## 6 Simulation and Analysis
In (34), \(a_{n}=\text{Logical}\{k_{n}>3.20\}\), \(b_{n}=\text{Logical}\{\{k_{n}\leq 3.20\}\cap[|\text{IMF}_{n}-\mu_{\text{IMF}_{n}}| \geq 3\sigma_{\text{IMF}_{n}}]\}\) and \(a_{n}\
eq b_{n}\), where \(\text{Logical}\{\{\,\cdot\,\}}\) is a logical judgment function, which satisfies the condition to return 1; \(k(\cdot)\) is the calculation of kurtosis; \(\sigma_{\text{IMF}_{n}}\) is the standard deviation of \(\text{IMF}_{n}\); and \(\mu_{\text{IMF}_{n}}\) is the mean value of \(\text{IMF}_{n}\). _Step (7):_ The improved wavelet threshold function is used to denoise R, and the noise-reduced PD signal is obtained. In addition, the noise reduction effects of noisy PD analog signals under the same conditions are compared via Spearman Variational Mode Decomposition (S_VMD) [13], Image Information Entropy and MVMD (IIE-MVMD) [14], and SVD and EWT [18]. According to the principles of each method, S_VMD and IIE-MVMD do not add narrowband interference suppression steps. Though SVD-EWT can suppress narrowband interference, its effect is weak when the interference amplitude is low. Thus, the proposed method in this paper has unique advantages in narrowband interference suppression. In addition, the modal parameter \(k\) of VMD in S_VMD only considers the thoroughness of decomposition and does not consider the accurate extraction of PD feature signals. IIE-MVMD deeply considers the setting of modal parameter \(k\), but the penalty factor \(\alpha\) still uses a fixed empirical value. In this paper, the MPA algorithm considering the MAEE is adopted, which can extract the characteristics of PD pulse signals to the greatest extent on the basis of adaptively obtaining \(k\) and \(\alpha\) values. SVD-EWT adopts the noise reduction strategy of truncating and retaining PD. Though this strategy can maximally remove white noise, precisely locating PD start and end positions is challenging, and its noise reduction reliability needs further consideration. Finally, the improved wavelet threshold method proposed in this paper can eliminate white noise to the greatest extent on the basis of retaining the PD characteristic signal. The results of different methods can be seen in Figure 13.  
According to Figure 13, the residual noise content of the signal denoised by S_VMD is large, and the noise reduction effect is not ideal. The noise reduction effect of IIE-MVMD is obviously improved, but there is still some spiking. Although SVD-EWT is used to segment and denoise the PD signal, and the removal effect of residual noise is significant, the starting position of the PD signal has shifted to a certain extent, which will affect the diagnosis and evaluation of defects. ISVD-MVMD can make the noise-reduced PD signal and the pure PD signal keep the waveform consistent as much as possible; the residual noise content is small, so the PD signal can eliminate narrowband interference and WGN as much as possible without distortion. The spectrograms of a pure PD signal and a PD signal denoised by the above four methods are obtained, respectively, as shown in Figure 14.  
In Figure 14, the useful information of the PD signal is mainly concentrated at 0 Hz, 3 MHz and 8 MHz. S_VMD and IIE-MVMD retain the waveform characteristics of the pure PD signal more completely, but the suppression effect on narrowband interference and WGN is general. SVD-EWT successfully suppresses narrowband interference by singular value decomposition, and the noise reduction effect on WGN is also good, but the PD signal has certain distortion and a large amplitude error. ISVD-MVMD successfully suppresses the periodic narrowband interference and WGN of the PD signal, and in the spectrum distribution, the distribution of the noise-reduced PD signal is basically the same as that of a pure PD signal. Figure 13: Noise reduction results of different methods in Simulated PD signals. (**a**) S_VMD; (**b**) IIE-MVMD; (**c**) SVD-EWT; (**d**) ISVD-MVMD.