## 3 Experimental Results and Analysis
### Testing for Damage Assessment (O2)
This means that for a given _ny_ satisfying the condition _ny_\(\geq\) 80, there is always a set of poles assigned to frequencies close to 40 KHz and another set for those close to 50 KHz. Hence, for the selected value of _ny_, the relative difference of pole damping values at each frequency may provide quantitative information on the damage level, exactly as when the power spectra of test signals are (qualitatively) examined. Four such models have been identified on data from type -C1 slabs. Another four CC-AR(80) models have been identified on data from -C2 slabs. As shown in Figure 11a, all eight models feature poles located at the frequency band of interest (around 40 and 50 KHz). The autocorrelation coefficients of CC-AR(80) residuals computed with test data from one -C1 and one -C2 slabs (with an indicative case shown in Figure 11b) appear uncorrelated, since they are located in-between the dashed lines designating statistical limits at the 5% risk level (see [21]). Then, clearly a CC-AR(80) representation is an adequate compromise for modeling test data from -C1 and -C2 slabs. The pole-zero maps of these eight CC-AR(80) models in Figure 11a show that at 40 and 50 KHz there is one group of four poles associated to models identified on data from -C1 slabs (red crosses) which slightly overlaps another group of four poles associated to -C2 slabs (green crosses). It is, thus, obvious that it is not possible to completely distinguish between the two groups, due to the small overlap. Figure 10: Stabilization plots with \({}^{\star\prime}\) indicating poles at each frequency: (**a**) type-C1 and (**b**) type-C2 slabs. For values _ny_\(\geq\) 80, poles are consistently assigned at the monitored frequencies of interest (around 40 and 50 KHz). However, it is also obvious that the poles associated to -C2 slabs (green crosses) have larger damping than that from poles associated to -C1 slabs (red crosses). This stems from the fact that the green crosses are closer to the dashed damping line (designating region of poles with damping coefficient equal to 0.1) than the red ones. In fact, damping of poles at 40 KHz ranges from 0.0389 to 0.0458 for -C1 slabs and from 0.0436 to 0.0508 for -C2 slabs. Damping of poles at 50 KHz ranges from 0.012 to 0.0272 for -C1 slabs and from 0.024 to 0.037 for -C2 slabs. These conclusions are identical to those resulting from the analysis based on the power spectral magnitude plots, presented above. Moreover, tests with _ny_ values up to 130 were also attempted only to find that, even for such high values of _ny_, the values in the damping of poles corresponding to -C1 and -C2 data respected the same relative order. Poles from -C1 consistently featured higher damping than those from -C2 slabs. Hence, if the relative order in damping values of poles resulting from slabs with different damage is monitored, then procedure P2 is able to provide quantitative indications about the level of damage in the tested slabs. Accordingly, the objective O2 was deemed as achievable, if only partly with respect to damage assessment. It is expected that fine-tuning P2 (or dropping the affordability condition by investing in high-tech equipment) should lead to smaller amplitude ranges for the power spectra of signals, thus achieving easier distinction of damage levels.