## 3 Performance Evaluation
### Experimental Study: Masorry Arch Bridge Model  
The test specimen shown in Figure 8 consisted of an arch ring with a span of 1.73 m and a rise of 0.94 m. It had an overall width of 1.4 m, encompassing both the spandrel walls and the fill. A 10 cm thick reinforced concrete slab, with plan dimensions of 3.20 \(\times\) 1.55 m, served as the foundation for the bridge model. The specimen was subjected to progressive damage by incremental increase in the vertically applied loading at the quarter length of the specimen. The load levels were set as 30 kN (Case 1) and 60 kN (Case 2) before the collapse load of 70 kN. Each loading case, except for the collapse case, included three repetitions of loading-unloading cycles, with impact tests conducted after the third cycle of unloading to monitor the structural response. Prior to pushing the structure to its collapse state, the accelerometers were disassembled to prevent damage to the instrumentation. Details of the static testing are available in [46]. \begin{table}
\begin{tabular}{l l l l l} \hline
**Damage** & **Damaged** & \begin{tabular}{l} **Predicted Damage** \\ **Location** \\ **PCA** \\ \end{tabular} & \
\begin{tabular}{l} **Predicted Damage** \\ **Location** \\ **AE** \\ \end{tabular} &
\begin{tabular}{l} **Predicted Damage** \\ **Location** \\ **AE** \\ \end{tabular} \\ \hline \multicolumn{5}{c}{**Accuracy**} \\ D. Case 1 & 2 & 2 () & 20/20 & 2 () & 20/20 \\ D. Case 2 & 3 & 4 () & 0/20 & 3 () & 20/20 \\ D. Case 3 & 4 & 5 () & 0/20 & 4 () & 20/20 \\ D. Case 4 & 5 & 5 () & 20/20 & 5 () & 20/20 \\ D. Case 5 & 6 & 7 () & 0/20 & 6 () & 20/20 \\ D. Case 6 & 7 & 8 () & 0/20 & 7 () & 20/20 \\ D. Case 7 & 8 & 9 () & 0/20 & 8 () & 20/20 \\ D. Case 8 & 9 & 9 () & 20/20 & 9 () & 20/20 \\ D. Case 9 & 10 & 10 () & 20/20 & 10 () & 20/20 \\ \hline \end{tabular}
\end{table} 
Table 3: Damage localization performance with the predictions of PCA vs. AE. Figure 7: Damage localization results using the AE: (**a**–**i**) D. Cases 1–9. A total of six accelerometers were mounted on the structure to collect acceleration measurements: four triaxial (A\({}_{2}\), A\({}_{4}\), A\({}_{5}\), A\({}_{6}\)) and two unidirectional (A\({}_{1}\), A\({}_{3}\)). The arrangement of the accelerometers and the impact locations are shown in Figure 9. The impact tests carried out at the baseline state were repeated five times to generate five independent datasets for training. The acceleration responses in the vertical direction (A\({}_{1}\), A\({}_{2}\), A\({}_{3}\), and A\({}_{6}\)) due to impacts in the same direction at locations I\({}_{1}\), I\({}_{2}\), and I\({}_{3}\) were processed to generate the local TFs: T\({}_{12}\), T\({}_{23}\), T\({}_{42}\), and T\({}_{62}\) at the baseline state. After loading the specimen to the preset load levels and inflicting damage states shown in Figure 10, the same measurements were collected in the same manner to obtain the TFs for damage scenarios of Cases 1-2. Using the baseline dataset, a conventional AE with a single hidden layer of 10 neurons was trained to reconstruct each transmissibility. Figure 11a,b displays the dataset for the baseline state and compares the measured with the AE prediction for T\({}_{12}\). The comparison between the measured and predicted values for the damage states of Case 1 and 2 is shown in Figure 11c,d. Figure 8: Test specimen: (**a**) static loading; (**b**) impact testing. Figure 9: Accelerometer (A\({}_{1}\)–A\({}_{6}\)) and impact locations (I\({}_{1}\)–I\({}_{3}\)). The reconstruction errors from the baseline state were then used as DSF for training an OC-SVM to aid in the damage detection decision. The detection performance of these  
Figure 11: T\({}_{12}\) comparisons (**a**) measured data at the baseline state (**b–d**) measured versus AE predicted for the baseline and the damage cases. Figure 10: Observed damage after loading up to: (**a**) 30 kN; (**b**) 60 kN; (**c**) collapse at 70 kN. features is clearly displayed in Figure 12a, where the first two features of the damage states are compared to those of the baseline state.