# Study on Seismic Performance of a Mold Transformer through Shaking Table Tests
## 3 Test Results and Discussion  
### Dynamic Identification  
The dynamic properties, including the natural frequencies, \(f\), and damping ratios, \(\xi\), of the test specimen were investigated in this study. The acceleration responses obtained from dynamic identification tests were analyzed to identify the dynamic properties of the test specimen in both the horizontal and vertical directions. The fundamental frequencies were evaluated based on the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test no.**} & \multirow{2}{*}{**Test Label**} & \multirow{2}{*}{**Remark**} & \multirow{2}{*}{**Scaling Factor (\%)**} & \multicolumn{3}{c}{**Input PGA (\(\times g\))**} \\ \cline{5-6}  & & & & **X-dir** & **Y-dir** & **Z-dir** \\ \hline \multirow{3}{*}{1–3} & Low-amplitude & Dynamic identification test. & & & \\  & random test & Random input signal, 1–50 Hz & & & \\  & AC156\_25 & & 25 & 0.08 & 0.07 & 0.07 \\  & AC156\_50 & & 50 & 0.15 & 0.13 & 0.14 \\  & AC156\_75 & & 75 & 0.21 & 0.17 & 0.18 \\  & AC156\_100 & & 100 & 0.28 & 0.25 & 0.23 \\  & Low-amplitude & Dynamic identification test. & & & & \\  & random test & Random input signal, 1–50 Hz & & & & \\  & AC156\_125 & & 125 & 0.33 & 0.30 & 0.27 \\  & AC156\_150 & & 150 & 0.42 & 0.36 & 0.31 \\  & AC156\_175 & & 175 & 0.50 & 0.43 & 0.39 \\  & AC156\_200 & & 200 & 0.57 & 0.50 & 0.47 \\  & Low-amplitude & Dynamic identification test. & & & & \\  & random test & Random input signal, 1–50 Hz & & & & \\  & AC156\_250 & & 250 & 0.70 & 0.64 & 0.58 \\  & AC156\_300 & & 300 & 0.90 & 0.79 & 0.66 \\
20–22 & Low-amplitude & Dynamic identification test. & & & & \\  & random test & Random input signal, 1–50 Hz & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Input and test protocol. PGA, peak ground acceleration. Figure 7: Comparison between the input spectra of AC156_100 and required response spectrum (RRS) target. transfer function method in the frequency domain. The transfer function amplitude was determined as the ratio between the Fourier transformation of the input signals, and the response output signals collected from accelerometer data installed on the several points of the mold transformer [7; 8; 11; 18]. The sampling frequency of the accelerometer in this study was equal to 512 Hz, and the size of each data block (window) was set to 5120, corresponding to 10 s. The transfer function amplitude has local peaks at the natural frequency of the system [18]. Figure 8 illustrates the dynamic identification results and transfer function curves evaluated from the data recorded at the top beam. To eliminate the noise from the experimental results and obtain the fitting curves, the estimation algorithm was used to obtain the continuous-time transfer function model using time-domain data from the input and output signals [19]. From the Fourier transformation results, the data gathering showed an inefficient trend in the high-frequency domain, due to the fluctuation. Therefore, to get an effective transfer function model, the frequency domain was defined as below 30 Hz to filter the input and output data. Figure 8: Transfer function amplitude versus frequency curves at top beam: (**a**) Test no.1–3; (**b**) Test no.8–10; (**c**) Test no.15–17; (**d**) Test no.20–22. Figure 9 shows the results of the fundamental frequency as a function of the scaling factor at different locations of the test specimen: the top beam, the left coil, and the center coil. In general, the initial fundamental frequencies of the mold transformer were almost the same regardless of the location, and those in the X, Y, and Z-directions were 7.87, 2.52, and 23.12 Hz, respectively. In the Y-direction, the specimen showed a low natural frequency, which indicated low stiffness in this direction. The fundamental frequency in the Z-direction was much larger than those in the X and Y-directions. This was attributed to the contribution of axial stiffness of all anchors in the vertical direction, leading to the high stiffness of the test specimen.