## 5 Case Study: Progressive Damage of a Masonry Arch Bridge Model
The longitudinal cracks propagated and reached 3-4 mm around the keystone. At this stage, transverse cracking in the arch barrel initiated and the formation of the first plastic hinge began. In the final stage of loading, as the load increased to 70 kN, a pronounced separation around the keystone occurred, along with the formation of hinges at the arch ring and at the abutment level, leading to large displacements beneath the loading beam. Loading was terminated after the second load-unload cycle, marking the announcement of collapse. Figure 7 displays the load-displacement curves and photos of the observed damage following the final load-unload cycle. Further details of the collapse investigation can be found in [60]. The acceleration responses in the vertical direction (A\({}_{1}\), A\({}_{2}\), A\({}_{3}\), A\({}_{4}\), A\({}_{6}\)) due to impacts in the same direction were recorded. Specifically, A\({}_{5}\) records the acceleration at the foundation level, and it is subtracted from the other measurements to account for baseline motion. This adjustment ensures that the measured responses reflect the system's dynamic behavior more accurately, isolating the effects of the structural components from the foundation motion. The processed data are then used to identify the transmissibilities between the sensor pairs, which provide valuable insight into the structural integrity by revealing variations in response patterns across different locations. In this study, transmissibility functions were computed over the 0-400 Hz frequency range to ensure broad spectral coverage while maintaining a high signal-to-noise ratio. Figure 8 illustrates the transmissibility functions  
Figure 6: (**a**) Load-displacement curves, (**b**) Initiation of the hinge, (**c**) cracking around on the wall and extrados during loading up to 30 kN (DS 1), (**d**) plastic hinge formation, (**e**) propagation of cracks during loading up to 60 kN (DS 2). calculated for the different sensor pairs, highlighting the impact of structural changes on the system's dynamic response. Since the number of training data was limited to five, OCSVM was preferred over the other learning models, and classification task was completed with the trained OCSVM. With  
Figure 8: Local transmissibility functions: (**a**) Baseline repetitions, (**b–d**) comparison of baseline and post load–unload states. Figure 7: (**a**) Load-displacement curves, (**b**) collapse at 70 kN, (**c**) side view, (**d–e**) keystone: frontside, (**d**), backside, (**e**), (**f–g**) springing point: frontside (**f**), backside (**g**). the DSFs extracted from the impact tests that were conducted after loading the specimen to 30 kN (DS 1) and 60 kN (DS 2), test data was classified as 'not-belonging' to the trained state in both cases. To visualize this damage decision with OCSVM, DSFs were projected onto 2-D space using principal component analysis (PCA). Figure 9 presents the principal components of the training data, test data, and the decision boundary. As shown in this 2-D representation, even at a loading level of up to 30 kN (DS 1), the proposed method successfully detected damage. Acceleration responses recorded in the vertical direction due to vertical impacts were processed for damage localization, as this orientation is the only practical one for in-field bridge testing. The transmissibility-based damage index (DI) was then formulated along two orthogonal axes, separately: (i) longitudinal (spanwise)--using T\({}_{12}\) and T\({}_{23}\) to distinguish between regions A\({}_{1}\)-A\({}_{2}\) and A\({}_{2}\)-A\({}_{3}\)--and (ii) lateral (widthwise)--using T\({}_{24}\) and T\({}_{46}\) to distinguish between regions A\({}_{2}\)-A\({}_{4}\) and A\({}_{4}\)-A\({}_{6}\). By comparing DI values in these two directions, one can identify not only where along the span the damage is, but also how far it has propagated through the depth of the arch.