## 6 Simulation and Analysis  
The process of the overall noise reduction method in this paper is shown in Figure 9. Based on Figure 9, The noise reduction methods in this paper are detailed as follows:  
Step (1): The amount of narrowband interference is adaptively determined by the FSWT frequency-amplitude mean graph. If the number of the narrowband interference is 0, the second step is skipped and the third step is performed. Step (2): The narrowband interference frequency is determined by the improved Rife method. On the basis of determining the amount and frequency of narrowband interference, the guidance signal is constructed, and the guidance signal is added to the noisy PD signal. The narrowband interference signal is filtered by setting the singular value to zero, and the obtained waveform is shown in Figure 10. According to Figure 10, the ISVD method can better suppress the narrowband interference signal. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Threshold** & **SNR (dB)** & **NCC** & **RMSE** \\
**Function** & & & \\ \hline Soft threshold & 7.8883 & 0.9528 & 0.0592 \\ Hard threshold & 9.1303 & 0.9390 & 0.0513 \\ Improved threshold & 13.0791 & 0.9769 & 0.0326 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Noise-reduced performance evaluation of different threshold functions. Figure 8: Noise reduction results of different threshold functions. Step (3): After the optimal mode number \(k\) and penalty factor \(\alpha\) are optimized by MPA, the PD signal (filtered narrowband interference) is decomposed with MVMD, and the obtained IMF\({}_{\rm n}\) waveform can be seen in Figure 11. According to Figure 11, the MVMD algorithm can effectively extract the waveform characteristics of the PD signal, and the obtained IMF\({}_{\rm n}\) component has good physical meaning. Step (4): The kurtosis of each modal component of IMF\({}_{\rm 1}\sim\) IMF\({}_{\rm 6}\) is calculated, respectively, as shown in Table 7.  
From Table 7, the kurtosis values of IMF\({}_{\rm 1}\)-IMF\({}_{\rm 4}\) are greater than 3.2; others are less than the threshold. Therefore, IMF\({}_{\rm 1}\)-IMF\({}_{\rm 4}\) are classified as PD characteristic information. \begin{table}
\begin{tabular}{c c c c c c c} \hline IMFn & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Kurtosis & 22.42 & 27.87 & 25.06 & 3.25 & 2.61 & 2.91 \\ \hline \end{tabular}
\end{table} 
Table 7: Kurtosis value of imf\({}_{\rm n}\). Figure 10: Noise reduction results of narrowband interference. (**a**) PD mixed signal without adding narrowband interference; (**b**) signal after noise reduction from narrowband interference. Figure 9: Flow chart of the overall noise reduction method in this paper. _Step (5):_ According to the size of the kurtosis, the characteristics of the modal components are determined. According to the calculation results, IMF\({}_{1}\)-IMF\({}_{4}\) are the PD-dominant components, while IMF5 and IMF6 are the noise-dominant components. Therefore, the 3\(\sigma\) criterion is used to filter IMF\({}_{n}\) from the noise-dominant components. The filtering results are shown in Figure 12. It can be seen from Figure 12 that the 3\(\sigma\) criterion preserves the gross error belonging to the PD signal and basically suppresses the WGN and narrowband interference signals. _Step (6):_ The reconstructed PD signal R is obtained by adding the noise-dominant component after filtering via the 3\(\sigma\) criterion and the PD characteristic information. The calculation of R is shown in (34). \[\text{R}=a_{1}\text{IMF}_{1}+\cdots+a_{n}\text{IMF}_{n}+b_{1}\text{IMF}_{1}+ \cdots+b_{n}\text{IMF}_{n} \tag{34}\]  
Figure 11: IMF\({}_{n}\) of the noisy PD signal. Figure 12: The filtering results of the 3\(\sigma\) criterion.