# Real-Time Stress Field Prediction of Umbilical Based on PyEf-U-Net Convolutional Neural Network
## 1 Introduction
[10] performed a numerical analysis of the umbilical, which compared the numerical simulation results with various load condition scenarios to demonstrate the feasibility of the numerical simulation. [PERSON] et al. [11] developed 2D and 3D models for umbilical subjected to crush load, which were used to predict the strain field of the umbilical with two different numerical methods. The results demonstrated that the numerical calculation of the 2D model can be faster under the crushing load, yet the calculation results of the two models have to be consistent. [PERSON] et al. [12] designed a new structure for umbilical to adapt to the working  
Figure 1: The structure of the umbilical: (**a**) the umbilical under operation; (**b**) types of umbilical components. environment of 400 m water depth and utilized UFLEX to study the stress and mechanical properties of the umbilical under 400 m water depth, which verified the rationality and reliability of the structural design of the umbilical. [PERSON] et al. [13] developed a novel manufacturing process for seam-welded stainless steel pipes that improves the mechanical properties of the pipes, which avoids the effects of water depth, pressure, and temperature on the structural properties of the umbilical. [PERSON] et al. [14] proposed a semi-analytical calculation method to calculate the nonlinear tensile-torsional coupling effect of an umbilical. Tensile experiments were conducted on the umbilical, which demonstrated the accuracy of the method. Simultaneously, it can provide beneficial data references for the design of an umbilical. Mechanical properties of the umbilical are normally analyzed with theoretical analysis, experimental testing, and numerical simulation. Due to the existence of substantial nonlinearities in umbilical, it is difficult to accurately solve the mechanical behavior of the umbilical via theoretical analysis, while the experimental cost is extremely high. Consequently, numerical simulation [15] has become the mainstream method for the current analysis of the mechanical behavior of an umbilical. Nevertheless, numerical simulation computation is frequently time-consuming and prone to non-convergence. Consequently, determining how to avoid the high cost of calculation time while ensuring the accuracy of the calculation results is essential. With the development of deep learning, considerable efforts have been focused on using deep learning for real-time computation [16; 17; 18; 19; 20; 21], which is applied to avoid time cost consumption. [PERSON] et al. [22] applied deep learning methods to predict the stress fields of fiber-reinforced composites to address the huge computational time cost associated with finite element analysis. The stress field of the composites with different numbers of fibers has been obtained via the U-Net network, which provides a reference for the subsequent material stress analysis. [PERSON] et al. [23] proposed two different deep learning models, SCSNet and StressNet, for predicting the stress field distribution in 2D cantilever beams, respectively. Among the existing studies on the mechanical properties of umbilical, few studies have been conducted to obtain the stress field distribution of umbilical in real time. [PERSON] et al. [24] combined finite element analysis with deep learning and proposed the NARX-CNN network model to predict the tension and curvature of the umbilical in the first time, and the accuracy of the proposed network model is higher than that of the finite element method, which avoids the disadvantage of the high computational cost of finite elements. [PERSON] et al. [25] employed a residual neural network to predict the load-displacement curve of umbilical under radial compression, which prevented the computational errors due to the consideration of elastic deformation in the traditional theoretical calculation.