# Real-Time Stress Field Prediction of Umbilical Based on PyEf-U-Net Convolutional Neural Network
## 3 Numerical Simulation and Experimental Verification  
The typical umbilical cross-section is shown in Figure 5, which is mainly composed of six steel pipes, three cables, one optical cable, an inner sheath, armor wires, an outer sheath, and filling bodies. The geometric size of each component of the umbilical is shown in Table 1. Due to the multi-component and multi-material characteristics of the umbilical, a large amount of contact and friction exists between the components, which can cause great difficulties when performing numerical simulations. Consequently, it has been found in existing studies [29; 30; 31; 32; 33] that certain parts are typically simplified in modeling due to the smaller contribution of these components to the overall strength of the umbilical. Cable is commonly simplified to the polymer dense-wrapped copper core structure, while the optical cable is simplified to polymer dense-wrapped steel shell structure. The simplified umbilical is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Quantity**} & \multicolumn{4}{c}{**Structure Size**} \\ \cline{3-6}  & & & **Inner Diameter (mm)** & **Thickness (mm)** & **Outer Diameter (mm)** \\ \hline \multirow{4}{*}{Steel pipe} & Duplex stainless steel pipe & \multirow{2}{*}{6} & \multirow{2}{*}{12.7} & \multirow{2}{*}{1.0} & \multirow{2}{*}{14.7} \\ \cline{2-6}  & Polyethylene sheath & & & & \\ \hline \multirow{4}{*}{Cable} & Copper conductor & \multirow{4}{*}{3\(\times\) (4 \(\times\) 7 mm\({}^{2}\))} & \multirow{4}{*}{3.15} \\ \cline{2-6}  & Polyethylene sheath & & & & \\ \cline{1-1} \cline{2-6}  & XLPE insulation & 12 & 3.15 & 0.725 & 4.6 \\ \hline \multirow{4}{*}{Optical cable} & Seamless steel & 1 & 2.6 & 0.2 & 3.0 \\ \cline{2-6}  & Inner wire layer & 7 & 3.0 & 2.0 & 7.0 \\ \cline{1-1} \cline{2-6}  & Outer wire layer & 13 & 7.0 & 2.0 & 11.0 \\ \cline{1-1} \cline{2-6}  & Polyethylene sheath & 1 & 11.0 & 2.5 & 16.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Umbilical structure size parameters [14]. Figure 4: Four different layout cases of the umbilical. (**a**) Umbilical Layout Style 1; (**b**) Umbilical Layout Style 2; (**c**) Umbilical Layout Style 3; (**d**) Umbilical Layout Style 4. Figure 5: Umbilical cable cross-section layout. Figure 6: Simplified Umbilical 3D Model. Numerical simulation analysis of the umbilical is performed via ABAQUS simulation software, which is compared and analyzed with subsequent experiments. The total length of the model is the same as the real size, with a total length of 200 mm. The mesh type, C3D8R, in ABAQUS, is chosen since the precision of the computation analysis is not greatly affected when deformation distortion occurs in the mesh. Since the internal components of the umbilical are mostly helical wound structures, the swept mesh division method is adopted to arrange the same mesh seeds in the axial direction, which makes the different components of the umbilical maintain the same size in the axial direction and ensures better mesh contact between adjacent layers. The whole mesh of the umbilical model is shown in Figure 7. The mesh independent validation is shown in Table 2. The number of mesh was selected as 150,960 for calculation  
The boundary condition for the ABAQUS numerical simulation is shown in Figure 8. Two reference points, RP-1 and RP-2, are established in ABAQUS, which are connected, respectively, to the two ends of the umbilical by the way of motion coupling. Apply load to RP-1 and constraint to RP-2. Since the non-linear characteristics of the umbilical are obvious during the stressing process, the ABAQUS/Explicit solver is adopted for the numerical simulation calculation, which calculates the entire process of force change of the umbilical via the dynamic display. To demonstrate the accuracy of ABAQUS numerical simulation, the mechanical properties of the umbilical have been evaluated with a servo control universal material testing machine.