# 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  
The performance of the proposed PyEf-U-Net network model is validated to be advantageous by comparing it with the other three deep learning network models, as shown in Figure 14. It can be seen that the USE-Net [37] and the SCSE-U-Net [38] have similar change patterns of loss value curves; however, both appear significant abrupt changes during the iterations, demonstrating the poor stability of the models, which causes low accuracy of the final prediction results and cannot achieve the final prediction purpose. Moreover, the value of loss declines slowly in the first 1500 iterations and the convergence speed of both deep learning models becomes slower. Additionally, although the U-Net [39] has no mutations throughout the training process, the network converges slowly and cannot adapt well to the dataset. By comparison, the loss-value curve of the PyEf-U-Net changes smoothly, the minimum loss value can be obtained without multiple iterations and gradually stabilizes, while the overall convergence speed of the network is faster than the other three network models. Consequently, the proposed PyEf-U-Net has superior performance than the other three deep learning network models. The stress field distribution of the umbilical with different layout forms is applied to verify the performance of the PyEf-U-Net, and the stress field prediction results as shown in Table 6. Compared with the numerical simulation results, the prediction results obtained from the PyEf-U-Net proposed have the best agreement with the numerical simulation results, while the other three network models present the problem of the imprecise numerical prediction of the stress field of the umbilical. It can be observed that U-Net obtained the worst prediction results, while both USE-Net and SCSE-U-Net outperformed U-Net, which is due to the fact that the mentioned deep learning model adding the attention module to the U-Net network, capturing feature information from the channel dimension, assigning higher weights to important feature regions, and suppressing irrelevant features. Nevertheless, the prediction results of the above network are frequently unsatisfactory in places where the stresses in the umbilical are concentrated. On the contrary, the proposed PyEf-U-Net can successfully avoid the above-mentioned situations and well distinguish the stress cases in different regions. More importantly, adding the EffCA module and Pyra-Con module to the PyEf-U-Net has combined the ability of the lightweight EffCA module to capture channel dependencies with the ability of the Pyra-Con module to fuse multi-scale features, which enables the prediction results of the PyEf-U-Net \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Positive** & **Negative** \\ \hline Positive & _TP_ & _FN_ \\ Negative & _FP_ & _TN_ \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification confusion matrix. The learning rate parameter determines whether the loss function can converge, which in turn affects the accuracy of the prediction results of the deep learning network. To investigate the effect of the learning rate on the PyE-U-Net deep learning model, the learning rate is set to 0.01, 0.001, 0.0001, and 0.00001. Comparing the change of loss values of the PyE-U-Net deep learning model with different learning rates, as shown in Figure 15. At learning rates of 0.01 and 0.001, the loss value decreases to around 0.2 in the early stage of iterative training; however, the network fluctuates drastically during the later iterations and the stability of the network is poor. It indicates that when the learning rate is 0.01 and 0.001, the network cannot consistently and steadily learn the feature information from the original dataset and has poor learning ability. Additionally, with the learning rate of 0.00001, the network performance is the worst, the loss value iterations converge slowly and eventually stay fluctuating around 0.3, which has no optimal learning ability.