## 4 Experimental Validation
### Experiment of 3-Story Steel Frame  
The 3-story specimen is a full-scale steel frame; it was designed and constructed at the National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan. In each story, the specimen is a single bay with 2.15 m by 3.15 m in floor area and 3.0 m in height, as shown in Figure 8. The beams and columns are made by wide flange H-beams (H150 \(\times\) 150) and each beam-column joint is designed as a bolted connection. Additional mass blocks are located on the floors so that the final weight of each story reaches 6 tons. Then, the 9.0 m height and 18 tons weight specimen are bolted on the shaking table and excited using the pre-specified earthquake. It should be noted that an extra brace is located in the first story. Due to the brace, the approximate stiffness of the first story is 2692 kN/m while the stiffness of the other two stories is 1346 kN/m. As a result, the modes can be identified using the white-noise excitation and the three modal frequencies are 1.23, 3.66, and 5.33 Hz, respectively. The extra brace is used to produce the stiffness change and, therefore, to mimic the structural damage. In order to achieve that, a lock-up system is designed to connect the brace and the base floor in the first story, as shown in Figure 8. A trigger is manually held by the technician and can be arbitrarily released during the shaking table test. Once the brace is released (un-connected), the inter-story stiffness is immediately reduced to simulate the abrupt change in stiffness. In the shaking table test, the El Centro earthquake is normalized to 100 gal and then inputted to the actuator system to excite the specimen. Here, the unit, gal, is an acceleration unit (1 gal is equal to 1 cm/s2). The lock-up system is assigned to release the brace around 15 s after the earthquake starts. To confirm the true releasing time, an additional displacement meter is installed on the lock-up system in such a way that the relative displacement between the brace and the base floor can be determined. For the application of SHM, RSI implementation using the bona fide recursive algorithm can detect the abrupt change in stiffness at any instant of time. The measurement was taken using a 200 Hz sampling rate in the test and is down-sampled to 50 Hz for efficient computation. Based on the suggestions given in Section 3, the row number of  
Figure 8: The photograph of the full-scale specimen and the close-up of the lock-up system. Hankel matrices, \(i\), is set as 20 and the window length, \(l_{w}\), is 199 (3.98 s). The threshold for MAC, \(C_{MAC}\), is set as 0.95 to discriminate between the physical and spurious modes. Hence, the modal parameters identified by RSI and the relative displacement measured by the displacement meter are shown in Figure 9.  
The structural damage represented by the stiffness change can be easily observed as the three modal frequencies are lower after 15 s in Figure 9a. The first mode close-up displays two distinct modal frequencies before 15 s and after 19 s, which points out that the dynamic behaviors of the frame have been changed during these 4 s. Considering the fixed window (produce by the bona fide recursive algorithm) and the window length (3.98 s in this test), the frame probably has a very rapid change at around 15 s. The relative displacement measured by the displacement meter can provide a more definite indicator. In Figure 9c, the brace is firmly locked until 14.74 s, generating no displacement at all. After this instant, the trigger is set and the brace is released with the result that the relative vibration is created between the brace and the base floor. To further confirm the stiffness change produced by the brace and the lock-up system, the hysteresis loop of each story before and after the releasing time is reconstructed using the measurement. Figure 10a-c show the hysteretic behaviors of the first, second, and third stories, respectively. It is noted that the force is reconstructed from the measured acceleration and the floor weights.