## 5 Parametric Study Based on the Numerical Model
### Effect of the Thickness of the Sample and the Position of the Fiber  
The thickness and the source position along the z-axis are varied. Figure 20a shows the results for the 2 DFFT obtained with a virtual perfect point-like contact sensor for two values of the thickness (e = 2.8 mm and e = 1 mm), when the fiber is located in the mid-plane of the specimen. A comparison can be made with the Figure 18b. When the source is located in the mid-plane (z = 0), only the longitudinal (L\({}_{01}\) in particular) or symmetrical modes are excited (Figure 20a). Even if the identification of the excited modes is complicated due to the reflections, we can observe that the excited modes are not the same. With decreasing the z-position, the spectral contributions above 500 kHz increase significantly.  
In Figure 20b, we investigate the effect of the thickness of the sample. It is not surprising to find the fundamental longitudinal mode L\({}_{01}\) excited mainly around 500 kHz in a 1 mm-thick sample, because this corresponds to the situation observed around the frequency 178.6 kHz in the 2.8 mm-thick sample. Indeed, in terms of guided wave dispersion, the frequency-thickness product is the reference invariant. The dispersion figure thus logically undergoes a homothety of the frequency axis, that it to say that the full extent of the frequency range (1000 kHz) of the Figure 20b,c correspond to the dashed box of Figure 20a. Consequently, less modes are observable and the excitability zone of the L\({}_{01}\) mode is now centered on the bandwidth accessible to the measurement.  
All things equal otherwise, when the source is out of the median plane of the sample (Figure 20c) the same conclusion could be drawn observing the dispersion of guided waves. As a matter of fact, the previously described outcomes, that is to say the homothety of frequency axis (here by a 0.6 factor compared to Figure 18b) resulting in a frequency shift of the excited portion of the dispersion curves accompanied by a switch of the nature of the excited modes, from longitudinal to flexural, remain valid.  
Figure 21 shows the evolution of the descriptors obtained with two kinds of sensors (nano30 and picoHF) for several thicknesses and positions of the fiber. The main differences are observed in the frequency content. The thickness of the specimens and the position of the fiber are major factors of influence for the frequency of the AE signals. By inserting modelling results taking into account these factors we enrich the experimental library of acoustic signatures, what can certainly improve the robustness of the supervised classification. In practice, it is arduous to obtain a sufficiently comprehensive library from an experimental point of view.  
Figure 19: Model and experimental: Evolution of the descriptors in the Frequency Centroid/Amplitude plane detected with five types of sensor. (e = 2.8 mm, z = 0.9 mm).  
Figure 20: Simulated dispersion curves via 2 DFFT of signals v(z) recorded on the top surface for a fiber break located at the position P2, (**a**) e = 2.8 mm and z = 0 mm, (b) e = 1 mm and z = 0 mm and (c) e = 1.7 mm and z = 0.35 mm.