## 5 Conclusions  
This study explored the possibility of using an ANN-based method to rapidly determine the seismic performance of RC columns, as well as the development of the LP model for them. An ANN model was established and validated based on the large database of 1163 cyclic tests of RC columns to predict the strength and the yielding, capping and ultimate deformation capacities, which are critical for the commonly-used LP model. The following conclusions are drawn:  
1. On the basis of a large historical experimental database and advanced humanlike information processing algorithm, the proposed model-free method in this study can rapidly get more accurate input parameters for any bilinear and tri-linear LP model than current explicit formulas. The accuracy of the proposed method can also have been improved with the increment of the sample quantity of the database. 2. The validation results through both the collected experimental data and several existing functions indicate that the ANN-based method can be effectively used to predict the most important characteristics of RC columns, which are also critical for the further modeling of structures. In addition, another advantage of the proposed model-free method is that the quantity of the input features could be easily changed according to the requirement of an arbitrary multi-linear model. 3. The ANN-based LP model can help reduce the subjective and experimental errors. The prediction results of the RC frame structures using the well-trained ANN-based LP model show a good agreement with both the quasi-static and shaking table test results, especially for the pre-collapse stage. Thus, the model-free method based on the machine learning theory will be an innovative and promising approach for a fast seismic performance evaluation of the buildings and bridges in the future. Thus, the model-free method based on the machine learning theory (e.g., ANN method) can be used as a promising surrogate for the rapid seismic performance evaluation of the buildings and bridges in the future. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Parameters** \\ \hline ANN model & \(F_{\text{max}}=36.62\) kN, \(\delta_{u}=4.53\%\), \(\delta_{c}=1.85\%\), \(\delta_{y}=0.99\%\) \\ \hline Bi-linear model & \(K_{e}=2720\) kN-m/rad, \(M_{y}=26.92\) kN-m, \(b=0.0494\) \\ \hline Tri-linear model & \(K_{e}=2720\) kN-m/rad, \(M_{y}=26.92\) kN-m, \(\beta_{l}=0.203\), \(\beta_{c}=-0.087\), \(M_{c}/M_{y}=1.17\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANN-based method for the LP model of RC column sample S2 [43]. Figure 15: Drift response comparison of the frame obtained from test and ANN-based LP model: (a) Ground motion record; and (b) drift response. **Supplementary Materials:** The well-trained ANN-based model for the LP parameters of RC columns has been already implemented in an efficient Matlab GUI, which is available for the users, including both of the researchers and engineers to quickly evaluate the seismic performance of RC columns as well as RC structures. Anyone who is interested in the ANN-based LP model of RC column in this study may contact the author or download the program from the following address: [[https://www.dropbox.com/s/8](https://www.dropbox.com/s/8) aq3 qreiochn26o/ANNLPGLzip?dl=0]([https://www.dropbox.com/s/8](https://www.dropbox.com/s/8) aq3 qreiochn26o/ANNLPGLzip?dl=0). **Author Contributions:** [PERSON] collected the test database, developed the ANN model and wrote the manuscript. [PERSON] contributed to the idea of the study, modified the computer program and supervised and verified the manuscript. **Funding:** This research was funded by the National Key Research and Development Program of China (2018 YFC0809404 and 2016 YFC0701107) and the National Natural Science Foundation of China (51725801). **Conflicts of Interest:** The authors declare no conflict of interest. * _[PERSON] et al. (1994)_ [PERSON]; [PERSON]; [PERSON] Seismic shear strength of reinforced concrete columns. _J. Struct. Eng._**1994**, _120_, 2310-2329.