## 3 Sample Building Structure and Seismic Excitation  
As explained previously, the Shiodome Sumitomo building [20] was used in this study as a sample building structure to construct the environment of reinforcement learning. Figure 5 presents the framing elevation of the 125.9 m tall sample building having 26 stories. A seismic insolation system is installed between the 11 th and 12 th stories. The nonlinear passive hysteretic dampers in the Shiodome Sumitomo building were changed to MR dampers in the SMIS of the sample structure. Rubber bearings were directly used in the SMIS of the sample building. Figure 5 shows the analytical model of the sample building with the SMIS. One horizontal degree-of-freedom (DOF) per story was used for this analytical model. Table 1 presents the stiffnesses and masses of the sample structure that were adopted from a previous study [20]. The damping matrix was calculated by the conventional methods of Rayleigh damping. The damping ratio of the sample building was set to be 2%, and that of the seismic isolation interface was 0%. The natural periods of vibration of the first three modes were calculated as 6.04, 1.17, and 0.96 s, respectively. Figure 4: Target network separation. Figure 5: Sample building structure with a mid-story isolation system: (**a**) elevation of the Shiodome Sumitomo building [20], (**b**) analytical model with SMIS. The Bouc-Wen model [29] was used to represent the MR damper as shown in Figure 5b. The MR damper force is calculated by the following simultaneous differential equations:  
\[f=c_{0}\dot{x}+\alpha z \tag{3}\]  
\[\dot{z}=-\gamma\big{|}\dot{x}\big{|}z\big{|}z\big{|}^{n-1}-\beta\dot{x}\big{|}z \big{|}^{n}+A\dot{x} \tag{4}\]  
where \(\dot{x}\) is the velocity of the damper piston, \(c_{0}\) is the viscous damping of the device, and \(z\) is the evolutionary variable that describes the history dependence of the response. The variables \(\gamma\), \(\beta\), \(n\), and \(A\) define the model shape in the unloading and the smoothness of the hysteretic behavior, representing the transition from the pre-yield to the post-yield region. The parameters \(\alpha\) and \(c_{0}\) in Equation (3) are defined as functions of the applied voltage \(v\) as follows:  
\[\alpha=\alpha_{a}+\alpha_{b}u \tag{5}\]  
\[c_{0}=c_{0a}+c_{0b}u \tag{6}\]  
\[\dot{u}=-\eta(u-v) \tag{7}\]  
where \(u\) is the control input defined by the first-order filter that accounts for the dynamics of the MR damper; \(v\) is the command voltage; and \(\eta\) is the time constant of this first-order filter. The parameters \(\alpha_{a}\), \(\alpha_{b}\), \(c_{0a}\) and \(c_{0b}\) account for the dependence of the damper force on command voltages applied magnetic current. The selected MR damper parameters are as follows: \(\alpha_{a}\) = 5.5319 \(\times\) 10\({}^{5}\) N/cm, \(\alpha_{b}\) = 2.5246 \(\times\) 10\({}^{6}\) N/(cmV), \(c_{0a}\) = 22.39 Ns/cm, \(c_{0b}\) = 223.9 Ns/(cmV), \(n\) = 1, A = 1.2, \(\gamma\) = 3 cm\({}^{-1}\), \(\beta\)= 3 cm\({}^{-1}\), and \(\eta\) = 50 s\({}^{-1}\). These parameters were adjusted from the parameter values of an experimental study [30] to make the maximum force of the MR damper about 2750 kN, with a saturation voltage of 5 V. The value of 2750 kN was determined based on a parameter study, and 10 MR dampers were used to make the SMIS of the sample building for optimal seismic control. The control voltage for the MR damper changes within the range of 0 and 5 V. Figure 6 shows typical displacement-force and velocity-force hysteresis loops for this MR damper model. The resisting force of the MR damper is proportional to the velocity and applied command voltage as shown in the figure. The ground acceleration was modeled as an excitation by a filtered Gaussian process. The Kanai-Tajimi shaping filter is widely used to make an artificial ground motion because it can successfully describe features of seismic ground motions [31].