# Real-Time Stress Field Prediction of Umbilical Based on PyEf-U-Net Convolutional Neural Network
## 5 Experimental Results and Discussion
### Analysis of Network Model Parameters and Discussion of Prediction Results
Nevertheless, although the Multiclass Dice loss functions smoothly during the early iterations, obvious fluctuations exist during the later period, with unstable model training and slowly decreasing loss values during the early period. Additionally, the Cross Entropy loss function selected has the most satisfactory performance, which can not only successfully avoid the shortcomings of the NLLLoss2d loss function and Multiclass Dice loss function but also has the characteristics of fast convergence, no sudden change, and stability, which gives the proposed network model a strong learning ability, with the best network performance for umbilical stress field prediction, which provides the accurate prediction of output results. Consequently, in comparison, the Cross Entropy loss function was chosen from the PyEf-U-Net deep learning network. Figure 17: Compared analysis of network performance with different optimizers. As shown in Table 7, the effect of the combination of four different modules on the accuracy of the network model is investigated. The Basic model in the first row refers to the U-Net without any modules, which obtains the accuracy of 0.854. The second row of the table refers to the accuracy of 0.882, only adding the EffCA module to the Basic model. The third row of the table refers to adding only the Pyra-Con module to the Basic model, which yields an accuracy of 0.895. Nonetheless, the last row of the table refers to the PyE-U-Net, which adds the EffCA module and Pyra-Con module to the low-level feature map and the last transition layer of the network, respectively, in comparison with the highest accuracy rate of 0.942. It has been experimentally demonstrated that each module is essential to improving the prediction accuracy, and the PyE-U-Net can only obtain the highest accuracy by adding both the EffCA module and Pyra-Con module, which can achieve high-accuracy umbilical stress field prediction results. The comparison of the time used for the numerical simulations with different layouts of the umbilical and the predicted time of the PyEf-U-Net is shown in Table 8. It is evident that the numerical simulation time exponentially increases with increasing the number, type, and number of layers of the components. The variation of such parameters can lead to the explosion increasing numerical simulation time, which will be costly in terms of time. Nevertheless, the prediction time of the proposed PyEf-U-Net network in this paper ranges from 2-5 s, which improves the computational efficiency; the time cost is almost negligible, and the prediction time is not affected by the number, type, and layers of the components. Consequently, the method of using deep learning networks for stress field prediction of the umbilical will significantly improve the efficiency of the mechanical property analysis of the umbilical in the marine engineering field. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Basic Model** & **EffCA** & **Pyra-Con** & **Accuracy** \\ \hline \(\surd\) & & & 0.854 \\ \(\surd\) & \(\surd\) & & 0.882 \\ \(\surd\) & & \(\surd\) & 0.895 \\ \(\surd\) & \(\surd\) & \(\surd\) & 0.942 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Analysis of ablation experiment results. Figure 18: Comparative analysis of network performance with different loss functions.