## 4 Results and Discussion
### Numerical Modelling as a Tool to Improve the AE Clustering: Effect of the Sensor  
#### 4.2.1 Relevant Parameters on the Surface with a Perfect Point Contact-Sensor  
In this work, a parameter is defined as relevant if: (1) its value is constant whatever the distance from the source, (2) it is independent of sample geometry, (3) its value depends on the source's characteristics. To identify relevant parameters, two distinct sources are placed in the gauge section of the sample. The first one simulates a mode I cracking placed at the midplane of the sample with a 0.1 \(\upmu\)s rise time and M\({}_{\rm x}\) = 500 N\(\cdot\)\(\upmu\)m (D\({}_{1}\) (M\({}_{\rm x}\) = 500 N\(\cdot\)\(\upmu\)m, 0 mm, 0.1 \(\upmu\)s)). The second one models a mode II cracking placed 0.95 mm away from the midplane towards the surface with a 1 \(\upmu\)s rise time and M\({}_{\rm x}\) = 100 N\(\cdot\)\(\upmu\)m (D\({}_{2}\) (M\({}_{\rm x}\) = 100 N\(\cdot\)\(\upmu\)m,0.95 mm,1 \(\upmu\)s)). Figure 12 shows the 2 DFT results for the two types of damage. Neither the stimulated modes nor the stimulated frequency ranges are the same in the two cases. As expected, the higher frequencies are not present in the AE sources as the source rise time is increased. The further the source is from the midplane, the more the modes of flexion are requested, to the detriment of the longitudinal modes. These results highlight the acoustic signature of each kind of source. The signals generated by each source are calculated for each geometry, and several descriptors are presented: rise time (RT), zero crossing rate (ZCR), frequency centroid (FC), spectral spread (SS), peak amplitude, energy, and the partial powers PPi. Figure 13 shows the evolution of several parameters as a function of distance from the source for each source and each geometry. These parameters are calculated based on the numerical signals extracted from the nodes. Figure 13a suggests that the RT cannot be considered to be a relevant parameter, as it is not constant with distance; it depends on the sample geometry, and it seems difficult to relate its value to a source characteristic. Moreover, this parameter does not exhibit a specific trend with the distance of propagation. Despite some fluctuations, there is a decreasing trend of peak amplitude with distance. There are relatively large losses in the peak amplitude and energy of the  
Figure 12: 2 DFT (wavenumber \(k\) versus frequency \(f\)) of simulated signals for the EPL3 specimen stimulated by sources D\({}_{1}\) (M\({}_{\rm x}\) = 500 N\(\cdot\)\(\upmu\)m, 0 mm, 0.1 \(\upmu\)s) (**a**), and D\({}_{2}\) (M\({}_{\rm x}\) = 100 N\(\cdot\)\(\upmu\)m, 0.95 mm, 1 \(\upmu\)s) (**b**). signal over the propagation distance from 0 mm to 20 mm. Moreover, Figure 13b shows that the signal in the thin sample (EPL3) has a higher amplitude than those in EPL16 or EPL80. This parameter is not relevant for classifications such as energy (Figure 13c). The feature ZCR (Figure 13d) is constant with distance, independent of geometry, and ZCR values calculated for source D\({}_{1}\) are higher than ZCR values calculated for source D\({}_{2}\). This last observation seems logical, as source D\({}_{1}\) varies faster than source D\({}_{2}\), so it is more likely to generate signals with a higher number of oscillations. Concerning frequency features (Figure 14), the frequency centroid does not exhibit large fluctuations with distance, like the spectral spread. The feature FC (Figure 14a) is pertinent. The SS (Figure 14b) is constant as a function of distance and independent of geometry, but is the same for the two sources. Consequently, it cannot be considered to be a relevant parameter for the identification of sources. The partial powers are calculated in the range of [100; 400] kHz for PP1, [400; 750] kHz for PP2, [750; 1000] kHz for PP3 and [1000; 1200] kHz for PP4. The last interval is situated in frequency range that is generally little-studied in EA. The partial powers seem to be a relevant except for PP2 (Figure 14c).