## 4 Results and Discussion
### Validation
It has been widely used in the seismic performance assessment in engineering ([PERSON] et al., 2017)  
\[M_{c}/M_{y}=(1.25)(0.89)^{n}(0.91)^{0.01/r_{c}^{\prime}} \tag{10}\]  
\[M_{y}=BD^{3}\phi_{y}\Bigg{\{}E_{c}\frac{k_{y}^{2}}{2}\bigg{[}0.5(1+\delta^{ \prime})-\frac{k_{y}}{3}\bigg{]}+\frac{E_{s}}{2}\bigg{[}\big{(}1-k_{y}\big{)} \rho+\big{(}k_{y}-\delta^{\prime}\big{)}\rho^{\prime}+\frac{\rho_{\text{ \tiny{$\circ$}}}}{6}(1-\delta^{\prime})\bigg{]}(1-\delta^{\prime})\Bigg{\}} \tag{11}\]  
where \(\phi_{y}\) is the yield curvature; \(\delta^{\prime}\) is the ratio of the distance of the compression reinforcement center from the extreme compression fibers to the span depth (\(D\)); \(k_{y}\) is the normalized compression zone depth; \(E_{s}\) is the reinforcement elastic modulus; \(\rho\), \(\rho^{\prime}\) and \(\rho_{\text{\tiny{$\circ$}}}\) are the reinforcement ratios of tension, compression and web reinforcement, respectively. Figure 7 shows a comparison of the experimental results, predicted strength of the ANN model and calculated results from the explicit formula. In Figure 7a, the test results of the shear-failed specimens were obtained using the formula by ([PERSON] et al., 2017), while the flexural failure specimens were selected from the database of this study. As shown in Figure 7a, the mean absolute error of the predicted shear strength of the ANN model is 0.107, which is smaller than those obtained from the three explicit formulas, 0.235, 0.207 and 0.217. In Figure 7b, it can also be observed that the mean absolute error of the ANN model is 0.087. However, the statistical result of the mean absolute error obtained from the design code is 0.101. It is illustrated that the results indicate that the ANN model yields a more accurate prediction of the structural strength of the columns. Figure 8 also shows a comparison of the test results of the ultimate drift of the column, and predicted results from the ANN model. It can be observed that the ANN model can also achieve a reasonable prediction of the ultimate drift. However, it is evident that the mean absolute error of the ultimate drift is larger than that of the strength prediction, particularly for specimens with large ultimate deformation capacity. The mean absolute error and goodness of fit are found to be 0.1761 and 0.8114, respectively, for the training set, and 0.1783 and 0.8216 for the test and validation set, respectively. This is because the ultimate deformation of the column is more strongly affected by the nonlinearity of the structures. Another reason for there being less accuracy is that the ultimate deformation is more difficult to measure. Figure 7: Comparison of the predicted results of the strength from the ANN model and existing explicit formulas. To assess the ultimate deformation of lightly reinforced columns, [PERSON] et al. [6] proposed an explicit formula given as follows:  
\[\frac{\Delta_{u}}{L}=\frac{3}{100}+4\rho_{t}-\frac{1}{40}\frac{F_{\text{max}}}{A_ {\text{c}}\sqrt{f_{c}^{\prime}}}-\frac{n}{40}\geq 1\%(\text{MPa}) \tag{12}\]  
where the effects of the transverse reinforcement ratio (\(\rho_{t}\)), axial load ratio (\(n\)) and strength (\(F_{\text{max}}\)) are taken into account. Furthermore, [PERSON] et al. [41] also developed an explicit method to evaluate the ultimate drift of flexural-dominated columns as follows:  
\[\frac{\Delta_{u}}{L}=\frac{\Delta_{y}}{L}+\frac{\Delta_{sp}}{L}+\frac{\Delta_{ f}}{L} \tag{13}\]  
where \(\Delta_{y}\), \(\Delta_{sp}\) and \(\Delta_{f}\) are the yield, slip and flexural displacement, respectively. The above explicit formulas for calculating the ultimate drift were also used to validate the accuracy and effectiveness of the ANN model. Figure 9 shows a comparison of results obtained from the formula methods and test results from the collected test database, which are divided into two parts, namely the shear-failed specimens and the flexural-dominated specimens. It can be observed that the ANN model also yields better prediction of the ultimate drift than the two explicit formulas.