## 3 Results
### Simulated Case Study
#### 3.1.2 Damage Detection and Quantification
For the tracking of nonlinear exposure, in particular, the proposed DSFs should be adept in discriminating between linear and nonlinear structural responses. To investigate such potential, performance indicators are analyzed for 21 GMs and scaled to increasing amplitudes that lead to changing structural conditions (from purely linear behavior to extensive damage). When simulating the \"healthy\" reference behavior, a pure WN excitation would lead to DSF values that are significantly differentiated with respect to realistic ambient or earthquake ground inputs, which typically comprise varying spectral and temporal components. In order to reflect realistic conditions, four 10 min AV datasets that have been measured at the base of an actual building in Switzerland during day-and-night time are used as input for simulation rather than artificial WN excitation. Figure 5: Derivation of performance indicators for the comparative assessment of the DSFs, illustrated with respect to the Park–Ang damage index (\(DI_{PA}\)). Correlation between each DSF and the DI (**a**); separation between no damage (\(DI_{PA}=0.025\)) and extensive damage (\(DI_{PA}=0.50\)), using probability of exceeding the respective DSF values (**a,b**); false damage detection (**c**); and minimum value of \(DI_{PA}\), for which damage is detected (**d**). The two last indicators (**c,d**) require a previous characterization of the behavior of the healthy structure under AVs (\(TAC_{05}^{h}\)). Figure 6 illustrates the values of \(Tcnt_{05,M1}\) with respect to four EDP values: hysteretic work (left), maximum transient roof displacement (center left), \(DI_{PA}\) (center right), and the residual stiffness drop (right). It is observed that the correlation is very good and the scatter due to the GM signals remains low. However, the significant uncertainty in the ambient reference distribution (\(Tcnt_{05,M1}^{h}\)) undermines the successful detection of damage. Reversely, the DSF based on the phase angle has a very low scatter in the ambient conditions and thus allows for a significantly better detection, even from lower levels of damage (see Figure 7). As the \(PAAC\) is derived from post-earthquake AVs, the correlation with the residual stiffness drop is the highest (see Figure 7, right). In addition, when comparing Figures 6 and 7, the variability of the \(PAAC\) for linear model instances is much lower than for the \(T_{cnt}\), highlighting the superior capacity of the \(PAAC\) to identify absence of damage and the reduced influence of GM signals, given the \(PAAC\) is derived from AVs. The systematic evaluation of all DSFs based on the four defined PIs--derived with respect to \(DI_{PA}\), which combines the influence of hysteretic work and maximum transient displacement--is shown in Figure 8. The evaluation of all DSFs allows ranking the DSFs with respect to their performance to detect and quantify structural damage. When focusing on the \(T_{cnt}\), shown in detail in Figure 6, the good correlation with \(DI_{PA}\) is reflected by a high ranking in the two first PIs, which evaluate damage quantification. In addition, the large variability in the healthy reference state avoids false positives (see PI3 in Figure 8) at the cost of very reduced capacity of early detection (see PI4 in Figure 8). While similar conclusions can be drawn for the quantification under use of the \(PAAC\), the much lower variability of the healthy reference values increase the risk for erroneous damage detection yet significantly increase the capacity for early damage detection. Figure 6: Evaluation of the correlation of the transmissibility-based indicator, \(Tcnt_{05,M1}\), with respect to four EDPs: hysteretic work (**left**), maximum transient roof displacement (**center left**), \(DI_{PA}\) (**center right**), and residual stiffness drop (**right**). While a good correlation and an almost linear relation with respect to hysteretic work and residual stiffness drop can be observed, damage detection is undermined by the large variance in the healthy reference distribution.