## 5 Results and Discussion
### Results and Discussion  
Figure 6 presents the anomaly detection result using the proposed U-TFF network. In this figure, background colors (white and yellow) indicate the event status of the manipulator in the ground truth, corresponding to normal operations and physical attacks, respectively. The \(x\)-axis of the figure represents time instants during operation, while the \(y\)-axis represents the reconstruction error generated by the proposed anomaly detection network. A higher value of reconstruction error indicates a higher likelihood of anomaly presence. The maximum reconstruction error of all training samples determines the threshold used in this work to distinguish anomalies from normal patterns. It has a value of 0.54 and is represented by the horizontal black dashed line in Figure 6. Therefore, all data points with reconstruction errors higher than the threshold are predicted as anomalies in the instant-level anomaly detection, and are denoted by red asterisks in the figure. Table 1 shows the confusion matrix of instant-level physical attack detection. As shown by Figure 6, some normal patterns are mistakenly detected as anomalies around time instant 1300. The proposed network produces 204 false positives for physical attack detection. On the other hand, most anomalous data instances are successfully detected by the proposed network, leading to 647 true positive samples. Moreover, the anomaly detection network yields a small number of false negative samples (131), confirming the detection model's utility. Table 2 summarizes the quantitative results concerning the three essential metrics of recall, precision, and accuracy in order to evaluate the performance of the proposed framework. For instant-level detection, the anomaly detection model exhibits an accuracy of 0.933. However, as shown in Figure 6, U-TFF reaches a precision of only 0.7603 due to the false positive samples. Most notably, the the model achieves a recall of 0.8316, indicating salient performance in detecting true positive samples. In event-level detection, the network exhibits a successful detection rate of 0.9375 for physical attack events. This matches the observation from Figure 6 that only one attack event failed to be detected, which occurred immediately after time instant 1500. On the other two metrics, precision and accuracy, it achieves values of 0.9375 and 0.9394, respectively. Table 3 presents comparison result with the other four benchmark models, with the best performer under each performance metric highlighted in **bold**. Regarding accuracy, the GAN model with one discriminator demonstrates slightly superior performance, only 0.018 and 0.038 higher than the GAN model with five discriminators and the proposed network. Anomaly Transformer ranks fourth with an accuracy value of 0.8881, followed by DAE (0.8554) and TadGAN (0.8522). On the other hand, Anomaly Transformer achieves the best performance in terms of precision, with a value of 0.9249. This value is approximately 0.1 higher than that of the GAN model with only one discriminator, which ranks second. The proposed U-TFF model detects anomalies with a precision of 0.7603, which is slightly \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Confusion Matrix**} & \multicolumn{2}{c}{**Predicted Label**} \\  & **Positive** & **Negative** \\ \hline \multirow{2}{*}{Ground Truth} & Positive & 647 & 131 \\  & Negative & 204 & 4018 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Confusion matrix results for physical attack detection. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Detection Manner** & **Recall** & **Precision** & **Accuracy** \\ \hline Instant-level & 0.8316 & 0.7603 & 0.933 \\ Event-level & 0.9375 & 0.9375 & 0.9394 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation metrics for physical attack detection results. Figure 6: Physical attack detection results using U-TFF. lower than the GAN with five discriminators (0.8044) but higher than DAE (0.7346) and TadGAN (0.6142).