**4. Evaluation of Models Recommended by Codes**

The models recommended by codes for PE and IC debonding are shown in Table 2. In all, 128 sets of PE debonding and 101 sets of IC debonding samples collected in 'Table 1 are used to analyze the two types of models separately. The computed values of the models are compared with the actual values of the samples in Figure 9. The evaluation of the model is based on two indicators: coefficient of variation and conservativeness. In general, the smaller the coefficient of variation, the smaller the dispersion between the two sets of data, indicating a better predictive value of the model. The model is conservative if more than ninety percent of the predicted values are less than the test values. The performance evaluation of the codes' models is shown in Table 3.


**Figure 9.** Evaluation of the models. (**a**) PE debonding; (**b**) IC debonding.

As can be seen from Figure 9 and Table 3, for PE debonding, the models suggested by ACI and *fib* are a bit conservative, and their calculated values are lower than the experimental values. The coefficient of variation between the calculated values of the models suggested by TR55 and AS and the experimental values exceeds 40%, which is difficult to apply in practice. For IC debonding, the models suggested by TR55, CNR, and JSCE are a little conservative, while the models suggested by ACI and CECS have the risk of overestimating the FRP strains in case of the IC debonding, and the coefficients of variation between the calculated values of all the models suggested by the codes and experimental values are above 38%, which is difficult to apply in practice. For PE and IC debonding, the DBO-BP model has the lowest coefficient of variation between predicted values and experimental values among all models, which are 19% and 10%, and its predicted values are more stable, which shows a relatively balanced proportion of conservative values in the predicted values of the models.


**Table 3.** Model Evaluation.

#### **5. Parametric Study**

The importance of the parameters is calculated based on the connection weights and excitation functions between the input layer and the hidden layer, and between the hidden layer and the output layer of the DBO-BP neural network model. In this study, the connection functions of the input layer and the hidden layer are "hyperbolic tangent function" and "linear function", which are expressed in Equations (6) and (7).

$$y\_i = f \cdot \left(\sum\_{i} w\_{ij} \mathbf{x}\_i + \phi\_{\dot{\jmath}}\right) = \frac{2}{1 + \varepsilon} \frac{2}{\frac{-2\left(\sum w\_{ij} \mathbf{x}\_i + \phi\_{\dot{\jmath}}\right)}{\dot{\imath}} - 1} \tag{6}$$

$$y\_i = f \cdot \left(\sum\_{i} w\_{ij} \mathbf{x}\_i + \phi\_j\right) = \sum\_{i} w\_{ij} \mathbf{x}\_i + \phi\_j \tag{7}$$

where *xi* denotes the value of the *i*th input metric, *wij* is the connection weight of the *i*th metric to the *j*th neuron, and *Φ<sup>j</sup>* is the bias of the *j*th neuron.

The interlayer connection weights and biases for PE and IC debonding are shown in Tables 4 and 5.

The importance results of the indicators calculated according to Tables 4 and 5 are shown in Figure 10.

**Table 4.** Layer-to-layer connection weights for the predictive model of PE debonding.



**Table 4.** *Cont.*

**Table 5.** Layer-to-layer connection weights for the predictive model of IC debonding.


**Figure 10.** Importance of parameters. (**a**) PE debonding; (**b**) IC debonding.

From Figure 10, it can be seen that for PE debonding, the degree of influence of each parameter on the output result is a5, a4, a6, a2, a3, a1, a7; for IC debonding, the degree of influence of each indicator on the output is b6, b4, b1, b2, b5, b8, b3, b7.
