## 4 Experimental Validation
### Experiment of 10-Story Concrete Frame  
The second specimen is a 10-story full-scale reinforced concrete (RC) frame, as shown in Figure 11. It was conducted on the world's largest three-dimensional (3D) earthquake shaking table test facility, E-Defense, at the National Research Institute for Earth Science and Disaster Resilience (NIED) in Hyogo, Japan. The dimensions of the base are 15.7 and 9.7 m in the longitudinal and transverse directions, respectively. On the standard floors, the dimensions are 13.5 and 9.5 m. The longitudinal direction has 3 spans with 4.0 m each and the transverse direction has 3 spans with 3.1, 1.8, and 3.1 m in each floor. The floor heights are 2.8 m for the first floor, 2.6 m for the second to the fourth floors, 2.55 m for the fifth to the seventh floors, and 2.5 m for the eighth to tenth floors. Considering the base, the total height reaches 27.45 m from the shaking table. Furthermore, the longitudinal direction is a simple frame structure composed of beams and columns, whereas the transverse direction is a frame structure with a multi-story shear wall from the first to the seventh floor. Because of some restrictions, the specimen is divided into upper and lower portions. They were constructed separately and steel beams in the sixth floor are designed to facilitate  
Figure 11: The photograph and schematic of the full-scale specimen. Figure 10: The hysteresis loop of each story before and after the brace is released. (**a**) First story; (**b**) second story; (**c**) third story. transportation and assembly. The approximate weight of the steam beams is 16 tons and taken into account in the specimen's design live load. The design load is around 6 tons for the second and the tenth floors and is around 3 tons for other floors. Moreover, the dead load variates from 70 tons to 97 tons for each floor. Consequently, the modes can be identified using the white-noise excitation; the first three modal frequencies in the longitudinal direction are 1.37, 4.05, and 7.31 Hz, and the three in the transverse direction are 1.49, 5.94, and 12.30 Hz, respectively. The Kobe earthquake is designated as ground excitation in the shaking table test. The excitation is simultaneously applied in three directions and the intensity of excitations is sequentially increased with 10%, 25%, 50%, and 100% PGA of the original time history. Moreover, white-noise excitations are individually applied in each direction before and after seismic excitations to extract the dynamic features. The sampling rate of measurement was 1000 Hz in all the tests and it is down-sampled to 50 Hz before RSI implementation. According to the suggestions, the row number of Hankel matrices, \(i\), is set as 18 and the window length, \(l_{w}\), is 431 (8.62 s). The threshold for MAC, \(C_{MAC}\), is set as 0.95 to discriminate between the physical and spurious modes. Due to limited space, only the identification result in the transverse direction of the 100% PGA's one is shown here. From Figure 12a, 0.761 g was achieved by the shaking table, which is 93.27% of the original time history, and the roof response reaches 1.379 g. It is noted that the specimen has been slightly damaged during the test of 50% PGA, so the first three modal frequencies in the transverse direction were reduced to 1.34, 5.25, and 10.96 Hz, respectively. Subsequently, the modal parameters identified by RSI illustrate severe damage, as shown in Figure 12b. The modal frequencies continuously decrease and, finally, converge to 0.87, 3.02, and 6.5 Hz, respectively. According to the literature, the beam-column joint failure further progressed until the concrete cover spalled and the compression side concrete at the base of the multi-story shear wall has crushed in the transverse direction [50]. Figure 12: The identification result of the 10-story RC frame during the shaking table test. (**a**) Ground excitation and structural responses; (**b**) identified modal frequencies over time (the gray grids indicate the results identified from the white-noise excitaitons).