# Partial Discharge Data Augmentation and Pattern Recognition Method Based on DAE-GAN +
## 4 Case Analysis
### Analysis of the Role of Introducing Complementary Samples  
To assess the impact of incorporating complementary samples into the generative model's training process, the model was trained under two different conditions: one without the inclusion of complementary samples and the other with these additional samples. This comparative approach helps highlight the effectiveness of introducing complementary data in enhancing the model's performance.  
By introducing a population diversity metric [34], as shown in Equation (6), the diversity of the model-generated samples is quantitatively evaluated. In Equation (6), \(loss_{dir}\) represents the diversity cost function, \(\Omega\) denotes the set of real and generated samples, \(\|K\|\) refers to the maximum diagonal distance in the space of \(\Omega\), and m is the total number of elements in the set.  
\[loss_{dir}=\frac{1}{m\|K\|}\sum_{u\in\Omega}\sqrt{\left(u-\overline{u}\right)^ {T}\left(u-\overline{u}\right)} \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Augmentation Methods** & \(\mathbf{\lambda}_{accuracy}\%\) & \(\mathbf{\lambda}_{\mathbf{F1}}\%\) & \(\mathbf{\lambda}_{G-mean}\%\) \\ \hline Original samples & 90.12 & 88.62 & 89.93 \\ ROS & 89.04 & 87.54 & 88.85 \\ SMOTE & 96.38 & 95.88 & 93.94 \\ CWGAN-GP & 97.57 & 97.58 & 97.20 \\ BEGAN & 97.17 & 97.06 & 96.81 \\ VAE & 96.77 & 96.47 & 94.75 \\ DAE-GAN & 98.36 & 97.82 & 97.62 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of classification effects with different data augmentation techniques.  
Following the method outlined in Section 4.3.2, the diversity variation plots for different sample sizes and the MS-SSIM metrics of the probability distribution images were obtained, as shown in Figure 10 and Table 7.  
As shown in Figure 10, the diversity evaluation metric for PD samples generated by DAE-GAN is consistently higher when complementary samples are included in the training compared to when they are not. The inclusion of complementary samples effectively enhances the diversity of the generated samples. From Table 7, it is evident that the MS-SSIM values of the probability distribution images are significantly higher when complementary samples are included in the DAE-GAN training. This indicates that the inclusion of complementary samples effectively improves the fitting accuracy of the probability distribution and can effectively mitigate the issue of insufficient probabilistic information caused by the small sample characteristics of partial discharge data.  
The DAE-GAN model was employed to augment the sample data under both experimental conditions, one without and one with complementary samples. These augmented datasets were then utilized to train the classifier for conducting pattern recognition tasks. The performance evaluation metrics derived from these experiments are detailed in Table 8.  
As shown in Table 8, when complementary samples are included, all classification performance evaluation metrics for the classifier trained with the augmented samples from the generative model are higher than when complementary samples are not included. The \(\lambda_{accuracy}\%\), \(\lambda_{F1}\%\), and \(\lambda_{G-mean}\%\) improved by 1.15%, 1.32%, and 1.12%, respectively. This demonstrates that the inclusion of complementary samples effectively enhances the classification performance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metrics** & **Without Complementary Samples** & **With Complementary Samples** \\ \hline MS-SSIM value & 0.8492 & 0.8680 \\ \hline \hline \end{tabular}
\end{table}
Table 7: MS-SSIM metrics for probability distribution maps under different conditions.  
Figure 10: Diversity comparison of samples generated by models under different conditions.