\_{i=1}^{n} (y\_i - p\_i)^2}{\sum\_{i=1}^{n} (y\_i - \overline{y}\_i)^2} \end{aligned} \tag{5}$$

where *yi* is the true value of the sample, *pi* is the predicted value of the model, and *y*<sup>i</sup> is the mean value of the sample.

The *MAE* and *R*<sup>2</sup> of the training set, the validation set, and the testing set of the machine learning model are shown in Figure 7; the ratio of the training, the validation, and the testing sets is 70%, 15%, and 15%. The validation set is the samples left during the model training, which can be used to adjust the hyperparameters of the model and evaluate the ability of the model. The testing set is used to evaluate the performance of the final model.

**Figure 7.** (**a**) *MAE* for PE debonding prediction model; (**b**) *R*<sup>2</sup> for PE debonding prediction model; (**c**) *MAE* for IC debonding prediction model; (**d**) *R2* for IC debonding prediction model.

From Figure 7a,b, it can be seen that for PE debonding, the *MAE* and *R*<sup>2</sup> of LR, RR, DT, and RF in the training set, the validation set, and the testing set differ significantly, indicating that the generalization ability of these models is poor, while the *MAE* of BP neural

network in the training set, the validation set, and the testing set are 5.42, 5.52, and 5.62, respectively, which are the most minor and most average among all models. Meanwhile, the *R*<sup>2</sup> of the training set, the validation set, and the BP neural network testing set are 0.97, 0.86, and 0.90, respectively, which are also the highest among all the models. From Figure 7c,d, it can be seen that for IC debonding, the *MAE* and *R*<sup>2</sup> of LR, RR, DT, and RF in the training set, the validation set, and the testing set differ greatly, indicating that these models have poor generalization ability, while the *MAE* of BP neural network in the training set, the validation set, and the testing set are only 576, 529, and 466, respectively, which are the lowest and the most average among all models. In addition, the *R*<sup>2</sup> of the BP neural network in the training, validation, and testing sets reach 0.87, 0.58, and 0.62, respectively. Although the *R*<sup>2</sup> of the training set is lower than that of the DT, the *R*<sup>2</sup> of its validation set is higher than that of the DT. In summary, the BP neural network outperforms other machine learning models regarding prediction accuracy and debonding failure's generalization ability.
