## 3 Establishing Finite Element Models
### Double Defect Pipe Structure with the Same Circumferential Position  
To investigate the feasibility of discriminating the relative axial position of defects in pipeline structures based on damage index values, double-defect pipeline structure models with the same circumferential location were established. To avoid the influence of the different defect sizes on the discrimination of the relative axial distance of double defects, both defects in this study were of the same size, with a length of 3/16 of the pipe's outer diameter circumference, a width of 4 mm, and a depth of 2 mm. Additionally, the double defects were located on the same generatrix. The specific operating parameters for this condition are presented in Table 4.  
The maximum value of L was set to 1800 mm, based on the reflection angle of the second defect. When the axial distance between the second defect and the piezoelectric transducer exceeded 1800 mm, the reflection echo from the second defect (the first reflection) would overlap with the boundary reflection echo (the second reflection), making it difficult to determine the time when the first reflection was received by the piezoelectric sensor. Therefore, the range of the axial distance between the second defect and the piezoelectric transducer was limited to 750 mm to 1800 mm. The defect plane layout of the double defects with the same circumferential position in the pipeline is shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & **First Defect Axial** & **Second Defect** & **Spacing of** \\  & **Distance/mm** & **Axial Distance/mm** & **Damage/mm** \\ \hline case 10 & 750 & 750 & 0 \\ case 11 & 750 & 900 & 150 \\ case 12 & 750 & 1050 & 300 \\ case 13 & 750 & 1200 & 450 \\ case 14 & 750 & 1350 & 600 \\ case 15 & 750 & 1500 & 750 \\ case 16 & 750 & 1650 & 900 \\ case 17 & 750 & 1800 & 1050 \\ \hline \hline \end{tabular}  
* The axial distances of the first and second defects are both the axial distances between the defects and the piezoelectric transducer sensor. The first and second defects are located on the same generatrix.  
\end{table}
Table 4: Operational parameters of the finite element model with the same circumferential position in pipeline structural health monitoring [3].  
Figure 4: Schematic of double defects with the same circumferential position in the pipeline structure.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure Name** & **Element Type** & **Grid Size/mm** & **Number of Grids** \\ \hline piezoelectric element & C3D8E & 12 & 20 \\ structural layer & C3D20R & 5 & 49,674 \\ insulation layer & C3D20R & 5 & 107,520 \\ anticrowicse layer & C3D20R & 5 & 36,960 \\ \hline \hline \end{tabular}  
* The insulation layer and anticrowicse layer in the subsequent analysis had different numbers of defects, compared to the number of grids presented in this table. However, the number of grids for other models remained the same. For the sake of simplicity, please refer to this table for the grid division of relevant models in the subsequent analysis.  
\end{table}
Table 3: Meshing of the finite element model [2].