## 4 Results and Discussion
### Temperature-Based Damage Identification
#### 4.2.1 Demonstration of LDR Concept for Face Layer Debonding Detection
For a better differentiation of regions in IR-images that show a deviating thermal behavior to the surrounding structure (typical for defects and damages) the more complex PCA method proposed by [PERSON] et al. [25] (cf. Section 2.3) is used as second data analysis algorithm. The results of this algorithm depicted in Figure 6(b) demonstrate the ability of the PCA technique to extract abnormal patterns in IR-images and enhance the contrast of a damage. Summarized can be noted that the results of both data processing algorithms show clearly the temperature increase caused by the excitation with the local resonance frequency of the debonded face layer, and thus, demonstrate the applicability of the combined concept of LDR and thermography for sandwich debonding detection, localization and quantification. To validate these promising results the local surface temperature difference changes are also evaluated by means of the four applied surface temperature sensors. Figure 7(a) shows the temperature difference \(\Delta T_{A}=T_{A,2}-T_{A,1}\) in the undamaged region and \(\Delta T_{B}=T_{B,2}-T_{B,1}\) for the debonded area measured by means of the Wheatstone half-bridges over time (cf. Figure 4). Both, \(\Delta T_{A}\) and \(\Delta T_{B}\) reflect the phases with and without excitation. The signals of \(\Delta T_{B}\) are significantly higher than those of \(\Delta T_{A}\), which clearly indicates the heating due to the debonded face layer excited at its first resonance frequency. The reflection of the excitation in the temperature difference measurement at the undamaged region is expected to be caused by a slight increase of the temperature over the whole considered sandwich structure due to the excitation. Consequently, the temperature at the sensor \(R_{A,1}\) is higher as it is closer to the excitation source. The minimal higher temperature increase of the sensor \(R_{A,1}\) is not visible at the temperature difference profile of the pixel-line \(L_{1}\), depicted in Figure 6(c), because of the low temperature difference and the low signal-to-noise level. Due to high noise, this measurement cannot be directly validatedby the thermography results. To overcome this issue and to enable the comparison of the temperature difference measurement results of the surface temperature sensors with the results of the IR-camera, spatially averaged values over the debonded area and the remaining bonded area with respect to the time are used. The set of pixels of the debonded area, cf. dashed circle in Figure 7a,b, is defined as \(\Omega^{\text{d}}\), and \(N^{\text{d}}\) is defined as the total number of pixels in this area. The set of pixels of the bonded area is defined as \(\Omega\setminus\Omega^{\text{d}}\) and \(N^{\text{P}}=N^{\text{i}}\times N^{\text{j}}-N^{\text{d}}\) is defined as the total number of pixels in the bonded area. To illustrate this approach, let us call  
\[\overline{T}_{k}^{\text{d}}=\frac{1}{N^{\text{d}}}\sum_{(i,j)\subseteq\Omega^ {\text{d}}}T_{ijk} \tag{7}\]  
is the averaged temperature data of pixels which are located inside the debonded area \(\Omega^{\text{d}}\), and  
\[\overline{T}_{k}^{\text{P}}=\frac{1}{N^{\text{P}}}\sum_{(i,j)\subseteq(\Omega \setminus\Omega^{\text{d}})}T_{ijk} \tag{8}\]  
the temperature data array of pixels which are located outside the debonded area. Consequently, the difference of the averaged temperature profile \(\Delta\overline{T}_{k}\), depicted in Figure 8, of the debonded and bonded area with respect to the time is defined as  
\[\Delta\overline{T}_{k}=\overline{T}_{k}^{\text{d}}-\overline{T}_{k}^{\text{P}}. \tag{9}\]  
Figure 7: **(a)** Temperature difference \(\Delta\overline{T}_{k}\) of five consecutive images before excitation and five consecutive IR-images at the end of the excitation sequence. **(b)** Thermography results of the principal component analysis (PCA)-based feature extraction algorithm. **(c)** Normalized temperature difference profile with respect to the pixel-line \(L_{1}\), whereas **(d)** shows the profile with respect to the pixel-line \(L_{2}\).