## 5 Experimental Validation  
### Experimental Setup  
The machine learning based optimal control performance was evaluated by conducting shake table testing in the small-scale structural laboratory located in National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan [21]. Figure 11 shows the experimental setup. A single-degree-of-freedom (SDOF) shear building specimen made of aluminum alloy was designed and fabricated for experimental validation. The weight of the specimen was 450 N. The AMD installed on the top of specimen was composed of an AC motor, a guide screw, and a mass block. The weight of the mass block was 20 N, which was 4.4% weight of the specimen. The entire structural system was fixed on a rigid bottom plate, which was installed on the rigid platen of a shake table. The shake table was driven by a dynamic servo-hydraulic actuator with maximum stroke and force capacity of \(\pm\)127 mm and \(\pm\)15 kN, respectively. The dimension of the rigid platen made of aluminum was 1000 \(\times\) 800 mm. An MTS FlexTest(r) Controller FT-100 digital controller, manufactured by MTS Systems Corporation, Eden Prairie, MN, USA was used to control the actuator using a proportional-integral-derivative control algorithm. An analog controller converted voltage into current was used to control the torque of the motor. Three high-resolution MEMS accelerometers manufactured by Silicon Designs, Inc., Kirkland, WA, USA were installed on the bottom rigid plate connected to the shake table, the roof of specimen, and the mass block to measure the absolute acceleration. Each accelerometer was able to measure a range of acceleration of \(\pm\)20 m/s\({}^{2}\). Note the control force of AMD was obtained by multiplying the mass of the mass block by the absolute acceleration measured from the accelerometer. Meanwhile, a Temposonics GH linear-position sensor, manufactured by MTS Systems Corporation, Eden Prairie, MN, USA was installed between the roof and the platen of shake table to measure the relative displacement of the specimen. In order to implement the controller of AMD, a Micro-Box 2000 developed by TeraSoft Inc., Taipei, Taiwan was adopted which provided multi-function platform for rapid control prototyping applications. Three controllers were designed and implemented including the LQR-SOS, MLP-150, and ARX. The three controllers were built on the host desktop using MATLAB/Simulink and connected to I/O hardware with blocks provided by Simulink Real-Time. Execut  
Figure 11: Experimental setup for the validating tests. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Controller** & \(\mathbf{J_{1}}\) & \(\mathbf{J_{2}}\) & \(\mathbf{J_{3}}\) & \(\mathbf{J_{4}}\) & **RMSE** \\ \hline LQR-SOS & 0.596 & 0.672 & 0.679 & 0.030 & 0 \\ MLP-120 & 0.596 & 0.671 & 0.676 & 0.030 & 0.014 \\ MLP-150 & 0.596 & 0.671 & 0.677 & 0.030 & 0.011 \\ MLP-200 & 0.596 & 0.672 & 0.678 & 0.030 & 0.012 \\ ARX & 0.594 & 0.669 & 0.669 & 0.030 & 0.039 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of each controller in terms of the average performance. and downloaded onto the Micro-Box 2000 to run the control application. Meanwhile, the LQR-SOS required structural states for feedback control which were not measurable during the tests. As a result, a Kalman filter was essential to estimate the structural states for feedback control. In addition, the MLP and ARX took the measured acceleration as the input to calculate the control force. However, the acceleration measurement contained noise which could result in high-frequency control force and enlarge the acceleration response. Therefore, a 4 th-order elliptic low-pass filter with a cutoff frequency of 15 Hz was designed. Both the Kalman filter and the low-pass filter were implemented using MATLAB/Simulink. The hardware and software layout for the experimental validation is depicted in Figure 12. The MATLAB/Simulink program was converted to C code and executed in Micro-Box 2000 which was running in real time.