# Real-Time Stress Field Prediction of Umbilical Based on PyEf-U-Net Convolutional Neural Network
## 6 Conclusions  
As an important equipment of marine engineering, it is essential to analyze the mechanical properties of the umbilical. A novel PyEf-U-Net convolutional neural network  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cross-Sectional Layout** & **Simulation Software Time Consumption** & **PyEf-U-Net Time Consumption** \\ \hline \hline
30 min and 15 s & 3.877 s \\ \hline
51 min and 12 s & 3.582 s \\ \hline
34 min and 40 s & 4.037 s \\ \hline
28 min and 10 s & 2.866 s \\ \hline
10 min and 41 s & 3.432 s \\ \hline \hline \end{tabular}
\end{table}
Table 8: Calculation time analysis of stress field for network model and numerical simulation.  
model has been proposed in this paper to overcome the drawbacks of the traditional finite element method, which is seriously time-consuming and hard to converge, and which achieves the purpose of real-time accurate prediction of mechanical properties of the umbilical. The experimental validation demonstrates that the proposed deep learning model can not only accurately predict the stress field layout of umbilical within 2-5 s, but also has an accuracy rate as high as 94.2% compared to other state-of-the-art deep learning models. Additionally, the effects of hyperparameters such as the optimizer, learning rate, batch size, and loss function of the PyEf-U-Net network model have been discussed in detail in the paper. Among the currently available studies, the feasibility of the proposed deep learning method has been verified with 2D arithmetic examples, which can accurately predict the stress field distribution of the umbilical in real-time, and which provides an effective way to predict other mechanical properties of the umbilical in real-time. Alternatively, the method can be extended to 3D models, which are not fundamentally different in concept and principle, except for the relatively high cost of the dataset collection process. In particular, the complex distribution of umbilical load forms in the marine environment will be an enormous challenge to predicting the mechanical properties of umbilical in real-time. In future work, more complicated 3D engineering cases will be utilized to input the network model, which will enhance the generalization ability of deep learning methods to predict the distribution of umbilical mechanical properties in real-time in a real marine environment. Simultaneously, it can be applied not only to the study of the mechanical properties of an umbilical but also extended to the analysis of the mechanical properties of similar structures such as cables.  
L.W.: conceptualization, methodology, software, formal analysis, investigation, writing original draft, writing--review and editing, visualization. B.Z.: conceptualization, resources, visualization, supervision, writing--review. G.L.: supervision. W.M.K.H.: supervision. D.S.: visualization, funding acquisition. M.Q.: resources, visualization. X.Y.: supervision. All authors have read and agreed to the published version of the manuscript.  
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (12172100).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.