## 4 Case Verification
### Case Verification
Since the L-M method uses error minimization for optimization, in a nonlinear network with multiple local minimums, it is easily trapped in the local minimum and it may not be able to achieve the global minimum, thus affecting the generalization ability of the network. The RMSE of the L-M algorithm increases by 0.2003 compared with the Bayesian regularization algorithm used in this paper. By comparing the results of the factor analysis algorithm for original variables with or without factor analysis, the accuracy of the result is significantly improved compared with the hot path guide method, although it is not preprocessed with factor analysis. However, when comparing the findings after factor analysis preprocessing, there are still issues of significant inaccuracies and inaccurate accuracy. When there is a strong correlation between input variables, the possibility of \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Gentile Fluctuation** & **Moderate Fluctuation** & **Frequent Fluctuation** \\ \hline RMSE & 0.2696 & 0.6250 & 0.6441 \\ MAE & 0.399 & 0.6037 & 0.6263 \\ MAPE & 1.47\% & 2.31\% & 2.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Error results under different fluctuations of the AWTT. Figure 10: The prediction results for frequent AWTT fluctuation. multicollinearity and redundant data contained in it increases. As a result, the network may be unable to accurately confirm the independent impact of each variable on the output. What is more, the network model becomes overly reliant on specific features and overfits the correlation, leading to the problem of network overfitting. Specifically, the network model is too complex to fit the correlation relationship in the training data, and cannot flexibly adapt to the new data, thus reducing the final prediction accuracy. Figure 11: The prediction effects corresponding to different methods. Figure 12: The absolute error corresponding to different methods. The absolute error results show that the maximum error between the predicted AWTT and the field measured value occurs from 9:00 to 12:00, and the maximum absolute error is 2.22 \({}^{\circ}\)C, 4.17 \({}^{\circ}\)C, and 2.74 \({}^{\circ}\)C, respectively, when based on the proposed method, the method without using factor analysis, and the L-M method. This period can be like the start-up process of the transformer. The corresponding load is stable in the late night and early morning periods, and it is approximately considered that the AWTT and the oil temperature are balanced and in a stable state. From 8:00 to 9:00, the load will change and fluctuate greatly, in contrast to the previous period. In addition, the load current increases and the AWTT rises. The external insulating oil is expanded by the heating volume, and the upward convection is carried out. At the same time, due to the large internal temperature difference, the winding heat dissipation accelerates and reaches the heat balance state faster. However, the transformer fails to achieve a thermal steady state, leading to fluctuations in its temperature. It keeps rising until it reaches the quasi-steady state. Currently, due to the large heat capacity of the transformer, the internal heat dissipation and heat generation are not equal, resulting in continuous temperature changes. Once the transformer reaches the thermal steady state, its temperature will remain relatively constant. The whole process is relatively slow and takes a long time. From 9:00 to 12:00, the winding is in a stage in which it has not yet reached a stable state, leading to a significant prediction inaccuracy during this period. After 12:00, the error between the predicted AWTT and the measured value noticeably decreases, and the maximum absolute error does not exceed 0.75 \({}^{\circ}\)C, indicating a strong agreement with the measured value.