## 4 Methodology  
### Anomaly Detection  
An autoencoder-model-based anomaly detection system is usually trained solely on data corresponding to the pristine signal condition. As a result, the model is equipped to precisely reconstruct input that closely reflects inherent signal trends. Consequently, we can determine whether an input is an anomaly by examining its reconstruction error. The system classifies the input as an anomaly if the error surpasses a well-defined threshold. However, if the reconstruction error stays below this cutoff, the input is regarded as normal and consistent with typical normal signal patterns. The strength of this approach depends on the ability to identify unique signal variations. Since the model is trained only on pristine data, any significant deviation in the input, even one that does not align with known signal patterns, would lead to a higher reconstruction error. This means that the autoencoder can detect or flag anomalies as long as patterns deviate from the learned normal patterns. In this study, mean absolute error (\(MAE\)) was used to identify the signal anomaly which is determined by the Equation (9).  
\[\widehat{MAE}=\frac{1}{N}\sum_{i=1}^{N}\abs{\widehat{X_{i}}-\hat{Y_{i}}} \tag{9}\]  
where \(N\) is the size of the signals and \(\hat{X}\) and \(\hat{Y}\) correspond to the regenerated signals by the encoder for the original/pristine signal and the damage/received signal, respectively.  
This study considers two damages placed at different locations, as shown in Table 4. For anomaly detection, we set the threshold value to be equal to 0.3, which was determined empirically by analyzing the baseline signals and validation data. Figure 13 presents the box plot for all three DL algorithms, explaining the statistical summary of the baseline data. We exploited maximum whisker value for determining the threshold values. Table 5 shows the threshold values for all DL algorithms.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Damage ID** & **x-Coordinates (mm)** & **y-Coordinates (mm)** \\ \hline D1 & 210 & 350 \\ D2 & 130 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Damage Positions in specimen.  
Figure 12: MAE for all three autoencoder architectures for subtle variations in signal.  
For damage identification D1, a total of 436 damage signals were extracted from the datasets, which were generated by conducting multiple experiments involving various damage sizes. Table 6 illustrates the results for true anomaly detection, false anomaly detection, and autoencoder accuracy. It was observed that the proposed method performed better than both biLSTM and 1D CNN methods. The MAE difference with the baseline signal obtained by the proposed scheme is shown in Figure 14. It can be observed that different bars surpassed the threshold value. Each bar represents a different pathway from the exciter sensor. Studying these bars, we can better understand which paths may pass through the damage. Similar to identifying anomalous signals, this visualization aids in detecting irregularities or deviations that might signify damage in specific paths. Similarly, Figure 15 shows error values for D2 which show significant deviations from the learner learned pattern. Peaks are also observed