# A Proposed Soft Computing Model for Ultimate Strength Estimation of FRP-Confined Concrete Cylinders
## 5 Comparison of the Proposed Strength Model with Existing Empirical Ones  
Five known models are selected [12, 13, 15, 16, 18, 56] to verify the proposed formula. It must be noted that no formula has been proposed in the most recent available publication [55]. The formula proposed in this paper can be implemented in a calculator, while, in the case of the neuro-fuzzy, neural network, multivariate adaptive regression splines and M5 model tree techniques (all considered in [55]), a computer and professional programs should be used.  
Figure 12 shows the values of the compressive strength of the FRPCCC obtained by the proposed and existing formula versus the experimental values. Table 1 in the Appendix section shows the experimental data that have been used to judge the ability of different methods. In fact, for all formulas,  
Figure 11: The correlation coefficient of the predicted data by optimized ANN structure and training data.  
the same data are applied to forecast the compressive strengths of the FRPCCC. Figure 12 shows that the presented formula can estimate the compressive strengths of the FRPCCC with a higher precision compared to the existing formulas.  
The mean percentage of error, correlation coefficient, root mean square error (RMSE), and average absolute error (AAE) for the studied methods are shown in Table 4 to verify the efficiency of the proposed method. Based on this table, it should be noted that the mean percentage of error and the correlation coefficient for the proposed method are equal to 3.49% and 0.9809, respectively. Meanwhile, the corresponding values for other existing methods are equal to over 13% and 0.41, respectively. This means that, for the proposed formula, more than 96% of the simulated results are entirely consistent with the experimental ones. Furthermore, the minimum values of RMSE and AAE are obtained for the proposed formula. Therefore, it should be pointed out that the proposed formula is very accurate compared to other existing ones, for which the accuracy is lower than 85%.  
Based on Figures 11 and 12, as well as Table 4, it is evident that the proposed formula has a good agreement with the actual values. Therefore, it can be used in the practical projects to evaluate the amount of column compressive capacity reinforced by FPR sheets in the initial design. It should be noted that the collected data (see Appendix A) are for different types of FRP sheets (carbon, aramid, and glass) and the FFBPNN method has been trained and tested with these data. Therefore, the proposed  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **[PERSON]** & **[PERSON] and** & **[PERSON]** & **[PERSON] et** & **[PERSON] and** & **[PERSON]** & **Proposed** \\
**Error** & **et al. [16]** & **[PERSON] [13]** & **et al. [15]** & **al. [12]** & **[PERSON] [18]** & **et al. [56]** & **Formula** \\ \hline Mean percentage & 17.77\% & 16.95\% & 13.14\% & 17.59\% & 15.42\% & 8.44\% & 3.49\% \\ of error & & & & & & & \\ RMSE & 31.83 & 14.96 & 13.95 & 31.20 & 20.64 & 12.86 & 3.99 \\ AAE & 0.28 & 0.15 & 0.14 & 0.25 & 0.18 & 0.11 & 0.035 \\ correlation coefficients & 0.6813 & 0.7897 & 0.8064 & 0.6835 & 0.7288 & 0.7686 & 0.9809 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between different studied models.  
Figure 12: Comparison between simulated and experimental results for the compressive strength of FRPCCC.  
formula can estimate the ultimate compressive capacity of FRP-confined concrete cylinders with a different type of FRP and arbitrary thickness.