## 2 The Basic Theory of EMD and DCNN  
### The Basic Theory of Empirical Mode Decomposition  
EMD uses time scale characteristics to decompose, which makes EMD have a good effect on the processing of nonlinear signals. EMD can retain the advantages of time-frequency localization in wavelet transform and overcome the difficulty of selecting a wavelet basis function in wavelet transform because it does not need a basis function. In \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Researcher** & **Method** & **Merit** & **Defect** & **Contribution** \\ \hline [PERSON] [11] & Feature extraction method based on high anti-noise principal component analysis (PCA). & & PCA is a linear dimension effect. & Through the collaborative design of noise modeling, multi-modal robust feature extraction, and transfer learning classification framework, [PERSON] overcame the problem of feature degradation and misclassification of XLPE cable joint partial discharge detection in a high noise environment. \\ \hline [PERSON] [12] & Partial discharge pattern recognition of the switch cabinet is adopted. & It can effectively identify the early discharge signal of insulation defects. & The scope of application is limited. & By improving the ResNet architecture, optimizing the time-frequency representation and noise robustness design, [PERSON] significantly improved the recognition accuracy and engineering applicability of the partial discharge mode of the switchgear. \\ \hline [PERSON] [13] & BP is used for PD feature recognition. & The nonlinear characteristics of partial discharge signals can be captured by a multi-layer structure. & Through algorithm improvement and systematic verification, [PERSON] established the effectiveness of the BP neural network in cable partial discharge the efficiency. & The huge workload greatly reduces the efficiency. & Analy network in cable partial discharge identification and provided a new tool for smart grid fault diagnosis. \\ \hline [PERSON] [14] & A partial discharge identification method of cable terminal based on an adaptive fuzzy logic network. & It is suitable for dealing with complex scenes with on-site noise interference or signal overlap. & Due to the subjectivity and complexity of fuzzy rule parameter setting, the recognition with has both a theoretical breakthrough and engineering practical value. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._this paper, this method is used to process the partial discharge signal of the T-type terminal, and a series of signals containing characteristic components are obtained. EMD can decompose the original signal into multiple intrinsic mode functions containing characteristic components (IMFs) [22; 23; 24]. Among them, the IMF has two characteristics: (1) the number of zero-crossing points and the number of extreme points differ by at most one; (2) at any time, the average value of the extreme envelope is 0. The EMD process for any signal \(x(t)\) is as follows:  
By fitting all the extreme points of the initial signal \(x(t)\) with its corresponding envelopes \(e_{+}(t)\) and \(e_{-}(t)\), let the average values of \(e_{+}(t)\) and \(e_{-}(t)\) be the mean envelope \(m_{1}(t)\) of \(x(t)\). The corresponding expression is as follows:  
\[m_{1}(t)=\frac{e_{+}(t)+e_{-}(t)}{2} \tag{1}\]  
Among them, \(m_{1}(t)\) is the mean envelope of the initial signal \(x(t)\), \(e_{+}(t)\) and \(e_{-}(t)\) are all extreme points of the initial signal \(x(t)\) and their corresponding envelopes. Using \(x(t)\) minus \(m_{1}(t)\) as the signal \(\mathrm{h}_{1}^{1}(t)\) to remove the low-frequency signal:  
\[{h^{1}}_{1}(t)=x(t)-m_{1}(t) \tag{2}\]  
In general, \(\mathrm{h}_{1}^{1}(t)\) is a non-stationary signal, so \(\mathrm{h}_{1}^{1}(t)\) does not meet the characteristic conditions of IMFs.