## 3 Results
### Simulated Case Study
#### 3.1.3 Damage Localization  
Beyond detection of the onset damage, the spatial information of the sensing network that is encoded within the various DSFs may also provide insights into the location of damage. In doing so, we resort to the use of input-output signal pairs, which are defined  
Figure 8: Evaluation of the damage detection and quantification performance of the DSFs: correlation between DSF and \(DI_{PA}\) (**first row**), overlap of damage-state exceeding probabilities (**second row**), probability of false detection (**third row**), and smallest detectable damage level (**fourth row**). The performance indicators are derived as illustrated in Figure 5. All DSFs are evaluated for the first mode (\(M1\)) between the ground and the roof level (05); the indices are omitted to enhance readability. Figure 9: Comparison of transmissibility-based DSFs derived from AVs with their counterpart derived from strong GMs. While the scatter is low for \(T_{c}nt\) (**left**), a noticeable scatter appears for \(T_{max}\) (**center**). When evaluating the \(TAC\) (**right**), the data obtained from ground motions are more sensitive to damage, with the values lying above the diagonal. locally, in order to assess the onset of damage at the substructural level. In buildings, a reasonable level of localization may be achieved through floor-wise damage assessment, since the need for repair quantities of main structural elements, such as columns/walls, is regulated on the basis of the experienced inter-story drift ratio [89]. While some OMA-based features, namely the difference in natural frequencies (\(\Delta f\)) and mode shapes (\(MAC\)), do not contain information about the location of damage, the difference in mode-shape curvature (\(\Delta MSC\)) does contain information about the location, but rather than relying on local sensor pairs, it requires the systematic monitoring of multiple DOFs (in case of buildings, all floors should be measured for instance). In order to assess the capacity of DSFs to achieve floor-wise damage localization, five alternate mass-spring models are created by limiting nonlinearity to a single link (storey) per model instance, while the other links remain linear elastic. The local evaluation of five DSFs for local input-output pairs is reported in Figure 10 for the Amatrice earthquake, and then, it is scaled to a PGA that leads to a hysteretic work of approximately 20 kNmm (analysis of all earthquake signals is done later on). Three models, differing in the location of the nonlinear link (left 01, center 23, and right 45), are compared (see Figure 3 for model definition). For ease of comparison, the DSFs are reported in terms of the modified Mahalonobis distance (see Equation (17)). The first row of Figure 10 reports the evolution of the first examined DSF, namely the TAC. The transmissibility of a sensor pair characterizes the entire substructure from the input sensor (\(i\)) to the rooftop, irrespective of the output sensor (\(o\)). Therefore, while for the first damaged case (Link 01) the TAC correctly identifies damage as limited to the first link (top left of Figure 10), more sensor pairs tend to pick up damage when this is located above their input level, \(i\). This is observed in the cases of damage in links 23 and 45, respectively. However, an absence of damage in links 34 and 45 is correctly identified in the case of damage in link 23. The second row of Figure 10 plots the evolution of the DSF based on the linear correlation of wavelet coefficients, \(WLC\). This DSF offers high localization precision, with distinct peaks occurring at the corresponding damage locations. The sensitivity to damage is the lowest at the ground floor, where linear correlation is influenced more by the ground motion than the structure, unlike in higher floors.