## 4 Results Analysis
### Sensor Signals of Pipeline Structures with Dual Defects at the Same Circumferential Position
4 The axial distance of damage in the figure is the distance between the second defect and the piezoelectric element sensor, with the first defect always located at a position 750 mm away from the piezoelectric element sensor. The axial distance between the second defect and the piezoelectric element sensor was set as 750 mm, such that the position of the first defect overlapped with that of the second defect, meaning that there was only one defect in the pipeline structure. Based on Figure 7 and Table 6, it can be concluded from the comparison between case 10 and case 11 that, although the reflected wave of the second defect overlapped with the mode conversion wave or reflected wave 1, the phase difference between them was close to \(\pi/2\) (the corresponding phase distance was 111 mm), resulting in the coherent cancellation of the waveform of the reflected wave of the second defect. Similarly, from the comparison between working conditions 10 and 12, it can be concluded that, although the reflected wave of the second defect also overlapped with the mode conversion wave, the phase difference between them was close to \(\pi\) (the corresponding phase distance was 221 mm), resulting in the coherent superposition of the waveform of the reflected wave of the second defect. Therefore, it can be concluded that when the phase difference is close to \(\pi/2\), the reflected waves of the two defects will produce coherent cancellation; when the phase difference is close to \(\pi\), the reflected waves of the two defects will produce coherent superposition, leading to a periodic variation trend in the damage index values of the double defects. Figure 7: Time-domain comparison plots for the operating conditions: (**a**) comparison of the piezoelectric time-domain signals between case 10 and case 11, (**b**) the partial detailed diagrams of case 10 and case 11, (**c**) comparison of the piezoelectric time-domain signals between case 10 and case 12, and (**d**) the partial detailed diagrams of case 10 and case 12. [PERSON]. [4] conducted a study on double defects in a single-layer pipeline structure, and found that when the relative axial distance between the double defects exceeded a certain value, the reflected wave packets of the double defects separated, and they could be regarded as two independent single defects. The guided wave wavelength (referred to as \(\lambda\)) was calculated based on the geometric and material parameters of the pipeline structure in this paper. When the relative axial distance between the defects exceeded \(1.36\lambda\) (specifically, when the first defect was located 750 mm away from the piezoelectric sensor, and the second defect was located more than 1350 mm away from the sensor), the reflected wave packets of the two defects separated, and the reflected wave could be clearly distinguished in the piezoelectric time-domain graph. This meant that the two defect reflection signals could be detected independently in the piezoelectric time-domain graph once the axial distance between the defects was greater than \(1.36\lambda\).