## 4 Training and Verification Data for the RNN Model  
The data required for the development of the RNN model were divided into training and verification data. Training data were used to learn and adjust the weights and biases of neural networks. Verification data were applied to the trained RNN model to substantiate whether or not the model was suitable when unknown input data were applied, and the seismic responses of the structure were to be predicted. Appropriate training and verification datasets should be prepared to develop accurate RNN simulation models for building structures having semi-active control systems. Figure 5 shows that the RNN model presents seismic responses by considering nonlinear interaction between the semi-active control devices and structures as an integrated simulation model. The acceleration, velocity, and displacement of ground motion, and command voltage sent for the MR damper were selected as inputs of the RNN model for both Examples 1 and 2 structures. Because the outputs of the previous time-step could be good reason for the outputs for the next time-step, they were also included in the inputs. In Example 1, the roof story displacement and acceleration were selected as outputs of the RNN model to evaluate the safety and serviceability of the structure, respectively. The RNN model of Example 2 provided four outputs of the 11 th inter-story drift, isolation story drift, and the roof story displacement and acceleration. Because the peak inter-story drift of Example 2 occurred at the 11 th story that was just below the isolator installed story, it needed to be included in the outputs, and was evaluated to validate the safety requirements. If the damping force of the MR damper is selected as the outputs of the RNN model as required, the control output can be easily provided by the RNN model. Table 2 shows a list of the seismic excitations used for the training and verification processes of the RNN model. The 10 ground excitations for training consisted of five historical earthquakes, and five artificial ground motions. Two artificial ground motions and one historical earthquake that were not used for training were applied to verification of the trained RNN model. Two types of ground motions, i.e., far-field and near-field, and different levels of P.G.A. were considered to increase the adaptability of the RNN model to diverse ground motions. The ground accelerations of the 13 seismic excitations listed in Table 2 were numerically integrated to generate ground velocity and displacement time histories for inputs of the RNN model. Figure 5: Input and output data of the RNN model: (**a**) RNN model for a building with semi-active TMD (Example 1); (**b**) RNN model for a building with SMIS (Example 2). The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Kanai-Tajimi shaping filter that is a viscoelastic Kelvin-Voigt unit (a spring in parallel with a dashpot), carrying a mass that is excited by a white noise [36]. The Kanai-Tajimi shaping filter [37] presented in Equation (1) was used to generate the seven artificial earthquakes in Table 2:  
\[F(s)=\frac{2\zeta_{g}\omega_{g}s+\omega_{g}^{2}}{s^{2}+2\zeta_{g}\omega_{g}s+ \omega_{g}^{2}}, \tag{1}\]  
where, \(\omega_{g}=17\) rad/s, \(\zeta_{g}=0.3\). After generating Gaussian white noise with a time-step of 0.005 s and PGA of 0.7\(\times\)_g_, the signal was filtered by passing it through the shaping filter, to give the filtered signal the characteristics of realistic earthquakes. The envelope presented in previous study [38] was used to make a more practical ground motion. Figure 6a shows one (EQ No. 6 in Table 2) of the developed seven artificial earthquakes. Inputs of training and verification data included the command voltage for the MR damper, as well as ground motions. For generation of the random command voltage data with the time-step of 0.005 s, a series of 6000 random numbers were generated to have a duration of 30 s between (\(-1\) and \(1\)).