## 4 Analysis and Comparison of Results
### Comparison of Acceleration Response Time Histories
\[\text{RMQ}=\sqrt[4]{\frac{1}{n}{\sum_{k=1}^{n}{x_{k}^{4}}}} \tag{4}\]  
\[\text{R}_{\text{RMS}}(i)=\frac{\text{RMS}_{a}(\text{floor})}{\text{RMS}_{a}( \text{base})},\text{R}_{\text{RMQ}}(i)=\frac{\text{RMQ}_{a}(\text{floor})}{\text{ RMQ}_{a}(\text{base})} \tag{5}\]  
In Equations (3) and (4), \(x_{k}\) represents the \(k\)-th value of the measured time history signal, and \(n\) is the total number of samples. In Equation (5), \(\text{RMS}_{a}(\text{floor})\) and \(\text{RMQ}_{a}(\text{floor})\) denote the RMS and RMQ values at each cabinet floor (A2-A4), and \(\text{RMS}_{a}(\text{base})\) and \(\text{RMQ}_{a}(\text{base})\) values at the shaking table base (A1). Tables 7 and 8 present RMS and \(\text{R}_{\text{RMS}}\) values, as well as RMQ and \(\text{R}_{\text{RMQ}}\) values, from the experimental and numerical results. Figure 17 shows RMS and RMQ differences, while Figure 18 depicts \(\text{R}_{\text{RMS}}\) and \(\text{R}_{\text{RMQ}}\) differences. In Figure 17, black and red indicate experimental and numerical results; circles and squares denote RMS and RMQ, respectively. As specified in Figure 17a, the RMQ difference for EQ1 reached a maximum of 13.23% at the top of the electrical cabinet model (A4), whereas differences in RMS and RMQ at other positions and directions ranged from 0.08% to 12.10%. Similarly, previous studies on numerical modeling postulate that discrepancies of less than 15% between numerical and experimental results are considered reasonable and reliable, indicating that the acceleration response magnitudes for EQ1 are in good agreement between the numerical and experimental results [53; 54; 55]. Prior to EQ3 (Figure 17a,b), differences in RMS and RMQ increase linearly with cabinet height, with RMQ variations consistently larger than RMS. For EQ3 (Figure 17c), RMS differs by up to 49.95% (X-direction) and RMQ by 58.81%. Discrepancies between the experimental and numerical results in EQ3 are significantly greater than those found in EQ1 and EQ2 across all locations and directions, with RMQ exhibiting greater variability than RMS. Unlike the trend observed in EQ1 and EQ2--where variations were more pronounced in the horizontal directions (X and Y) than in the vertical (Z)--EQ3 showed a reversal, with the largest variation occurring in the vertical direction, reaching up to 87.24%. Figure 18 shows the experimental results in black and the numerical results in red. Data points corresponding to the X, Y, and Z directions are represented by circle, square, and triangle markers, respectively. \(\text{R}_{\text{RMS}}\) increased linearly with height as input seismic motion increased (Figure 18a). In Figure 18b, \(\text{R}_{\text{RMQ}}\) was greater than \(\text{R}_{\text{RMS}}\) and was higher at A2 than at A3. Figure 19 describes \(\text{R}_{\text{RMS}}\) and \(\text{R}_{\text{RMQ}}\) differences at A4, where the trend of acceleration response amplification was most evident. The figure clarifies the variation in directional differences as the input seismic motion increases. \(\text{R}_{\text{RMQ}}\) differences exceeded \(\text{R}_{\text{RMS}}\) across all directions, and notably, in EQ3, RMQ differences in the vertical direction surpassed those in the horizontal direction. Accordingly, the \(\text{R}_{\text{RMS}}\) values obtained from the experimental results increased linearly with height along all three axes as the input seismic motion increased, whereas the \(\text{R}_{\text{RMQ}}\) values showed greater amplification in the vertical direction and exhibited a nonlinear trend along the height of the electrical cabinet model. While cabinet response amplification generally increases with height, RMQ analysis revealed that internal impacts can cause the peak amplification to occur at any location previously discussed in [31].