# Real-Time Stress Field Prediction of Umbilical Based on PyEf-U-Net Convolutional Neural Network
## 1 Introduction  
An umbilical is the core equipment of the entire production system, which is widely applied to connect a floating body to the subsea manifold, providing hydraulic transmission, chemical injection, electrical energy, and control signal transmission for sub-sea trees. The subsea production system's umbilical structure is shown in Figure 1[1]. The umbilical is typically a multi-layer elongated helical wound armored structure, which generally consists of internal components such as cables, optical cables, steel pipes, etc. During the operation of the umbilical, it is subject to complex loads such as waves and currents. Hence, the safety of the umbilical structure has been directly related to the normal operation of the entire underwater production system. The mechanical properties of the umbilical can directly reflect the safety of the structure. Nevertheless, the umbilical consists of a multi-material and multi-component composite structure, with a large amount of nonlinear contact and friction, which is a typical heterogeneous anisotropic structure. The above factors bring great challenges in solving the mechanical properties of the umbilical [2, 3]. During operation, the umbilical is subjected to tension at the top of the umbilical where it connects to the floating body, and the mechanical behavior of the umbilical at the touchdown point is also subjected to axial compression. Mechanical behaviors such as tension and compression act on the umbilical structure over the long term. Consequently, it is essential to analyze the mechanical properties of the umbilical. To effectively restore the working environment of the umbilical, the industry normally adopts Deepwater Immersion Performance (DIP) experiments that simulate the actual working conditions to perform relevant research. [PERSON] et al. [4] reproduced the lateral slip instability damage pattern of the umbilical helical armor layer by the DIP experimental method, which revealed that the bending load plays an important role in inducing the lateral slip instability of the armor layer. [PERSON] et al. [5] observed the lateral slip instability of the armor layer under combined bending and compression loads while conducting structural simulation certification experiments for the umbilical at 3000 m water depth, and then determined the limit capacity of the armor layer of the umbilical to resist lateral slip instability damage through experimental data analysis. Considering the extremely high cost and difficult operation of DIP experiments, most scholars have tried to investigate the umbilical from indoor equivalent loading experiments, theoretical analysis, and numerical simulations. [PERSON] et al. [6] constructed an indoor simulation experimental setup to simulate the umbilical structure with combined bending and compression loads and carried out the corresponding destabilization damage research. The experimental data on the displacement and torsion angle of the steel armor wire have been analyzed, which has verified the feasibility of the numerical simulation and explained the destabilization damage mechanism. [PERSON] et al. [7] designed an experimental setup to simulate combined bending, compression, and external pressure loads, and performed instability damage simulation experiments for umbilical with 2.5-inch and 4-inch diameters, simultaneously comparing the traditional results with the data to prove the validity of the developed numerical simulation. [PERSON] et al. [8] used a formula that allows a preliminary estimation of the service life of the umbilical by calculating the inter-layer slip and stresses caused by bending. Nevertheless, the method must be completed by experimentally determining the friction coefficient. [PERSON] [9] pioneered a new set of equilibrium equations that were used to solve the cable stiffness matrix under tension and torsion. [PERSON] et al.