## 5 ANN-Based Prediction Models  
Figure 3 presents the flow chart of this study to predict the properties of FRP-confined concrete. Figure 3: Flow chart of this study. Table 3 shows the change in ANN performance of \(f_{\alpha c}\) for various sets of input variables. As shown, the Levenberg-Marquardt and Bayesian regularization algorithms showed the lowest AAE compared to the scaled conjugate gradient. Moreover, the hidden layer with 25 or 30 neurons generally developed the lowest AAE value, although some exceptions can be observed, especially for the Levenberg-Marquardt algorithm. It is also observed that the Bayesian regularization algorithm had the lowest AAE and RMSE among all the studied cases, and the accuracy of the prediction by this algorithm increased by increasing the input variables number. Additionally, a third set of input variables offered lower values of AAE compared to other analyzed sets. As a result, the third set of variables was selected as best combination of variables. It should be noted that \(K_{l}\)/\(f_{\alpha c}\), as normalized lateral stiffness, was also considered as an input variable, although \(f^{\prime}_{\alpha c}\) and \(K_{l}\) (lateral stiffness) existed in the input variables set. As can be seen in Table 2, the correlation coefficient for \(K_{l}\) and \(K_{l}\)/\(f_{\alpha c}\) was 0.747. \(K_{l}\)/\(f_{\alpha c}\) was  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Levenberg–Marquardt**} \\ \cline{2-13}  & \multicolumn{4}{c}{**10 Neurons**} & \multicolumn{4}{c}{**15 Neurons**} & \multicolumn{4}{c}{**20 Neurons**} & \multicolumn{4}{c}{**25 Neurons**} & \multicolumn{4}{c}{**30 Neurons**} \\ \hline
**Input** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** \\
**Variables** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** \\ \hline \hline \(f_{\alpha c}\), \(K_{l}\), \(\epsilon_{\mu_{l}}\) & 11.7 & 102.0 & 12.9 & 10.6 & 100.0 & 11.6 & 103.0 & 101.1 & 11.3 & 10.0 & 101.1 & 12.8 & 9.8 & 101.7 & 15.9 \\ \hline \(f_{\alpha c}\), \(K_{l}\), \(\epsilon_{\mu_{l}}\) & 10.8 & 101.7 & 11.3 & 10.6 & 101.4 & 11.3 & 12.0 & 104.7 & 12.3 & 10.7 & 101.1 & 11.9 & 10.1 & 101.4 & 10.6 \\ \hline \(f_{\alpha c}\), \(K_{l}\), \(\epsilon_{\mu_{l}}\), & & & & & & & & & & & & & & & \\ \(K_{l}\)/\(f_{\alpha c}\), \(\tilde{F}_{\mu}\), \(\tilde{F}_{\mu}\) & 12.6 & 103.2 & 12.4 & 16.1 & 105.6 & 16.0 & 10.7 & 97.5 & 11.3 & 9.1 & 100.8 & 8.8 & 10.8 & 100.8 & 9.9 \\ \(f_{\mu}\), \(f_{\mu}\) & & & & & & & & & & & & & & & \\ \hline \(f_{\alpha c}\), \(K_{l}\), \(\epsilon_{\mu_{l}}\), & & & & & & & & & & & & & & & \\ \(K_{l}\)/\(f_{\alpha c}\), \(\tilde{F}_{\mu}\), \(\tilde{F}_{\mu}\) & 13.5 & 106.2 & 12.6 & 10.8 & 103.0 & 11.2 & 9.0 & 101.0 & 10.5 & 9.9 & 102.7 & 10.2 & 8.7 & 100.7 & 9.3 \\ \(f_{\mu}\), \(f_{\mu}\), \(f_{\
u}\) & & & & & & & & & & & & & & \\ \hline \multicolumn{13}{c}{**Bayesian Regularization**} \\ \cline{2-13}  & \multicolumn{4}{c}{**10 Neurons**} & \multicolumn{4}{c}{**15 Neurons**} & \multicolumn{4}{c}{**20 Neurons**} & \multicolumn{4}{c}{**25 Neurons**} & \multicolumn{4}{c}{**30 Neurons**} \\ \hline
**Input** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** & **AAE** & **M** & **RMSE** \\
**Variables** & **(\%)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** & **(\%)** & **(\%)** & **(MPa)** \\ \hline \(f_{\alpha c}\), \(K_{l}\), \(\epsilon_{\mu_{l}}\) & 10.7 & 102.0 & 11.2 & 10.0 added to the variable set as an independent variable due to its significance in the mechanical characteristic of FRP-confined concrete. Equation (5) presents the best composition of input variables to obtain the highest accuracy for prediction of \(f_{cc}\).