# Numerical Voids Detection in Bonded Metal/Composite Assemblies Using Acousto-Ultrasonic Method
## 4 Results and Discussion  
### Summary of the Experimental Results  
Figure 4 shows the amplitude and frequency values recorded for the undamaged \(\alpha\) sample and the \(\beta\) samples. A box plot is used to summarize the results for the 70 measurements. This offers a straightforward way to compare values of datasets. The figure consists of a box which indicates the positions of the upper and lower quartiles, i.e., the 25 th and 75 th percentiles, respectively. The interior of this box indicates the area corresponding to 50% of the distribution. The central mark (red line) indicates the median. Lines are extended to a multiple such as 1.5 of the interquartile range. Outliers are represented individually by symbols (+). The data visualization shows that the measurements were very reproducible, even after detachment and recoupling of the sensors. A significant difference in terms of amplitude and centroid frequency can be observed for the sensor located at the epicenter of the defect (sensor 2). In contrast, for sensor 1, there is little difference between the reference material \(\alpha\) sample and the \(\beta\) samples for amplitude, energy and centroid frequency. Therefore, the analysis of the descriptors indicates that defect detection was not straightforward using sensor 1, since some of the descriptors were similar for specimens with or without defects (Figure 4a,c). Only the difference in the centroid frequency recorded by sensor 1 is noticeable for the \(\beta\)2-type sample. In contrast, there is a clear difference between the descriptors obtained using sensor 2 for samples with and without defects (Figure 4b,d). The location of the sensor with respect to the defect location therefore seems to be of primary importance for robust defect detection. However, the size of the defect does not seem to have a significant influence on the descriptors calculated at the epicenter of the defect. The correlation coefficients in the frequency domain between the signals received for the reference sample and those collected for the samples with defects were about 0.7 for sensor 1 and 0.5 for sensor 2, whatever the size of the defect. In the time domain, these coefficients were 0.3 for sensor 1 and 0.20 for sensor 2. It was therefore not possible to establish a link between the values of the correlation coefficients and the size of the defect. With a single-parameter analysis, it seems impossible to determine the size of the defect, and detection only seems possible using a sensor at the defect epicenter (sensor 2). However, the decrease in the correlation coefficients in position 2 but also in position 1 clearly indicates an effect of the defect on the signal. The received signals can be analyzed more thoroughly by means of a principal component analysis (PCA) applied to the signal descriptors. The first principal component versus the second principal component is depicted in Figure 5. The data are described by 10 descriptors extracted in the time and frequency domains (amplitude, duration, rise time, counts, energy, counts to peak, peak frequency, centroid frequency, signal strength and absolute energy). The first two principal components account for 82% of the variance. When analyzing the data obtained from sensor 2 and sensor 1 simultaneously, it is not straightforward to establish a clear separation between the assembly with no defects and the assemblies containing voids (Figure 5a). A significant improvement can be made by considering the sensors separately (Figure 5b,c). The detection of the defect was relatively clear using data obtained from only one sensor (especially from sensor 2 (Figure 5c)). Furthermore, it was not impossible to distinguish the different types of defects. Another analysis of the received signals consisted of setting a supervised classification with a decision tree forest (RFCAM, [45]). This approach first requires a training step based on data acquired by the receiver sensors. Then, the classification method was applied to signals other than those used for the training step.