## 4 Analysis and Result
### Nonlinear Separation with Multiple SVMs  
Given that linear hyperplane analysis and nonlinear single SVMs are not suitable for the distribution of basic data, a nonlinear analysis was performed using multiple SVMs with the kernel function. The kernel function used was the radial basis function. When using a hyperplanar analysis and a single SVM, the classes were classified into normal and defect classes; however, in this analysis, the classes were classified into three categories: cristobalite, alumina, and defect. The SVM essentially  
Figure 8: Binary linear hyperplane separation with the SVM.  
Figure 9: Nonlinear separation with a single SVM using kernel function.  
involves binary classification; therefore, we created an individual SVM model for three classes and analyzed them through a parallel operation. Ten data points were randomly extracted and evaluated using the developed SVM model. The results are presented in Table 2. According to the criterion to classify cristobalite into cristobalite, the value of the SVM1 prediction model should be close to 1 in the three prediction models and close to 0 in the SVM2 and SMV3 models. According to the criterion for judging alumina as alumina, the value should be close to 1 in the SVM2 model and close to 0 in the SVM1 and SVM3 models. According to the criterion for determining defects as defects, the value should be close to 1 in the SVM3 model and close to 0 in the SVM1 and SVM3 models.  
The post-distribution range for the entire data was calculated using the multi-SVM model, and the results are shown in Figure 10. The prediction results for these three classes are presented in Table 3. The results confirmed that most cristobalite data were distributed in the negative range based on the zero value of PC1 and that the alumina data were distributed in the positive range. Based on this, the boundary between the cristobalite and alumina data was separated with high accuracy. In addition, it was possible to set the range to accurately classify defect data and general data. However, when there is a boundary (margin) region owing to the SVM analysis characteristics, it may be difficult to determine the correct class when some data are distributed at the boundary.  
The results of classifying the normal and damaged porcelain insulators using the three SVM classification methods showed that the linear hyperplane classification and the nonlinear single SVM method are not suitable for data classification in this study. In contrast, the nonlinear multiple SVM method is considered suitable for data classification. However, data exist in the boundary region owing  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**True Label**} & \multirow{2}{*}{**Predict Label**} & \multicolumn{4}{c}{**Posterior**} \\ \cline{3-5}  & & **SVM1** & **SVM2** & **SVM3** \\ \hline Alumina & ‘Alumina’ & 0.1043 & 0.8955 & 0.0002 \\ Cristobalite & ‘Cristobalite’ & 0.9990 & 0.0001 & 0.0009 \\ Cristobalite & ‘Cristobalite’ & 0.9990 & 0.0001 & 0.0009 \\ Cristobalite & ‘Cristobalite’ & 0.9993 & 0.0006 & 0.0001 \\ Cristobalite & ‘Cristobalite’ & 0.9993 & 0.0002 & 0.0005 \\ Alumina & ‘Alumina’ & 0.0000 & 0.9899 & 0.0101 \\ Cristobalite & ‘Cristobalite’ & 0.9992 & 0.0000 & 0.0008 \\ Alumina & ‘Alumina’ & 0.0000 & 0.9936 & 0.0063 \\ Defect & ‘Defect’ & 0.0589 & 0.0116 & 0.9295 \\ Cristobalite & ‘Cristobalite’ & 0.9986 & 0.0003 & 0.0011 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prediction values by nonlinear separation with multiple SVMs.  
Figure 10: Nonlinear separation with multiple SVMs using kernel function.  
to various errors depending on the use environment of the porcelain insulator, and it is necessary to apply another machine learning method to distinguish these data.  
Therefore, an analysis was performed by applying the ensemble technique, which is used for creating a suitable model by sequentially selecting the appropriate model and assigning weights to errors in each training step.