## 2 Experimental Method and Results
### Experimental Results Discussion  
The application of the thresholding approach for recording acoustic signals is one of the main reasons for the AE source positioning error growing determined by the 1D linear location method. Since higher frequencies were attenuated more rapidly with propagation distance, significant changes in the initial steepness of the AE signals envelope have been observed. This fact led to a considerable increase in the parameter \(\Delta t\). In Figure 3, the waveforms and spectra of low-amplitude acoustic signals recorded by AE sensors at a distance of 100 mm and 700 mm from the acoustic source were presented, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Coordinates of AE** & **Amplitudes Interval of** & **Positioning Error** & **Average** \\
**Source X, mm** & **Record AE Signals** & **\(\gamma\), \%** & **Positioning Error** \\  & [\(u_{\text{min}}\):\(u_{\text{max}}\)], dB** & **\(\gamma\), \%** & **\(\gamma_{av}\), \%** \\ \hline  & [40:60]  
The waveform registered-by AE sensor #1 was depicted in Figure 3a. It can be inferred that the maximum AE signal amplitude corresponded to the \(u_{max}\) = 56 dB, and the rise time equaled to \(t_{n}\) = 64 \(\upmu\)s.  
The spectrum of this signal was shown in Figure 3b, where three special frequency ranges can be distinguished: 40-160 kHz, 160-250 kHz, 250-400 kHz. With attenuation of high-frequency modes, the energy decreased and the slope of the AE signal envelope at the initial moment declined as well. It caused a significant effect on the value of the parameter \(\Delta t\)[19; 20].  
In Figure 3c the signal waveform registered by the further receiving transducer (AE sensor #2) was represented. Its maximum amplitude constituted \(u_{max}\) = 52 dB, and the rise time was about \(t_{n}\) = 102 \(\upmu\)s. The growth in the rise time of the AE signal correlated with the fall in the partial energy of the spectrum in the frequency range 250-400 kHz. Thus, the rapid attenuation of high-frequency modes influenced the recording time of acoustic signals, and hence, on the level of the investigated positioning error. This fact was confirmed by the estimation of relative changes in the high-frequency portion of the spectrum \(\delta\) revealed in Figure 4. The dependence of the attenuation of high-frequency spectral components on the AE signal propagation length \(L\) was evaluated according to the equation [14]:  
\[\delta=\frac{\left|H(f)_{1}-H(f)_{2}\right|}{H(f)_{1}},\ [\%] \tag{3}\]  
where \(H(f)_{1}\) and \(H(f)_{2}\) cumulative amplitudes of AE signals harmonics registered by AE sensor #1 and AE sensor 2 in the range of 250-400 kHz. The approximation of the calculated results of the parameter \(\delta\) was performed by the least-squares method fitting with a second-degree polynomial.  
Figure 3: Comparison of the signal waveforms and spectra recorded by **(a,b)** AE sensor #1 and **(c,d)** AE sensor #2 located at a distance of 100 mm and 700 mm from the AE source, respectively.  
From the curve shown in Figure 4 and results from Table 1, it can be indicated that the considerable attenuation of high-frequency waves leads to a great change in the energy parameters and the signal waveform. Therefore, to determine the correct location of an AE source, it is essential to take into account not only the TDOA parameter of signals but also their energy and spectral characteristics [21].