## 6 Numerical Investigation--Results  
As previously demonstrated, the training error was recorded at 0.0133, with the prediction error slightly higher at 0.0143. These errors represent the mean absolute errors (MAEs) computed at the pixel level between the predicted and target spectrograms, encompassing both magnitude and phase. However, as structural engineers, our primary concern lies in understanding the core problem at hand: the prediction of seismic responses in terms of acceleration. To address this, all spectrograms were transformed back into time histories, enabling us to evaluate their similarities in magnitude and trend. For this comparative analysis, we selected two key metrics: the mean absolute percentage error (MAPE) (Equation (5)) for assessing magnitude congruence and the mean directional accuracy (MDA) (Equation (6)) to gauge the directional accuracy of the time history regression between each time step. To address the challenge posed by small, near-zero values in the data, we employed a modified version of both metrics. This adaptation necessitates the introduction  
Figure 8: Training and validation loss function value during 80 epochs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Decoder**} \\ \cline{2-6}  & **C4**1  & **C5**1  & **C6**1  & **C7**2  \\ \hline Filters: & 9 & 16 & 16 & 16 & 2 \\ Kernel size: & (3,3) & (5,5) & (10,10) & (3,3) & (1,1) \\ Dilation: & (3,3) & (1,1) & (1,1) & (1,1) & (1,1) \\ Stride: & (1,1) & (1,1) & (1,1) & (1,1) & (1,1) \\ Padding: & Valid & Valid & Valid & Valid & Valid \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Architecture of MLPER—Part III. ‘C’ indicates a convolutional layer (Conv2D). of a threshold mask (\(T\)) to assess signal similarities specifically for values exceeding certain magnitudes (m/sec\({}^{2}\)). \[Modified\ MAPE=\frac{100\%}{n}\sum_{t=1}^{n}\left|\frac{A_{t}-F_{t}}{A_{t}} \right|=\
icefrac{{1}}{{n}}\sum_{t=1}^{n}\left|\frac{\ddot{u}_{true}-\ddot{u}_{ pred}}{\ddot{u}_{true}}\right|\ \ for\ \ \left|\ddot{u}_{true}\right|\geq T \tag{5}\]  
\[Modified\ MDA=\frac{100\%}{N}\sum_{t}sgn\left(\ddot{u}_{prediction}^{t}-\ddot{u }_{true}^{t-1}\right)\ \ \ for\ \ \left|\ddot{u}_{true}^{t-1}\right|\geq T \tag{6}\]  
When employing small threshold mask values (\(T>0.0001\)), the mean modified MAPE registers an average of 32%, as demonstrated in Figure 9, while the modified MDA maintains a robust average of 95%, as illustrated in Figure 10. It is worth noting that there is a more substantial deviation in accuracy observed in lower-frequency signals, suggesting potential avenues for enhancing the model's performance. These potential modifications will be discussed in greater detail in the forthcoming chapter, Discussion. For signals with a higher frequency (\(\geq\)3000 signal, equivalent to 4 Hz), the mean MAPE averages at 24.09%, and the MDA at an impressive 97.46%. To offer greater clarity to the reader regarding the extent of masking, Figures 11 and 12 provide a comprehensive listing of the omitted values from the time history, which primarily include values that are in close proximity to zero, as dictated by the chosen threshold \(T\) mask. When utilizing larger threshold mask values (T \(>0.01\)), the mean modified MAPE averages out at 18%, as indicated in Figure 13, while the modified MDA maintains a strong average of 95%, as shown in Figure 14. The deviation pattern observed remains consistent with that observed when using lower mask values, with deviations being more prominent for lower-frequency signals. For signals with a higher frequency (\(\geq\)3000 signal, equivalent to 4 Hz), the mean MAPE stands at an average of 14.09%, and the MDA at an impressive 97.19%. To provide greater clarity to the reader regarding the extent of masking, Figures 15 and 16 list the values from the time history that are omitted when the threshold \(T\) mask is applied. These omitted values typically correspond to those close to zero.