## 6 Conclusions  
In this paper, for accurately estimating the dynamic mechanical behaviors of RC column members, predictive models of the dynamic modified coefficient (\(DMC\)) were developed based on the random forest method and a numerical model database. The main conclusions are summarized as follows:  
Figure 15: Validation results of \(DMC\) models using available dynamic loading test data.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{\(SRI\) (Total)} & \multicolumn{2}{c}{\(SRI\) = 4} & \multicolumn{2}{c}{\(SRI\) = 3} & \multicolumn{2}{c}{\(SRI\) = 2} \\ \cline{2-9}  & \(\mathbf{R^{2}}\) & \(MSE\) & \(\mathbf{R^{2}}\) & \(MSE\) & \(\mathbf{R^{2}}\) & \(MSE\) & \(\mathbf{R^{2}}\) & \(MSE\) \\ \hline \(DMC_{F_{y}}\) & 0.67 & 0.01 & 0.61 & 0.01 & 0.70 & 0.02 & 0.61 & 0.01 \\ \(DMC_{F_{x}}\) & 0.77 & 0.03 & 0.69 & 0.02 & 0.82 & 0.03 & 0.77 & 0.03 \\ \(\mu\) & 0.70 & 0.02 & 0.61 & 0.02 & 0.75 & 0.02 & 0.68 & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Evaluation results of \(DMC\) model precision.  
By training a large number of data using the random forest method, the _DMC_ predictive models of yielding capacity, ultimate capacity and ductility coefficient for RC columns were developed. Accuracy of the proposed models has been verified using the reserved 20% data and experimental data. Given the structural design parameters as inputs, the proposed models can be used to rapidly evaluate the dynamic mechanical behaviors of RC columns under seismic loading rates.
2. The numerical model of RC columns was established by dynamic modification to different deformation sub-elements. It can provide accurate and effective simulated results of the dynamic mechanical behaviors of RC columns, making up for the deficiency of insufficient test data. By comparing the simulated hysteretic curves using numerical models with different complexities, the necessity of incorporating shear and bond-slip sub-elements and dynamic modification was revealed.
3. By analyzing the feature importance, it was found that the shear span ratio was the most important factor affecting the _DMC_ models, followed by the stirrup spacing and the concrete compressive strength. For the three _DMC_ models, differences were found as to the order of the 4 th to 6 th important features. The results of feature importance were dependent on the training data; however, it provided a reference to measure the contribution of input parameters to the results of the developed predictive models.
4. In future research works, the accuracy of predictive models can be improved by distinguishing different failure modes of RC columns and the machine learning method can be improved to develop explainable predictive models. For dynamic analysis of structural systems considering the change in strain rate, a program of real-time dynamic modification to constitutive models of deformation sub-elements needs to be developed. Moreover, the proposed numerical model and method can be applied to other types of structural members.  
Conceptualization, R.-H.L.; methodology, R.-H.L., M.-Y.L. and X.-Y.Z.; software and validation, M.-Y.L. and X.-Y.Z.; resources and writing--original draft preparation, R.-H.L. and X.-W.Z.; review and editing, R.-H.L.; visualization, M.-Y.L. and X.-Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number No. 52108438) and the Open Fund of National Center for International Research of Subsea Engineering Technology and Equipment grant number No. 3132023362.  
The data supporting the conclusions of this article will be made available by the authors on request.  
The authors express great thanks to [PERSON] (an engineer from the Northeast Branch of China Construction Eighth Engineering Bureau Division Corp. Ltd.) for providing valuable technical support in completing this research work.  
The authors declare no conflict of interest.