## 2 Experimental Analysis
### Results and Discussions
The horizontal axis is the same for all figures. (**g**) Evolution of \(\Pi(\phi)\) with AE data from the Lunitek system for the true coincidence instants (black circles in (**f**)) in normalized time equal to (from left to right): 0.7492, 0.7877, and 0.8506. Figure 6: \(b\)-value and NT analysis, data from the Mistras system: (**a**) compressive-load and AE signal amplitudes, (**b**) average frequency (\(AF\)), (**c**) signal duration, (**d**) instantaneous and accumulated signal counts and normalized AE energy (\(E_{AE}\) ), (**e**) \(b\)-value evolution, and (**f**) natural time analysis. The horizontal axis is the same for all figures. (**g**) Evolution of \(\Pi(\phi)\) with AE data from the Mistras system for the true coincidence instants (black circles in (**f**)) in normalized time equal to (from left to right): 0.698, 0.7601, 0.8621. We now investigate the effect of the sensor location, as illustrated in Figure 9, which depicts the distribution of AE sources along the \(z\) coordinate of the sample (see Figure 4) according to the localization methodology proposed in [1]. The AE activity is preponderant along the positive semi-axis in both plots. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Coefficient of Variation** & **Lunitek** & **Mistras** \\ \hline Amplitude (db) & \(CV_{A}=\sigma_{A}/\langle A\rangle\) & \(6.4/57.45=0.11\) & \(6.2/50.27=0.12\) \\ \hline \(AF\)(kHz) & \(CV_{AF}=\sigma_{AF}/\langle AF\rangle\) & \(32.44/44.27=0.73\) & \(33.44/58.54=0.57\) \\ \hline Duration (\(\mu\)s) & \(CV_{Dur}=\sigma_{Dur}/\langle Dur\rangle\) & \(5194.79/1595.56=3.25\) & \(1040.94/740.94=1.40\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coefficient of variation (\(CV\)), average values (\(\langle\,.\,\rangle\)) and standard deviations (\(\sigma\) ) of the AE signal parameters. Figure 8: AE parameters statistical analysis for Lunitek and Mistras systems: (**a**) amplitude, (**b**) average frequency, (**c**) duration. Figure 7: Relation between counts versus duration for: the (**a**) Lunitek and, (**b**) Mistras system. Amplitude in db is present in the colorbar. When an elastic wave hits a piezoelectric AE sensor coupled to the surface of a material under damage, the surface displacement at the nanometer scale is converted into an electric signal. The wave mode and frequency content of the AE signal arriving at the sensor are affected by the geometry and the wave propagation properties of the material between source and sensor. An AE signal is detected if the arrival of the AE wave causes an electric signal in the AE sensor whose amplitude exceeds the selected detection threshold. Transient AE signals are analyzed and reduced to a set of parametric features which are recorded by the data acquisition system. Essential AE signal features that are extracted and stored are arrival time at the sensor, maximum peak amplitude, signal duration, and energy. Most AE signal features depend on the selected measurement parameters, e.g., the detection threshold. Therefore, it is not possible to speak in absolute terms of the accuracy of experimental results in tests with AE. Too many parameters influence the obtained outcomes: the signal attenuation properties of the analyzed material, environmental noise, sensor sensitivity, and the predetermined detection threshold, in particular. In this way, when comparisons are made between the energy of AE signals detected by the piezoelectric sensors and those actually emitted by the materials under stress, they can only be made with arbitrary units or by normalizing the current values to the maximum values obtained. Only by taking into account the problem of the AE source localization in various materials can an efficient study on the accuracy of results from AE tests be conducted. In the literature, there are various studies on this problem; see for example [51; 52; 53].