## 2 Materials and Methods
### Testing Procedure  
The case study consists of a CFRP (Carbon Fiber-Reinforced Polymer) laminated square panel with dimensions of side length L = 300 mm and thickness t = 1.5 mm, as depicted in Figure 1. The panel is made of 8 unidirectional laminae with the stacking sequence of \([0]_{8}\) aligned along the \(x\)-axis of Figure 1b. This stacking sequence was intentionally defined so as not to exclude from the investigations the slowness phenomenon (i.e., the dependency of the signal group velocity on the measurement angle). This phenomenon can influence UGW propagation mechanisms and consequently impact damage classification. In contrast, quasi-isotropic laminates tend to mitigate this effect. The transducers network encompasses 5 surface-bonded circular PI Ceramics PIC255: one placed at the center of the plate (S-C) and four (S2, S3, S4, and S5) located at a distance h = 79.29 mm from the plate edges, as shown in Figure 1b, covering the corner positions of a square 140 mm \(\times\) 140 mm sized. The diameter of the transducers is \(d_{PZT}\) = 10 mm, and the thickness is \(t_{PZT}\) = 0.25 mm. Table 1 lists the mechanical properties of both the plate and the transducers. \begin{table}
\begin{tabular}{c c c c c} \hline
**Material Property** & **Symbol** & **Units** & **CFRP Lamina** & **PZT** \\ \hline Mass density & \(\rho\) & \([\mathrm{kg\,m^{-3}}]\) & 1534 & 7800 \\ Longitudinal & E\({}_{11}\) & \([\mathrm{GPa}]\) & 123.182 & 62.1 \\ Young’s modulus & E\({}_{22}\) & \([\mathrm{GPa}]\) & 7.700 & 62.1 \\ Transversal Young’s & E\({}_{33}\) & \([\mathrm{GPa}]\) & 7.700 & 48.3 \\ modulus & G\({}_{12}\) & \([\mathrm{GPa}]\) & 3.60 & 23.5 \\ Shear modulus & G\({}_{13}\) & \([\mathrm{GPa}]\) & 3.60 & 21 \\ Shear modulus & G\({}_{23}\) & \([\mathrm{GPa}]\) & 2.70 & 21 \\ Poisson’s ratio & v\({}_{12}\) & – & 0.360 & 0.32 \\ Poisson’s ratio & v\({}_{13}\) & – & 0.360 & 0.44 \\ Poisson’s ratio & v\({}_{23}\) & – & 0.4 & 0.44 \\ \hline \end{tabular}
\end{table} 
Table 1: Material mechanical properties of CFRP composite lamina and PIC255 sensors. Figure 1: (**a**) Case study; (**b**) schematic of the considered plate companion with the number of sensors, their locations, and the regions (R classes). Figures 2 and 3 illustrate the significant influence of the propagation direction on the group velocities (Cg) of both \(S_{0}\) and \(A_{0}\) modes, with higher values along the fiber's direction (\(0^{\circ}\) measurement angle). Specifically, the values of the group velocities were extracted by means of a proprietary code developed in MATLAB(r) that enabled the identification of the time of flight of the diagnostic signal for each actuator-sensor path (pitch-catch approach) by reference to its energetic center defined by the Hilbert Transform (HT). According to the arrangement of the sensors on the panel, measurements were taken at \(0^{\circ}\), \(45^{\circ}\), \(-45^{\circ}\), \(90^{\circ}\) measurement angles, and the Cg extracted values (indicated by markers in Figure 2) were subsequently interpolated, as previously demonstrated in [7; 8], to define the dispersive behavior of UGW (solid lines in Figures 2 and 3). The interpolation allows the characterization of the dispersive behavior of the UGW, demonstrating the dependency of the Cg on the excitation frequency, given the plate thickness. Figure 3: Group velocities (units in [m/s]) at different carrier frequencies for (**a**) \(S_{0}\) and (**b**) \(A_{0}\) modes in the investigated CFRP panel—polar representation. The UGW actuation was performed by exciting the central sensor (S-C) with a five-cycle Hanning windowed tone burst signal having a central frequency of 200 kHz and a peak-to-peak amplitude equals to 12 V, as illustrated in Figure 4.  
Two two-channel TiePie oscilloscopes (Handyscope HS5) were used for both UGW actuation and reception; the sampling frequency is of 200 MHz, the duration is 200 us for a total of 40,000 sample points, and the resolution is of 12 bits.