## 3 Results  
In this study, four different soft computing techniques, i.e., RBNN, ANFIS-SC, ANFIS-FCM and M5 Tree, are employed for predicting strength (\(f^{\prime}_{cc}/f^{\prime}_{co}\)) and strain (\(\epsilon_{cc}/\epsilon_{co}\)). For the model simulations, a MATLAB neural network and fuzzy tool boxes are used, and 519 experimental data are adopted from [PERSON] and [PERSON] [48; 49]. Figure 3 shows the usual test setup for confined cylinders. Also, the statistical analyses of the input data employed in this study are summarized in Table 1. The data are used to develop models for ultimate strength and strain based on the strain ratio (\(\rho_{c}\)) and the confinement stiffness ratio (\(\rho_{K}\)) inputs, which are defined as follows [48]:  
Figure 2: M5 tree; splitting the input space into subspaces and the resultant diagram [47]. \[f_{l}=\rho_{K}\rho_{\varepsilon}f^{\prime}_{co}=\frac{2E_{f}\varepsilon_{h,rup}t}{D} \tag{5}\]  
\[\rho_{K}=\frac{2E_{f}t}{({f^{\prime}}_{co}/\varepsilon_{co})D} \tag{6}\]  
\[\rho_{\varepsilon}=\frac{\varepsilon_{h,rup}}{\varepsilon_{co}} \tag{7}\]  
In the equations, \(f^{\prime}_{co}\) is the unconfined concrete strength, \(\varepsilon_{co}\) is the corresponding axial strain of \(f^{\prime}_{co}\), \(E_{f}\) is the elastic modulus of the FRP wrap in the hoop direction, \(t\) is the total thickness of the FRP wrap, \(\varepsilon_{h,rup}\) is the actual hoop rupture strain of the FRP wrap, and \(D\) is the diameter of the concrete core. The confinement ratio (\(f_{l}/f^{\prime}_{co}\)) is a frequently used parameter in existing confinement models, which is equal to the product of \(\rho_{K}\) and \(\rho_{\varepsilon}\). Several equations have been proposed for estimating the strain and strength of FRP-confined concrete cylinders which depend on \(\rho_{K}\) and \(\rho_{\varepsilon}\)[9; 48]. According to [PERSON] et al. [11], instead of the more approximate value of 0.002 for \(\varepsilon_{co}\), it is assumed as follows:  
\[\varepsilon_{co}=9.37\times 10^{-4}\sqrt[4]{f^{\prime}_{co}},\ \ f^{\prime}_{co}\ in\ MPa \tag{8}\]  
The data set is randomly grouped into two subsets; the first data set is adopted for training, and the second data set (20% of the whole database) is adopted for the testing stage. Before application of the RBNN, the training values of input and output are normalized between 0.2 and 0.8 as follows:  
\[b_{1}\frac{x_{i}-x_{\min}}{x_{\max}-x_{\min}}+b_{2} \tag{9}\] \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **D** & **t** & \(f^{\prime}_{co}\) & \(f^{\prime}_{cc}\) & \(\varepsilon_{co}\) & \(\varepsilon_{cc}\) & \(\varepsilon_{h,rup}\) & \(\rho_{\varepsilon}\) & \(E_{f}\) & \\  & **(mm)** & **(mm)** & **(MPa)** & **(MPa)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(GPa)** & **(GPa)** & **(GPa)** \\ \hline Min. value & 51.00 & 0.09 & 19.70 & 31.40 & 0.20 & 0.23 & 0.10 & 0.29 & 10.50 & 0.01 \\ Max. value & 406.00 & 7.26 & 188.20 & 372.20 & 0.35 & 6.20 & 4.98 & 23.03 & 662.50 & 0.68 \\ Average & 158.46 & 0.89 & 46.52 & 83.88 & 0.24 & 1.68 & 1.12 & 4.80 & 183.09 & 0.07 \\ Standard deviation & 52.74 & 1.06 & 27.05 & 42.18 & 0.03 & 1.05 & 0.53 & 2.44 & 124.73 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics for the experimental data. Figure 3: Test setup and instrumentation [50]. In the equation, \(x_{\text{max}}\) and \(x_{\text{min}}\) are the maximum and minimum values of the training data. Here values of 0.6 and 0.2 are respectively assigned for \(b_{1}\) and \(b_{2}\), and the input data are normalized within a range of 0.2 to 0.8, as recommended in Cigizoglu [51]. According to that study, input parameters ranging from 0.2 to 0.8 allow the artificial neural network the flexibility to appraise beyond the training range. The applied models are compared with the mean absolute relative error (MARE), root mean square error (RMSE) and determination coefficient (\(R^{2}\)).