## 3 Simulating MFL Signals Using FEA
### FEA Cases  
A series of FEA models are created and analyzed with the same magnetization conditions and pipe attributes, but they vary in corrosion types, geometric parameters, and locations in this study. The simulation involves 9600 analysis cases, with 1600 cases allocated to each of the six scenarios as illustrated in Figure 4, namely internal general corrosion (\(\mathrm{G_{in}}\)), external general corrosion (\(\mathrm{G_{ex}}\)), internal pinhole (\(\mathrm{P_{in}}\)), external pinhole (\(\mathrm{P_{ex}}\)), internal PIC defect (\(\mathrm{PIC_{in}}\)), and external PIC defect (\(\mathrm{PIC_{ex}}\)). The general corrosion is idealized as cuboidal-shaped, defined by the width (\(w_{g}\)), depth (\(d_{g}\)), and length (\(l_{g}\)), and the pinhole is idealized as cylindrical-shaped, defined by the radius (\(r_{p}\)) and depth (\(d_{p}\)). Note the center of the pinhole in a PIC defect is assumed to be coincident with that of the general corrosion, which is defined by two coordinates, i.e., its longitudinal location (\(h\)) and circumferential location (\(\phi\)), within a 160 \(\times\) 160 mm designated area as shown in Figure 5. This area is marked in light blue, with its center specified by the coordinates (\(r\), \(\varphi\) = 0, \(h\) = 0), where \(r\) represents the inner radius of the pipe. This specific 160 \(\times\) 160 mm square area on the inner pipe wall was selected because it encompasses the largest area, showing a consistent magnetic flux density profile between the neighboring magnets. The analysis cases involving general corrosion only, i.e., \(\mathrm{G_{in}}\) and \(\mathrm{G_{ex}}\), include four values of \(w_{g}\), i.e., 30, 50, 70, and 90 mm, four values of \(d_{g}/t\), i.e., 20, 40, 60, and 80%, where \(t\) denotes the pipe wall thickness, and four values of \(l_{g}\), i.e., 30, 50, 70, and 90 mm. This results in 64 general corrosions in total with varying sizes. In terms of the corrosion location, five values of \(h\) (\(-\)50, \(-\)25, 0, 25, and 50 mm) and five values of \(\phi\) (\(-\)10, \(-\)5, 0, 5, and 10 degrees) are considered. The permutations of 64 defects and 25 locations lead to 1600 cases for each of \(\mathrm{G_{in}}\) and \(\mathrm{G_{ex}}\). The analysis cases involving pinhole corrosion only, i.e., \(\mathrm{P_{in}}\) and \(\mathrm{P_{ex}}\), include eight values of \(r_{p}\), i.e., 1, 1.5, 2, 2.5, 3, 3.5, 4, and 4.5 mm, and eight values of \(d_{p}/t\), i.e., 10, 20, 30, 40, 50, 60, 70, and 80%. This results in 64 pinhole corrosions in total with varying sizes. In terms of the corrosion location, five values of \(h\) (\(-\)50, \(-\)25, 0, 25, and 50 mm) and five values of \(\phi\) (\(-\)10, \(-\)5, 0, 5, and 10 degrees) are considered. The permutation of 64 defects and 25 locations also leads to 1600 cases for each of \(\mathrm{P_{in}}\) and \(\mathrm{P_{ex}}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Elements** & **Pipe Section** & **Magnets** & **Brushes** & **Yoke** \\ \hline geometry (mm) & 600 \(\times\) 610 \(\times\) 10 a  & 300 \(\times\) 81 \(\times\) 105 b  & 300 \(\times\) 81 \(\times\) 20 b  & 300 \(\times\) 300 \(\times\) 40 a  \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometry of every component within the proposed 3D CMFL model. Figure 3: Illustration of CMFL tool. Figure 4: _Cont._  
Figure 4: Six types of corrosion situations: (**a**) \(\text{G}_{\text{in}}\) and \(\text{G}_{\text{ex}}\); (**b**) \(\text{P}_{\text{in}}\) and \(\text{P}_{\text{ex}}\); (**c**) \(\text{PIC}_{\text{in}}\) and \(\text{PIC}_{\text{ex}}\). Figure 5: Cylindrical coordinate system defining location parameters \(h\) and \(\phi\). Analysis cases involving PIC defects, i.e., PIC\({}_{\text{in}}\) and PIC\({}_{\text{ex}}\), include \(w_{g}=l_{g}=50\) mm and four values of \(r_{p}\), i.e., 1, 2, 3, and 4 mm. In terms of the sizes of general and pinhole corroosions, three groups are considered to capture a wider range of relative relationships between general and pinhole corroosions.