## 3 Results
### Acoustic Waveguide Modeling Results  
Acoustic waveguide modeling allows for determining the waveform and spectrum of the AE signal when diagnosing dissimilar welded joints of process pipelines. To confirm the correctness of the modeling results, Figure 11 shows the distribution of the object surface displacements. The displacement map is shown at different moments in time relative to the moment of generation of the probing impulse. The modeling result corresponds to the case when the AE source is located on the pipeline surface along the fusion line on the side of grade 20 steel. Five microseconds after acting, the source (Figure 11a) at the wavefront was localized in the source location zone; after 50 and 100 \(\upmu\)s (Figure 11b,c), the propagation of the spherical wavefront along the acoustic waveguide of the monitored object can be observed. To verify the results, a comparison was made between the time-frequency parameters of the signals obtained by simulation and the signals measured experimentally. The experiment was performed on a laboratory model of a pipeline with a welded joint; the diameter and wall thickness of the pipeline corresponded to the model parameters (outer diameter 100 mm, wall thickness 3 mm). The AE signals were simulated using a Hsu-Nielsen source at different distances from the AE sensor. Measurements were performed using the A-Line 32D system in the same configuration as in mechanical tests. To ensure a correct comparison, the signals obtained by simulation were subjected to additional processing, including  
Figure 10: Distribution of AE impulse amplitudes for defect-free samples (red markers with a different shape corresponds to two different defect-free samples) (**a**), for samples with diffusion interlayers (blue markers with a different shape corresponds to three different defective samples) (**b**), averaged amplitude distributions (graph with red markers corresponds to defect-free sample, graph with blue markers corresponds to the sample with diffusion interlayers) (**c**). the convolution with the impulse response of the AE sensor. The comparison results are shown in Figure 12.  
Figure 11: Simulation result—total displacement of the object surface: 5 \(\upmu\)s (**a**), 50 \(\upmu\)s (**b**), and 100 \(\upmu\)s (**c**) after the application of the probing excitation. Figure 12: Signals at a distance of 0.3 m from the AE source: simulated AE signal (**a**), measured AE signal (**b**), wavelet spectrograms for the simulated signal (**c**), and for the measured signal (**d**). As can be seen from Figure 12, the signal obtained as a result of simulation (Figure 12a) and the measured signal (Figure 12b) have a similar waveform, and the wavelet spectrograms show a correct dispersion structure characteristic of Lamb wave propagation. The similarity of the signals obtained as a result of modeling and the measured signals confirms the reliability of the finite element model. Analysis of signals obtained with different modeling parameters showed that variations in the position of the source and receiver do not lead to significant changes in the signal waveform. The greatest influence on the waveform is exerted by a change in the coordinate of the signal recording point in the axial direction. Figure 13 shows signals recorded at a distance of 0.1, 0.3, and 0.5 m from the emission point; with an increase in the distance of signal propagation along the waveguide, signs of a change in waveform characteristic of dispersive propagation are noted--a decrease in amplitude and an increase in the rise time (Figure 13a-c), on the wavelet spectrograms one can also notice a shift in the spectrum to the low-frequency region (Figure 13d-f). Changing the azimuthal coordinate also does not have a significant effect on the signal waveform; Figure 14a,b show signals measured at a distance of 0.3 m from the source; the signal shown in Figure 14a has the same azimuthal coordinate as the source, and the signal shown in Figure 14b is shifted by 180\({}^{\circ}\).