## 4 Detection of Artificial Delaminations
### Defect-to-Background Ratio and Local Defect Resonance  
Using Equation (5), the \(DBR^{\text{lin}}(f)\), \(DBR^{\text{HH2}}(f)\) and \(DBR^{\text{HH3}}(f)\) curves are calculated for both the shallow as well as the deep delamination. The curves are shown in Figure 5a,e, respectively. In order to improve the readability of the graphs, the frequency axis is scaled with the order of the higher harmonic. As an example, the red line in Figure 5a indicates the \(DBR\) of the linear component at 17.3 kHz, the second harmonic component at \(2\times 17.3=34.6\) kHz and the third harmonic component at \(3\times 17.3=51.9\) kHz.  
The shallow delamination shows pronounced LDR behavior due to the high reduction in local bending stiffness (see also [9]). This LDR behavior corresponds to the local maxima in the \(\text{DBR}^{\text{lin}}(\text{f})\) curve, for instance at 17.3 kHz. The operational deflection shape corresponding to the linear component at 17.3 kHz reveals the (second order) LDR of the delamination, see Figure 5b.  
The \(DBR\) curves of the higher harmonics show a value higher than 1 at the majority of frequency bins. This indicates that the delaminations show distinct nonlinear behavior. As expected, the higher harmonics are observed, especially when the defect is under LDR behavior. This is seen in Figure 5a because the \(\text{DBR}^{\text{HH2}}(\text{f})\) and \(\text{DBR}^{\text{HH3}}(\text{f})\) curves show local maxima at the same scaled frequency as where the \(\text{DBR}^{\text{lin}}(\text{f})\) is high. As an example the amplitude maps are shown for the second and third higher harmonic corresponding to the LDR frequency of 17.3 kHz (see Figure 5c,d). An intense nonlinear response of the defect is revealed by these amplitude maps. Especially for the third harmonic,  
Figure 5: Defect-to-background ratio (\(DBR\)) curves for linear and nonlinear higher harmonic components with amplitude maps at local maxima. Results for (**a-d**) shallow delamination, and (**e-h**) backside-delamination.  
the defect is revealed with much greater contrast compared to the linear defect response. As such, examining these higher harmonic components for LDR behavior leads to an improved sensitivity to defects compared to the examination of the linear response.  
For the deep delamination near the backside, no LDR behavior is observed in the linear response due to the limited reduction in local bending stiffness at the delamination [9]. Indeed, the \(\text{DBR}^{\text{lin}}(\text{f})\) curve (see blue curve in Figure 5e) is close to 1 at all frequencies and does not show any significant local maximum.  
On the other hand, the \(DBR\) curves corresponding to the higher harmonic components do reveal an increased nonlinear activity at the defect at a multitude of frequencies. As an example, the vibration maps of the linear and higher harmonic components are shown for the frequency of 36 kHz. No sign of the delamination is visible in the linear response at 36 kHz (Figure 5f). However, an increased activity at the defect is seen in both the second and the third higher harmonic components (Figure 5g,h, respectively). The efficient generation of nonlinear components at the deep defect is related to LDR of the thin material section between the delamination and the backside [34].  
These observations indicate that the monitoring of higher harmonic components leads to a more robust defect detection and localization compared to the monitoring of only the linear response. Moreover, it is shown that a delamination which is close to the backside can exclusively be detected through the analysis of the higher harmonic components.