## 3 Results
### Simulated Case Study
#### 3.1.3 Damage Localization
The DSF based on energy accumulation in the time-domain, \(TS\), is reported in the third row of Figure 10. This further proves sensitive to the location of damage; however, spurious peaks appear when the damage is located above the first floor, where the energy accumulation is less influenced by the ground motion itself. In addition, when the damage occurs in the last link 4-5, it is not picked up. Perhaps the most broadly established DSF for damage localization, in a more global sense, the change in mode-shape curvature, \(\Delta MSC\) is formulated with respect to DOFs and not sensor pairs. This implies that this DSF does not directly pinpoint damaged links. However, when the damage appears at an extreme of the structure, either at the ground or at the top, the location is correctly identified, as shown in the fourth line of Figure 10. When damage appears at an intermediate level, the localization is less clear. Given that for unreinforced masonry buildings, which comprise the most vulnerable building type in central Europe and are a major contributor to seismic risk worldwide, the most common failure mechanisms are a soft story at the ground floor or the out-of-plane failure of walls in the highest floors, this indicator--albeit global in nature--can still be useful for rapid post-event assessment. It should be noted that the change in mode-shape curvature of the first mode (plotted in the fourth line of Figure 10) is most sensitive to damage in the lower links and is insufficient to achieve localization for all DOFs (see Table A2 in Appendix C). Finally, the stiffness proxy derived from accelerations (\(KPRX\)) is shown to successfully localize damage for the two lower locations of damage (link 01 and 23), as shown in the last row of Figure 10. However, the low difference in signals on the highest floor and the related large variance in the healthy reference case undermines successful localization of damage at the last floor. As aforementioned, it is suggested that a robust localization scheme would require a combination of multiple DSFs, given the fact that individual DSFs perform well for a specific part of the structure (when relying on the first mode). In order to systematically evaluate the damage localization potential, the results for all 21 GM signals (see Figure 4) are reported in Figure 11. In a similar manner to confusion matrices for machine-learning applications, the true damage location is reported in each line, and the identified damage locations are reported in each column. Perfect localization corresponds to diagonal entries equaling 1 and zero off-diagonal entries. The confusion matrix of the _TAC_ (top right of Figure 11) confirms the previous findings: while the location of damage is correctly picked up, identifying the absence of damage is restricted to the links above the damaged link, and undamaged links cannot be discovered when their position is below the damaged one. Good localization performance is achieved by \(WLC\) and \(KPRX\) (Figure 11 top center and top right, respectively), despite some spurious detection for the \(WLC\) and the incapacity of the \(KPRX\) to detect damage at the last floor. The \(TS\) indicator yields satisfactory localization performance (Figure 11 bottom left); however, false positives are observed on the first floor, irrespective of the true damage location, and on the second floor when the real damage is at the third or fourth floor. In addition, damage at link 12 and 45 is not identified in all 21 cases. The \(MER\), shown in Figure 11 (bottom center), performs well in picking up the damaged links and, in a similar manner to \(TS\), to identify the links above the damaged one as being undamaged. However, as with many features that rely on the modal characteristics of the structure, spurious  
Figure 10: Local evaluation of five DSFs: _TAC_ (**first row**), _WLC_ (**second row**), _TS_ (**third row**), _\(\Delta MSC\)_ (**fourth row**), _KPRX_ (**last row**).