## 5 ANN-Based Prediction Models
\[f\prime_{cc}=f\left({f^{\prime}}_{cc},\ K_{l},\ \frac{K_{l}}{{f^{\prime}}_{cc}},\ \varepsilon_{fu},\ E_{f},\ t_{f},\ f_{f}\right), \tag{5}\]  
where \(t_{f}\) is the FRP total thickness, \(\varepsilon_{fu}\) is the fiber ultimate tensile strain, \(E_{f}\) is FRP elastic modulus, and \(f_{f}\) is fiber ultimate tensile strength. As a second step, the influence of adding a second hidden layer and a number of neurons at each layer was investigated. It should be noted that using a higher number of hidden layers could increase the accuracy, but this would lead to more complicated models. Therefore, the hidden layers number was limited to two, and the variation of a neuron number in hidden layers was studied. Table 4 displays the influence of adding a second hidden layer to an ANN on \(f^{\prime}{}_{cc}\) prediction. It should be noted that all the analyzed cases were not presented in this table due to the similarity of results. Furthermore, a scaled conjugate gradient algorithm was not studied in this step due its lower accuracy compared to the other algorithms. According to Table 4, two hidden layers with 15 neurons in first hidden layer and 10 neurons in second hidden layer using the Bayesian regularization algorithm developed the most accurate prediction for \(f_{cc}\). Comparing the most accurate model with one hidden layer (presented in Table 3) to that with two hidden layers (presented in Table 4) revealed that a more accurate prediction was obtained by two hidden layers; however, the accuracy improvement was not notably significant. The influence of a transfer function on the accuracy of \(f^{\prime}{}_{cc}\) prediction is shown in Table 5. Due to the highest accuracy obtained by the Bayesian regularization algorithm, the influence of the transfer function was examined using this algorithm. Various transfer functions, such as tansig, logsig, pureline, Elliot sigmoid (elliotsig), and triangular basis (tribas), were studied. It should be noted that various combinations of a transfer function were initially studied to find the highest accuracy for \(f^{\prime}{}_{cc}\) prediction. However, only a few of them are displayed in Table 5 due to the similarity of results. According to the table, tansig was the transfer function developing the most accurate prediction for \(f^{\prime}{}_{cc}\). Table 6 displays the final ANN parameters for \(f^{\prime}{}_{cc}\) model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Levenberg–Marquardt**} & \multicolumn{3}{c}{**Bayesian Regularization**} \\ \cline{2-7}  & **AAE (\%)** & **M (\%)** & \
\begin{tabular}{c} **RMSE** \\ **(MPa)** \\ \end{tabular} & **AAE (\%)** & **M (\%)** &
\begin{tabular}{c} **RMSE** \\ **(MPa)** \\ \end{tabular} \\ \hline Two layers (4,5) & 10.1 & 100.9 & 10.5 & 10.1 & 101.0 & 10.7 \\ Two layers (5,4) & 11.1 & 102.8 & 11.7 & 9.5 & 101.6 & 10.1 \\ Two layers (6,8) & 8.7 & 100.9 & 10.1 & 9.0 & 101.4 & 9.8 \\ Two layers (8,6) & 10.9 & 99.3 & 12.9 & 8.2 & 101.4 & 9.3 \\ Two layers (8,9) & 9.2 & 101.7 & 9.7 & 9.3 & 101.4 & 10.0 \\ Two layers (9,8) & 8.5 & 101.0 & 8.9 & 9.2 & 101.4 & 10.0 \\ Two layers (8,10) & 14.6 & 102.8 & 15.7 & 9.3 & 101.6 & 10.1 \\ Two layers (10,8) & 7.7 & 101.1 & 8.6 & 10.4 & 101.8 & 11.3 \\ Two layers (10,15) & 9.9 & 101.5 & 10.9 & 9.4 & 102.1 & 10.0 \\ Two layers (15,10) & 10.2 & 101.4 & 12.0 & 6.4 & 100.4 & 7.4 \\ Two layers (15,20) & 7.5 & 101.0 & 8.3 & 9.2 & 102.1 & 10.1 \\ Two layers (20,15) & 9.4 & 101.3 & 10.4 & 8.8 & 101.6 & 9.4 \\ Two layers (20,25) & 8.9 & 102.6 & 9.1 & 6.6 & 100.6 & 7.9 \\ Two layers (25,20) & 9.4 & 102.2 & 10.2 & 9.2 & 101.6 & 9.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of different studied cases for different layers in predicting \(f^{\prime}{}_{cc}\). The developed model performance in predicting \(f^{r}_{cc}\) is illustrated in Figure 4. According to Figure 4a, experimental and predicted \(f^{r}_{cc}\) had a close consistency. In this figure, a 45\({}^{\circ}\) line was added, which is a representative of the perfect agreement.