## 4 Results and Discussion
### Temperature-Based Damage Identification
#### 4.2.1 Demonstration of LDR Concept for Face Layer Debonding Detection  
The demonstration of the LDR concept (excitation at a resonance frequency of a defect or damage causes local heat generation) is realized by a piezoelectric stack actuator combined with an amplifier for excitation and an IR-camera for spatial temperature measurement (cf. Figure 4). The infrared temperature measurement is analyzed by typical thermography data processing algorithms. The excitation frequency was selected as 5.641 kHz in order to match the first resonance frequency \(f_{0}\) of the debonded face layer (cf. Section 4.1). The excitation is applied sequentially, where one minute with excitation follows one minute without excitation and so on. This procedure is repeated three times during a measurement to verify the repeatability of the results. The resolution \(N^{\text{i}}\times N^{\text{j}}\) of the IR-camera was \(N^{\text{i}}=288\) and \(N^{\text{j}}=382\) pixels, and the sample frequency \(f_{s}\) was speci \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Excitation** & & **Velocity** \\
**Excitation Source** & **Voltage** & **Offset Voltage** & **Response** \\  & **Amplitude** & & **Amplitude** \\  & **[V]** & **[V]** & **mm/s** \\ \hline piezoelectric stack actuator & 40 V & 20 V & 338.42 \\ PWAS & 150 V & 0 & 75.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of maximum dynamic out-of-plane velocity response to a sinusoidal excitation at the the local resonance frequency \(f_{0}=5.641\) kHz for selected excitation sources and scan point at the debonding center. Figure 6: Dynamic out-of-plane velocity response to a sinusoidal excitation at the local resonance frequency \(f_{0}=5.641\) kHz for considered excitation sources and scan point at the debonding center. fied as 0.5 Hz. This leads to an array \(T_{ijk}\), where \(i=1,...,N^{\text{i}}\) and \(j=1,...,N^{\text{j}}\) are the image pixels discretizing the surface coordinates and \(k=1,...,N^{\text{k}}\) is the time step according to \(k=t_{k}/\Delta t=t_{k}/(1/f_{\text{s}})\). The array has thus the dimension \(N^{\text{i}}\times N^{\text{j}}\times N^{\text{k}}=288\times 382\times 180\), c.f. Section 2.3 and can be defined as  
\[T_{ijk}=T(x_{i},y_{i},t_{k}). \tag{3}\]  
The measured IR-images and temperature sensor signal are post-processed by Matlab R2019a(r). As described in Section 2.3 there are several common analyzing algorithms for thermography data. For the present investigation different algorithms are used for analysis. First, the spatial temperature difference \(\Delta\overline{T}_{ij}\) is calculated by subtracting IR-images from before (\(t^{\text{ex,on}}\) is the time when excitation starts, \(k^{\text{ex,on}}=t^{\text{ex,on}}/(1/f_{\text{s}})\)) and at the end (\(t^{\text{ex,off}}\) is the time when excitation ends, \(k^{\text{ex,off}}=t^{\text{ex,off}}/(1/f_{\text{s}})\)) of the first excitation period. To reduce measurement noise, five consecutive images \(N^{\text{a}}=5\) are averaged [23; 24; 33]. Let us define  
\[\overline{T}_{ij}^{\text{ex,off}}=\frac{1}{N^{\text{a}}}\sum_{k=k^{\text{ex,on }}-N^{\text{a}}}^{k^{\text{ex,on}}}T_{ijk} \tag{4}\]  
as the averaged temperature data of five consecutive images before the first excitation period starts and  
\[\overline{T}_{ij}^{\text{ex,on}}=\frac{1}{N^{\text{a}}}\sum_{k=k^{\text{ex, off}}-N^{\text{a}}}^{k^{\text{ex,off}}}T_{ijk} \tag{5}\]  
as the temperature data of the five consecutive images at the end of the first excitation period. Consequently, the spatial temperature difference \(\Delta\overline{T}_{ij}\) can be defined as  
\[\Delta\overline{T}_{ij}=\overline{T}_{ij}^{\text{ex,off}}-\overline{T}_{ij}^ {\text{ex,on}}. \tag{6}\]  
Figure 6(a) depicts the normalized temperature difference results \(\Delta\overline{T}_{ij}\). This simple post-processing algorithm enables already to make the artificially introduced face layer debonding visible. Figure 6(c) and d shows the normalized temperature profile according to the pixel-lines \(L_{1}\) and \(L_{2}\) marked in Figure 6(a).