# Transformer Fault Diagnosis Method Based on Incomplete Data and TPE-XGBoost
## 4 Application Results and Analysis
### Discussion  
Based on the DGA dataset with a missing data rate of 20%, the TPE-XGBoost method is compared with other methods, including kNN, RF, CART, Natural Gradient Boosting (NGBoost) and 100-layer deep neural networks (DNN) [29]. The accuracy of each model is evaluated by the five-fold cross-validation method, as shown in Figure 10. The yellow line in the box diagram indicates the median of diagnostic result.  
The performance of the TPE-XGBoost method is better than other algorithms, with an average accuracy of 89.5%. The diagnostic accuracy of the linear classification algorithm is lower than that of the other non-linear models. The kNN method is prone to misjudgment between different fault types corresponding to the same fault properties, especially for partial discharge and low energy discharge faults. This may be caused by the non-linear relationship between the DGA data and the energy of the transformer fault. In addition, the performance of integrated algorithms, such as RF and XGBoost, is much better than single models, such as CART and DNN. The accuracy of the NGBoost algorithm is higher than the XGBoost algorithm but slightly lower than the TPE-XGBoost algorithm. However, according to the results of multiple cross-validations, the robustness of the XGBoost and NGBoost models is worse than that of the TPE-XGBoost models, indicating that the TPE algorithm improves the accuracy and robustness of the fault diagnosis models effectively.  
Subsequently, the statistical differences in the diagnosis accuracy of the above methods are analyzed by a one-sample \(t\)-test [30]. Considering that the IEC Three Ratio method has a diagnostic accuracy of 86.0% in the case of complete data, the null hypothesis is that the accuracy of the diagnostic model is equal to 86.0%. The results are shown in Table 5.  
Figure 10: Comparison of the accuracy of different diagnostic models.  
Figure 9: Evaluation metrics for TPE-XGBoost diagnostic model.  
The results show that for kNN, CART and TPE-XGBoost methods, the null hypothesis is clearly rejected based on the test with a 95% confidence level. According to the \(t\) and \(p\) values of the above three methods, the accuracy of the TPE-XGBoost algorithm is significantly higher than 86%, while the other two are lower than 86%. This also shows that the method proposed in this paper has a significant improvement in dealing with the fault diagnosis problem of incomplete DGA data.  
Lastly, the diagnostic accuracy of the TPE-XGBoost model with different data missing rates were analyzed and discussed, as shown in Figure 11. The results show that the data missing rate has a significant impact on the diagnostic accuracy of the model. However, when the data missing rate is greater than 20%, the decreased rate of accuracy is significantly accelerated. When the data missing rate is below 30%, the diagnostic accuracy of the model is below 80%. This indicates that the method proposed in the paper still has limitations in dealing with cases of a high missing rate, such as more than 30%, and its diagnostic result still needs to be improved.