# 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
In comparison, with the learning rate of 0.0001, the network rapidly decreases and gradually stabilizes the loss value at the beginning of training, which converges to the minimum value of around 0.04, with no sudden mutations occurring during the entire process. Consequently, 0.0001 is selected to be the learning rate parameter for the PyE-U-Net network. Batch size has an impact on the accuracy of the stress field prediction results of the umbilical. Comparative analysis for different batch sizes is performed, and the umbilical prediction results are shown in Figure 16. With batch sizes 2, 8, and 16, inaccurate predictions of the stress field at the boundary of the umbilical can occur, especially in the \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{1}{c}{\(F=4\) MPa} & \multicolumn{1}{c}{\(F=4\) MPa} \\ \hline  & & \\  & & \\  & & \\  & & \\  & & \\  & & \\  & & \\  & & \\  & & \\  & & \\  & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._region of stress concentration. Through comparison and analysis, it was found that when the batch size is 4, the above existing problems can be successfully avoided, which can ac-curately predict the area where the stress of the umbilical concentration is. Consequently, the batch size parameter was eventually chosen to be 4. The optimization algorithm is the significant network parameter that affects the iterative training of deep learning models, whose selection directly influences the performance of the PyEf-U-Net deep learning. To investigate the effects of different optimization algorithm selections for the PyEf-U-Net deep learning model, four different types of optimizers are chosen for comparative analysis, as shown in Figure 17. It can be seen that the SGD has the worst performance with slow iteration of the loss value curve and the loss value  
Figure 16: Stress prediction results for umbilical with different batch sizes. Figure 15: Comparative analysis of network performance with different learning rates. decreases slowly, which results in the poor learning ability of the network. This is due to the fact that SGD is prone to training in the direction of deviating from the optimal network strength and the network training is unstable. Nevertheless, with regard to the Adagrad optimizer, due to the inclusion of the momentum matrix, the network is able to adapt to changes in the learning rate, which is overall superior to the curve of variation in the loss values of SGD. Nevertheless, the accuracy of the PyEf-U-Net cannot be guaranteed due to the high loss values during the late iterations. Additionally, the RMSProp updates the parameters through adjusting the learning rate, and its loss value change is superior to that of the SGD and Adagrad; however, the algorithm has a slower loss value decrease and slower convergence in the pre-iterative training period, with significant abrupt changes during the late stage of iteration. By comparison and analysis, the loss value variation curves obtained by the Adam significantly outperformed those obtained by the other three optimization algorithms. Rapid decrease and gradual stabilization of the loss value in the pre iterative training period, stabilizing at about 0.04, which is substantially lower than the loss values obtained by the other three optimization algorithms, simultaneously, without any sudden fluctuation during the whole network training process. Hence, the Adam has the best performance. The loss function is commonly associated with optimization problems as a learning criterion, i.e., the performance of the model prediction is measured by minimizing the loss function. The variation of loss values with different loss functions during the iterative training of the network is shown in Figure 18. The NLLLoss2d loss function is prone to sudden changes during the 1500-2400 network iterations, and the low learning efficiency of the PyEf-U-Net deep learning network leads to unsatisfactory prediction results.