## 5 Performance Evaluation of the RNN Simulation Model
12): (**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 13: Comparison of the time history responses of Example 2 between FEM and RNN models (EQ No. 13): (**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. In order to grasp the difference between the FE model and the RNN model more closely, the response errors between two models, namely the FE model responses minus the RNN model responses, were calculated. The response difference time histories between the FE model and the RNN model for Example 1 subjected to an artificial ground motion are presented in Figure 14. Figure 15 shows the different time histories of four outputs of Example 2 subjected to a historical earthquake. It can be seen from the figures that the differences between the FE model and the RNN model increase when the seismic responses of the structure increase. Root Mean Square Error (RMSE) is the standard deviation of the prediction errors. Because the peak responses in the seismic analysis are very important values for the structural design process, it would be desirable that the objective function for optimization of the RNN model should consider not only the commonly used RMSE but also the maximum prediction errors. Figure 14: Response error time histories of Example 1 (EQ No. 11): (**a**) Displacement error time history; (**b**) Acceleration error time history. Figure 15: Response error time histories of Example 2 (EQ No. 13): (**a**) 11 th story drift error time history; (**b**) Isolation story drift error time history; (**c**) Top story displacement error time history; (**d**) Top story acceleration error time history. Figure 16 shows the variation of loss and RMSE values according to epoch for Example 2. The wiggle shown in the loss and RMSE graphs is usually related to the batch size. When the batch size is the full dataset, the wiggle will be minimal. The figure represents that the loss of training process consistently decreased. On the other hand, the RMSE value decreased until about 2000 epochs, but increased after that. This means that overfitting started at around 2000 epochs. Therefore, variation of the verification error should be monitored to avoid overfitting of the RNN model. The averages of computational times for 10 simulation runs of the FE model were 23.38 and 45.87 s for Examples 1 and 2, respectively. If the time-step of numerical integration is too large, the nonlinear equation solver fails to converge. Therefore, the time-step of 0.001 s, which was the maximum time-step for stable analyses of all the ground motions, was employed for FE model analysis using Matlab. The computational times of 0.0130 and 0.0142 s for Examples 1 and 2, respectively, were calculated from the average of 10 simulation runs for the RNN model. The ratios of simulation time of the RNN model to the FE model were 0.06 and 0.03% for Examples 1 and 2, respectively. Compared to the FE model, the RNN model could greatly reduce simulation time, and provide very accurate results. Because the computational time difference between the RNN models was trivial, the larger the FE model, the more effective the RNN model. When designing a control algorithm for a semi-active control system, it is necessary to perform many numerical simulations. Using the RNN model, the simulation runs of 1798 and 3230 for Examples 1 and 2, respectively, could be carried out; while using the FE model, only one simulation could be executed. This means that when a soft computing-based optimization algorithm is applied to the design of a semi-active control system, the RNN model can allow a far larger search area to be explored. Therefore, the proposed RNN model can be an efficient means for the numerical simulation of a building structure with a semi-active control system.