## 4 Analysis and Comparison of Results  
### Comparison of Acceleration Response Time Histories  
The acceleration response time histories obtained from the experimental and numerical results for EQ1 through EQ3 are presented in Figures 14-16, for each axial direction at locations A2 to A4. As drawn in Figure 14, the acceleration time histories from the experimental and numerical results under EQ1 exhibited a high degree of similarity. The responses showed close agreement in both horizontal and vertical directions as well as across the full height of the electrical cabinet model, confirming the validity of the numerical model. Although no structural damage was observed at EQ2, minor impact responses began to appear, specifically at the upper levels of the cabinet, as depicted in Figure 15. These responses are attributed to the increased seismic input. At EQ3, where damage occurred due to plastic deformation of the anchor bolts, significant amplification of the acceleration responses and multiple impact signals were observed (Figure 16). In particular, the vertical (Z) direction exhibited numerous noise-like signals, likely caused by substantial impact events. To quantify the similarity between the acceleration responses from the experimental and numerical results, cross-correlation coefficients were calculated, as outlined in Table 6. The coefficient ranges from -1 to 1, with values closer to \(\pm\)1 indicating higher similarity, and 1 denoting identical signals. At EQ1, the cross-correlation coefficients ranged from 0.912 to 0.978 in the horizontal directions and from 0.675 to 0.726 in the vertical direction. Notably, the horizontal directions--representing the dominant dynamic behavior of the cabinet--showed strong agreement with coefficients exceeding 0.912. As the input seismic motion increased, the variability in correlation across different elevations also increased. At EQ3, the coefficients significantly declined, ranging from 0.638 to 0.832 in the horizontal directions and from 0.506 to 0.605 in the vertical direction. Figure 13: Location of output nodes for response comparison. Figure 14: Comparison of acceleration response time histories (EQ1): (**a**) A2; (**b**) A3; (**c**) A4. Figure 15: Comparison of acceleration response time histories (EQ2): (**a**) A2; (**b**) A3; (**c**) A4. RMS, a representative measure of the effective amplitude of a time history signal independent of frequency, is widely used to quantitatively assess the acceleration response of electrical equipment [8; 51]. In addition, root mean quad (RMQ) can serve as a more sensitive indicator when the signal contains impacts or irregularities, making it useful in capturing impulsive characteristics [52]. To compare the seismic behavior between the experimental and numerical results, RMS and RMQ values were computed using Equations (3) and (4) to quantify the magnitude of acceleration response signals. Based on these values, the RMS ratio (\(\mathrm{R_{RMS}}\)) and RMQ ratio (\(\mathrm{R_{RMQ}}\)) were calculated using Equation (5) to evaluate amplitude amplification according to the cabinet's height. \[\mathrm{RMS}=\sqrt{\frac{1}{n}\sum_{k=1}^{n}x_{k}^{2}} \tag{3}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Direction**} & \multicolumn{3}{c}{**Test ID**} \\  & & **EQ1** & **EQ2** & **EQ3** \\ \hline \multirow{3}{*}{A2} & X & 0.975 & 0.957 & 0.811 \\  & Y & 0.978 & 0.973 & 0.832 \\  & Z & 0.675 & 0.761 & 0.605 \\ \hline \multirow{3}{*}{A3} & X & 0.945 & 0.906 & 0.722 \\  & Y & 0.963 & 0.951 & 0.737 \\  & Z & 0.726 & 0.801 & 0.549 \\ \hline \multirow{3}{*}{A4} & X & 0.912 & 0.855 & 0.638 \\  & Y & 0.950 & 0.936 & 0.725 \\ \cline{1-1}  & Z & 0.717 & 0.785 & 0.506 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Cross-correlation coefficients of acceleration responses between experimental and numerical results. Figure 16: Comparison of acceleration response time histories (EQ3): (**a**) A2; (**b**) A3; (**c**) A4.