## 5 Predicted Results Using the Model
### Validation of DMC Models  
Figure 13 shows the validation results of \(DMC\) models in terms of the yielding bearing capacity, the ultimate bearing capacity and the ductility coefficient, respectively. The prediction points marked by the red triangle and the y = x line denoted by the dash line are plotted in the figure. If the predicted value was exactly the same as the actual value, the point is on the y = x line. In other words, the closer the point was to the y = x line, the more accurate was the predicted result. From the distribution of the scatter plots, it can be observed that the predicted points are distributed around the y = x line, indicating that the developed \(DMC\) models were capable of predicting the influences of dynamic effect on the mechanical behavior parameters, i.e., the yielding bearing capacity, the ultimate bearing capacity and the ductility coefficient of RC columns.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(DMC\) Model} & \multicolumn{6}{c}{**Ranking of Feature Importance**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{2}{*}{\(DMC_{F_{y}}\)} & \(\lambda\) & \(S\) & \(f_{c}^{\prime}\) & \(n_{0}\) & \(f_{y}\) & \(SRI\) \\  & 0.2896 & 0.2264 & 0.1374 & 0.1247 & 0.1147 & 0.1071 \\ \hline \multirow{2}{*}{\(DMC_{F_{m}}\)} & \(\lambda\) & \(S\) & \(f_{c}^{\prime}\) & \(SRI\) & \(n_{0}\) & \(f_{y}\) \\  & 0.2585 & 0.2147 & 0.1908 & 0.1485 & 0.1158 & 0.0717 \\ \hline \multirow{2}{*}{\(DMC_{\mu}\)} & \(\lambda\) & \(S\) & \(f_{c}^{\prime}\) & \(n_{0}\) & \(SRI\) & \(f_{y}\) \\  & 0.3691 & 0.2008 & 0.1369 & 0.1137 & 0.0950 & 0.0845 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Results of feature importance and ranking.  
Figure 12: Feature importance of the developed \(DMC\) models.  
To further verify the model accuracy, the developed models were employed to predict the _DMC_ values in terms of the yielding capacity, the ultimate capacity and the ductility coefficient (i.e., \(DMC_{F_{y}}\), \(DMC_{F_{u}}\) and \(DMC_{\mu}\)) of RC columns at three levels of strain rate, i.e., \(10^{-3}\)/s, \(10^{-2}\)/s and \(10^{-1}\)/s, respectively, as shown in Figure 14. It was found that the predictive models provided good estimated results of the _DMC_ values at different strain rate levels.  
Moreover, the effectiveness of the developed models was verified by the test results of 13 RC column specimens from available dynamic loading experiments [9]. Figure 15 shows the comparison results of measured and predicted _DMC_ values. It is noted that the test strain rate of the longitudinal reinforcement was used to obtain the strain rate index. The  
Figure 14: Validation results of _DMC_ models at different strain rate levels.  
Figure 13: Validation results of the developed _DMC_ models.  
R-square and the mean square error were 0.72 and 0.003 for the predictive model of \(DMC_{F_{y}}\), 0.76 and 0.001 for the predictive model of \(DMC_{F_{x}}\), 0.68 and 0.001 for the predictive model of \(DMC_{\mu}\), respectively. By taking the structural design parameters and the calculated \(SRI\) of each column specimen as inputs, it was found that the predictive models developed by the random forest method provided accurate results estimating the change in yielding and ultimate bearing capacity and ductility coefficient of column members under different seismic loading rates.