## 3 Shaking Table Test
### Conversion Process of Each Method
#### 3.3.1 Method 1  
The acceleration response measured three times on the basis of the applied force is converted into velocity and displacement using the Penzien filter in Figures 12-14. A description of the conversion steps and the graphs of the results are provided below. First, the applied load is discretized. The duration of the acceleration (\(t_{d}\)) input for the shaking table test was 53.50 s for the Manjil earthquake, 22.29 s for the Superstition Hills earthquake, and 40.95 s for the Kobe earthquake. The measured time interval (\(\Delta t\)) was 0.05 s. The Manjil earthquake had 10784, the Superstition Hills earthquake had 4764, and the Kobe earthquake had 9784 data points. Therefore, FFT was applied, and the analysis time (\(T_{0}\)) was selected in consideration of the period component of the response and the load, with it duration being longer than that of the excited load. In the case of the Manjil earthquake,\(\Delta t\) was 0.005 s, and the number of data points (N) was 10784. The analysis time (\(T_{0}\)) was then calculated using Equation (20). Here, the size of the first load and the magnitude of the load after the end of the load measurement were assumed to be zero, and zero padding was performed. \[T_{0}=(10784-1)\times 0.05\;\sec=53.915\;\sec \tag{20}\]  
Figure 11: Dynamic response and roof displacement of the model for the Kobe earthquake; (**a**) base acceleration, (**b**) 4 th floor acceleration, (**c**) 7 th floor acceleration, (**d**) roof acceleration, and (**e**) roof displacement. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Filter** & **Technique** \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{Penzien filter} & DFT \\  & & \(H_{2}(\omega)\) \\  & & Frequency-domain \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{Cosine correction filter} & Zero padding \\  & & Baseline correction (1 st order) \\ \cline{1-1}  & & Cosine correction filter \\ \cline{1-1}  & & Time-domain \\ \hline \multirow{2}{*}{3} & \multirow{2}{*}{Butter-worth filter} & Least-square fitting \\  & & Butter-worth filter (4 th order) \\ \cline{1-1}  & & Frequency-domain \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Techniques for AVD conversion methods. Figure 12: Analysis process for the 10 th-story acceleration in the Manjil earthquake using Method 1: (**a**) discrete Fourier Transform of the applied load; (**b**) transfer function; (**c**) acceleration; (**d**) velocity; and (**e**) displacement. Figure 13: Analysis process for the 10 th-story acceleration in the Superstition Hills earthquake using Method 1: (**a**) discrete Fourier Transform of the applied load; (**b**) transfer function; (**c**) acceleration; (**d**) velocity; and (**e**) displacement. Next, the discrete Fourier transform of the applied load was performed. When the applied load in the time domain is converted into the frequency domain using the discrete Fourier transform (DFT), the discrete Fourier transform \(\mathrm{F}(f)\) is calculated. The \(\mathrm{F}(f)\) of the applied load of the Manjil earthquake is shown in Figure 12a, that of the Superstition Hills earthquake is shown in Figure 13a, and that of the Kobe earthquake is shown in Figure 14a. In the discrete Fourier transform \(\mathrm{F}(f)\) of the excited load of the Manjil earthquake, the sampling frequency \((f_{s})\), the maximum frequency \((f_{max})\), and the frequency interval \((\Delta f)\) were obtained from Equations (21) to (23). \[f_{s}=\frac{1}{dt}=\frac{1}{0.005}=200\:Hz \tag{21}\]  
\[f_{max}=\frac{f_{s}}{2}=\frac{200}{2}=100\:Hz \tag{22}\]  
\[\Delta f=\frac{1}{T_{0}}=\frac{1}{53.915}=0.018548\:Hz \tag{23}\]  
Next, the complex frequency response function (or compliance) \(\mathrm{H}(f)\) was calculated using Equation (12). The complex frequency response function \(\mathrm{H}(f)\) of the Manjil earthquake is shown in Figure 12b, that of the Superstition Hills earthquake is shown in Figure 13b, and that of the Kobe earthquake is shown in Figure 14b.