## 4 Experiments and Result Analysis
### Result Analysis  
Totally, 160 pieces of signals were collected by sensors, 40 for each kind of defect. To make a comparison with the common method for defect diagnosis of GIS, the peak value, RMS, 50 Hz correlation, and 100 Hz correlation were also extracted for identification. With these features, it was easy to discover the existence of insulation defects, but it was time-consuming and difficult to recognize the type of defects based on the experience of testers, which has verified the inefficiency of the traditional method.  
With the classification system, the detected signals were processed according to the steps in Figure 2. The denoised signals of different kinds of insulation defects are shown in Figure 6. The length of the ultrasonic signal was 500 ms. The frame length was 20 ms and the overlap rate was set as 50%. Consequently, one piece of collected signals could be divided into 49 frames. Static MFCC features and delta MFCC features were extracted from signals. The static MFCC features owned 12 dimensions. Because delta MFCC features contained the first- and second-order differences of the static features and each maintained the same dimensions of the static ones, the dimensions of delta features were 24. The static and delta MFCC features of different kinds of insulation defects are presented in Figures 7 and 8, respectively. Since the features under different dimensions have a large gap, normalization was applied to static MFCC features and delta MFCC features separately to reduce the negative effect of the large gap on defect recognition.  
Figure 5: The experimental site. **(a)** Photo of the GIS; **(b)** A defect model placed in the GIS.  
For each kind of defect, 20 samples were selected randomly into the training set and the rest were the test set. The construction of SMO-SVM and SVM multi-classifiers was realized on MATLAB R2019b and the convex programming solver CVX was used. Both of them were trained by the training set, and then used to recognize the samples in the test set to test the recognition accuracy of the system in order to compare the performance in defect identification. The recognition system was evaluated from two perspectives, i.e., accuracy and sensitivity. Accuracy is the proportion of samples which are correctly classified. Sensitivity is the proportion of samples correctly classified into a certain type of defect. The results of the insulation defects identified by different classifiers are listed in Table 1.  
Figure 6: Collected and denoised ultrasonic partial discharge (PD) signals of GIS with different defects.  
**(a)** Free metal particles; **(b)** Floating electrode; **(c)** Creeping discharge; **(d)** Metal protrusions.  
Figure 7: Static mel frequency cepstral coefficient (MFCC) features extracted from ultrasonic PD signals of GIS under different kind of insulation defects. **(a)** Free metal particles; **(b)** Floating electrode; (c) Creeping discharge; **(d)** Metal protrusions.  
It is obvious that SMO-SVM has achieved better performance of defect diagnosis than SVM, with an accuracy value of 93.75% and sensitivity value of 94.14%. To verify the computational improvement, the operation time of classifiers was recorded as follows: the SMO-SVM multi-classifier took 4.65 s to train and test samples, whereas the SVM multi-classifier took 13.78 s. The comparison indicates that the classification system with SMO-SVM is more efficient to diagnose insulation defects.