## 4 Case Verification
### Case Verification  
(1) Parameter setting:  
Based on the above preprocessing, two factor scores are obtained after factor analysis. Therefore, the input layer node of the network is set to 2; the output of the network is the AWTT predicted with the model, so the output layer node of the network is set to 1. The number of hidden layers and the number of nodes are dynamically altered and determined based on the actual situation. In order to guarantee the precision and effectiveness of the network model, the number of hidden layers is 1 and the number of nodes in each layer is 6 by debugging the network model. In the training process, 70% of the sample data constitute the model training set, and 15% of the sample data are set aside to constitute the verification set. Adjust model \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Common Factor**} & **Ambient** & **Load Current** & **Top Oil Temperature** \\  & **Temperature** & & \\ \hline
1 & 0.889 & \(-0.576\) & 0.508 \\
2 & \(-0.503\) & 1.267 & \(-0.021\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Component score coefficient matrix. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Factor**} & \multicolumn{6}{c}{**Total Variance Interpretation**} \\ \cline{2-10}  & \multicolumn{3}{c}{**Initial Eigenvalue**} & \multicolumn{3}{c}{**Extract the Sum of Squared Loads**} & \multicolumn{3}{c}{**Rotating Load Sum of Squares**} \\ \cline{2-10}  & \multicolumn{1}{c}{**Total**} & **Variance**} & **Accumulate** & **Total** & **Variance** & **Accumulate** & **Total** & **Variance** & **Accumulate** \\  & **\%** & **\%** & **\%** & **\%** & **\%** & **\%** & **\%** & **\%** \\ \hline
1 & 2.451 & 81.688 & 81.688 & 2.451 & 81.688 & 81.688 & 1.610 & 53.652 & 53.652 \\
2 & 0.353 & 11.775 & 93.463 & 0.353 & 11.775 & 93.463 & 1.194 & 39.811 & 93.463 \\
3 & 0.196 & 6.537 & 100.000 & / & / & / & / & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Total variance explanation table. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Common Factor**} & **Ambient** & **Load Current** & **Top Oil Temperature** \\  & **Temperature** & & \\ \hline
1 & 0.913 & 0.376 & 0.796 \\
2 & 0.313 & 0.922 & 0.497 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Rotated component matrix. parameters and preliminarily evaluate model capabilities. Then, 15% of the sample data are used as a test set to evaluate the generalization ability of the final model. In order to show the validity of the model, the root mean square error (RMSE) and goodness of fit (\(R^{2}\)) of the model prediction are selected as the indexes to evaluate the accuracy of the model prediction results. RMSE is the square root of the square of the difference between the predicted value and the actual value of the sample and the ratio of the number of samples, which can characterize the difference between the predicted value and the real value of the sample. \[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n}{(y-\hat{y})^{2}}}{n}} \tag{8}\]  
where \(R^{2}\) describes how well the data fit the model and characterizes the regression fitting effect. \[R^{2}=1-\frac{\sum\limits_{i=1}^{n}{(y-\hat{y})^{2}}}{\sum\limits_{i=1}^{n}{(y -\overline{y})^{2}}} \tag{9}\]  
where \(y\) is the measured value, \(\hat{y}\) is the predicted value, and \(\overline{y}\) is the average value. (2) Results analysis:  
Figure 8 shows the results of the AWTT curve measured in the field and predicted with the method in this paper. It can be seen from the diagram that the predicted curve is basically consistent with the actual curve. Further calculation shows that the RMSE between the predicted result and the actual value of AWTT is 0.62498, the \(R^{2}\) is 0.9714, the average error is 0.6037 \({}^{\circ}\)C, and the maximum error percentage is 2.23%. That is, the average difference between the predicted result and the actual value is small, and the actual value can be well fitted.