## 3 Feature Analysis of Vibration Information in GIS
### Uniform Feature-Extraction Analysis  
During the actual test diagnosis, the GIS current is known but not controllable. In other words, the characterization differences between different faults need to consider the effects of different current amplitudes. It can be seen from Equation (4) that different current amplitudes will cause the amplitude of the excitation source to change, which will also affect the vibration response. In order to analyze the influence of the current amplitude, under normal circumstances, the spectrum distribution of the GIS at 500 A, 1000 A, and 1500 A is shown in Figure 5.  
Figure 4: Time domain and frequency domain chart of various classes at 1000 A: (**a**) Class 1; (**b**) Class 2; (**c**) Class 3. In Figure 5, some conclusions can be described as follows:  
(1) Under different current amplitudes, the amplitudes of the same frequency point of the same working condition are different. For example, the diagnostic accuracy is deteriorated only by the amplitude. (2) The energy at different currents is concentrated at 0.1 kHz and 0.7-1.2 kHz, and the trend of spectrum amplitude is similar, only the magnitude of the amplitude is different. (3) A GIS fault may cause the system natural frequency change, and 0.1 kHz is the excitation frequency, which is directly affected by the current (excitation) amplitude and does not characterize the inherent properties of the system. Removing the vibration information near the 0.1 kHz part can further improve the GIS fault diagnosis result. According to the analysis result of Figure 5, the characteristic family of the three-phase common box GIS vibration information is designed, as shown in Table 2, wherein feature family 4 is the method proposed here. Where \(i\) denotes the frequency of the \(i\)-th hundred Hertz and \(G_{i}\) represents the amplitude of the \(i\)-th hundred Hertz. The element \(H_{i}\) in the feature sets 3 and 4 represents the ratio of the energy of the \(i\)-th hundred Hertz to the sum of the energy of the partial frequency points, and the specific formula is as shown in (5). \[H_{i}=\frac{G_{i}}{\sum\limits_{i=i_{0}}^{N}G_{i}} \tag{5}\]  
In this paper, the variable \(N=12\), \(i_{0}=1\) in feature set 3, and \(i_{0}=\)7 in feature set 4. Feature set 4 is based on feature set 3, removing signal of vibration excitation frequency of 100 Hz and the 200-600 Hz signal which has low vibration amplitude and is susceptible to noise interference. Defining the feature analysis process of the feature set 4 is the MFER feature-extraction method by forming the description of the vibration feature set proposed in this paper. \begin{table}
\begin{tabular}{c c} \hline
**Feature Set Number** & **Feature Set Expression** \\ \hline Feature Set 1 & \(\{G_{i},i=1,2,\ldots 12\}\) \\ Feature Set 2 & \(\{G_{i},i=7,8,\ldots 12\}\) \\ Feature Set 3 & \(\{H_{i},i=1,2,\ldots 12\}\) \\ Feature Set 4 & \(\{H_{i},i=7,8,\ldots 12\}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Feature set definition. Figure 5: Frequency spectrum distribution of normal case at different current levels. In order to more vividly illustrate the advantages and disadvantages of different feature families, note the comparison of the feature spatial distribution of the measured samples under different faults and current levels, as shown in Figure 6. Here, only the common parts of the four feature families are compared, that is, the six feature dimensions in the interval of 0.7-1.2 kHz. It can be seen from the distribution of category 2 in Figure 6a that the samples of class 2 are divided into three categories, in which II-A represents the samples at 1500 A current level, II-B and II-C represent the sample at 1000 A and 500 A current levels, respectively. The distribution of measured samples in feature set 1 and 2 has significant relationship with different currents level. Although the difference between different faults is more obvious, the diagnostic model constructed by different current data will have a huge difference in the feature space.