## 6 Analysis Results and Discussion
### The Feasibility of the Predicted Database by the Proposed ANN Model  
The 1080 numerical results calculated by FE simulation are compared with the predicted database of the ANN model in the logarithmic space, as shown in Figure 14. With regard to the correlation from the simple linear regression, the values predicted by the ANN model are strongly associated with the calculated values of the FE dynamic analysis of the CFHT, as shown in Figure 14. In general, the higher the correlation coefficient between the predicted database and the simulation database, the better the ability of the ANN model to predict the structural response. Meanwhile, the statistical distribution characteristics of the structural response for the ANN model and simulation results are studied, as shown in Figure 15. In this figure, the purple rectangle represents the relative frequency of SDIs, and the orange curve is the final result of the Gaussian function fitting. It can be found that the distribution of the predicted EDP of the CFHT under the ANN model has a slight difference from the target database. The difference in the corresponding mean value and the standard deviation is 0.01, which means that the proposed ANN model can predict the nonlinear behavior of CFHTs during low-strength and high-strength seismic events.  
To further demonstrate the application of the ANN model in seismic performance assessment, the PSDM of the traditional seismic vulnerability analysis is utilized to derive the statistical seismic IM-demand measure relation, as shown in Figure 16. It can be seen from Figure 16 that the correlation coefficient of the PSDM from the FE simulation data is 0.86, showing a better correlation between the targeted database and PGV. Mathematically, the higher the correlation coefficient between the PGV and EDP, the better the ability of the PGV to explain the EDP and to decrease the uncertainty induced by seismic events. For the predicted database, the correlation coefficients (R\({}^{2}\) = 0.90) of the PSDM between the PGV and EDP are significantly larger than that of the PGV and FE simulation EDP. In other  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **Seismology Features** & **Database** & **RMSE** & **MSE** & **MAE** & **R\({}^{2}\)** \\ \hline \multirow{2}{*}{Case 1} & \multirow{2}{*}{PGV} & Train & 0.34 & 0.11 & 0.23 & 0.81 \\  & & Test & 0.34 & 0.11 & 0.24 & 0.81 \\ \hline \multirow{2}{*}{Case 2} & \multirow{2}{*}{PGV and Vrms} & Train & 0.32 & 0.10 & 0.22 & 0.84 \\  & & Test & 0.33 & 0.11 & 0.24 & 0.82 \\ \hline \multirow{2}{*}{Case 3} & \multirow{2}{*}{Peak values (PGA, PGV, PGD)} & Train & 0.29 & 0.09 & 0.21 & 0.86 \\  & & Test & 0.30 & 0.09 & 0.22 & 0.86 \\ \hline \multirow{2}{*}{Case 4} & \multirow{2}{*}{Amplitude} & Train & 0.24 & 0.06 & 0.17 & 0.91 \\  & & Test & 0.22 & 0.05 & 0.16 & 0.92 \\ \hline \multirow{2}{*}{Case 5} & \multirow{2}{*}{Integral} & Train & 0.47 & 0.22 & 0.37 & 0.66 \\  & & Test & 0.46 & 0.21 & 0.36 & 0.65 \\ \hline \multirow{2}{*}{Case 6} & \multirow{2}{*}{Frequency content} & Train & 0.37 & 0.13 & 0.27 & 0.80 \\  & & Test & 0.33 & 0.11 & 0.24 & 0.79 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of RMSE, MSE, MAE, and R2 for the training and testing datasets under different seismology features.  
words, the ANN model has sufficient potential and reliability to bridge the gap between the PGV and EDPs for structural performance assessment. Moreover, the efficiency (\(\beta_{EDP|IM}\)) of the PSDM related to the PGV and EDP is displayed in Figure 16b. With the consideration of the ANN model and FE simulation, it can be found that the PSDM developed by the predicted database presents better efficiency, \(\beta_{EDP|IM}=0.34\), than the target database, \(\beta_{EDP|IM}=0.39\). Obviously, the ANN model has the potential to reduce the computational costs and develop appropriate PSDMs for the CFHT.