## 5 Performance Evaluation of the RNN Simulation Model
However, the increment of the average correlation coefficients gradually decreased with the increment of the hidden layer size. The simulation results show that compared to the sequence length, the size of the hidden layer had a greater effect on the accuracy of the RNN prediction model. Figure 7 presents the RMSE variation of the verification data according to epoch. When the size of the hidden layer was greater than 10, similar results could be seen in the figure. After about 500 training epochs, the RMSE values of the RNN model with more than 10 hidden layers were hardly changed. The three most common types of recurrent neural networks are vanilla RNN, LSTM, and gated recurrent units (GRU) [30]. The simulation results of Example 1 show that the errors of the LSTM and GRU RNN models were almost similar, presenting an accuracy that was improved by about 6% compared to Vanilla RNN. In order to evaluate the prediction performance of the trained RNN model, Figures 8-10 compare the predicted seismic response time histories of verification data with those of the FE model. The hyperparameter values and functions in Table 3 were used to evaluate the RNN model, except the hidden layer size of 20. Three earthquake loads and command voltages that were not used for training were applied to the trained RNN model. The average RMSE value for all the six seismic responses, i.e., displacement and acceleration responses due to three earthquakes, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sequence Length** & **Average Loss** & **Average RMSE** & **Average CC** \\ \hline
1 & 2.648 & \(11.490\times 10^{-3}\) & 0.988597 \\
2 & 2.317 & \(9.408\times 10^{-3}\) & 0.995088 \\
5 & 2.273 & \(8.623\times 10^{-3}\) & 0.995840 \\
6 & 2.248 & \(8.141\times 10^{-3}\) & 0.995981 \\
7 & 2.496 & \(8.925\times 10^{-3}\) & 0.995625 \\
10 & 2.535 & \(9.279\times 10^{-3}\) & 0.995115 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Effect of sequence length on accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hidden Layer Size** & **Average Loss** & **Average RMSE** & **Average CC** \\ \hline
2 & 6.207 & \(19.516\times 10^{-3}\) & 0.974948 \\
5 & 2.263 & \(8.509\times 10^{-3}\) & 0.995678 \\
10 & 1.278 & \(6.733\times 10^{-3}\) & 0.996786 \\
15 & 1.004 & \(6.561\times 10^{-3}\) & 0.996964 \\
20 & 0.769 & \(6.053\times 10^{-3}\) & 0.997070 \\
30 &  
The same hyperparameter values and functions applied to Example 1 were used to evaluate the prediction performance of the RNN model trained for Example 2. Because the outputs of the RNN model for Example 2 were four seismic responses, Figures 11-13 compare four response time histories predicted by the RNN model with those of the FE model. It is evident that the predicted responses were very close to the target responses of the FE model. Note that the trained RNN model shows a stable prediction performance for ground motions having different characteristics, despite the peak top story displacement of Jiji earthquake (1999), i.e., the verification earthquake No. 13, being almost 10 times greater than that of the other two artificial earthquakes, i.e., the verification earthquakes Nos. 11 and 12. The average RMSE values for four seismic responses of three verification data from EQ No. 11-13 in Table 2 were \(1.232\times 10^{-3}\), \(1.103\times 10^{-3}\) and \(5.249\times 10^{-3}\), respectively. Figure 11: Comparison of the time history responses of Example 2 between FEM and RNN models (EQ No. 11): (**a**) 11 th story drift time history; (**b**) Isolation story drift time history; (**c**) Top story displacement time history; (**d**) Top story acceleration time history. Figure 10: Comparison of time history responses of Example 1 between FEM and RNN models (EQ No. 13): (**a**) Displacement time history; (**b**) Acceleration time history. Figure 12: Comparison of the time history responses of Example 2 between FEM and RNN models (EQ No.