## 4 Experimental Validation of STST Based on TVCM-VPF
### Comparison between STST and Conventional STT  
To further validate the effectiveness of the proposed method, a comparison between STST and the conventional full structure STT was conducted. The TLD frame structure under the excitation of the El Centro (NS, 1940) and Taft earthquake wave records with a peak ground acceleration of 0.70 m/s\({}^{2}\) were investigated using the two methods. The STT and STST were conducted with the proposed TVC-VPF control, and the input motion in the STST was the measured acceleration response of the shaking table in the corresponding STT. The experimental results of the conventional full structure SST were regarded as the reference solution. The results of STST based on the TVCM-VPF were expected to be close to the reference solutions of the conventional full structure STT. The displacement and acceleration  
Figure 9: Shaking table substructure testing (STST) results with a three-variable control method with velocity positive feedback (TVCM-VPF).  
The performance indicators in terms of amplitude deviation and the correlation coefficient of the displacement and acceleration responses for the two types of tests are summarized in Table 4. From this table, it can be observed that the amplitude deviations of the displacement responses of the top floor of the frame structure are 4.48% and 12.17% for the two earthquakes, and the amplitude deviations of the acceleration responses are 11.38% and 4.84% for the two earthquakes. The correlation coefficients of the displacement responses are 97.39% and 92.03%, whereas the correlation coefficients of the acceleration responses are 66.21% and 65.47%, respectively. The results show that the displacement results of STST based on the TVCM-VPF are very close to those of the conventional full structure STT. However, the acceleration results of the former are not in good agreement with the precise solutions of the latter. There are two reasons for this. First, a simplified 3 DOF model was used for the numerical calculation of the three-story frame structure in STST, which inevitably induces errors.  
Figure 11: Experimental results with the Taft earthquake.  
Second, the loading facility, i.e., the shaking table at the Harbin Institute of Technology, is considerably old. It was a challenge to conduct such sophisticated STST using an old and large-scale shaking table. Although several cases of STST with good performance have been reported, the loading facilities are all newly developed small-scale shaking tables with sophisticated controllers. Therefore, the contribution of this paper is the proposal of a TVCM-VPF for STST, and the realization of the method with an old and large-scale shaking table originally designed using the traditional displacement control mode. The proposed TVCM-VPF is a reliable experimental strategy for evaluating the seismic performance of civil engineering structures, such as a frame structure with TLD. The proposed method has broad application prospects in the performance evaluation of dynamic systems in the fields of structural engineering, offshore platform, bridge engineering, human-structure interaction system, and the vehicle-bridge vibration system, etc.