## 3 Results and Discussion
### Principal Component Analysis Results  
The extraction of characteristics for the analysis of the main component was performed from two perspectives: Time data and frequency response data. As an advantage over the frequency response data analysis, the time-data analysis does not require energy in the use of the impact hammer [29]. Various characteristics that can be calculated using time data were considered to set up the basic matrix. The features extracted according to the procedure in Figure 9 were employed in the default matrix; this means that 11 features were derived for each sample of porcelain insulators. Figure 8: Internally defective samples and FRF results. Figure 9: Features extracted from time series of experimental data. The entropy of time data was computed and used as one of the features. Here, entropy pertains to the Shannon entropy of discrete distribution; it is a measure of the uncertainty or disorder within a system. A signal that is more chaotic generates a larger value of entropy and vice versa; the entropy (H) of an entire signal, \(X_{i}\) [\(x_{1}\), \(x_{2}\),..., \(x_{n}\)], is given by Equation (5):  
\[\mathrm{H}=-\mathrm{x}_{i}\sum X_{i}\log(x_{i}). \tag{5}\]  
Skewness measures the degree of asymmetry with respect to the sample mean; in a normal distribution, skewness is zero. The skewness (S) of a discrete signal, \(x\), is defined by Equation (6):  
\[\mathrm{S}=\frac{E(x_{i}-\mu)^{3}}{\sigma^{3}}. \tag{6}\]  
The kurtosis (K) of a discrete distribution function, \(X_{i}\), measures how peaky the distribution is with respect to the normal distribution. It is mathematically given by Equation (7):  
\[\mathrm{K}=\frac{E(x_{i}-\mu)^{4}}{\sigma^{4}}. \tag{7}\]  
The basic matrix with 11 feature values for each of the 67 samples was first assembled. Thereafter, the principal component analysis procedure in Figure 1 was followed. Through PCA, it was found that the vector with the greatest contribution of data variances was kurtosis (99.74%), second was average (0.15%), and third was skewness (0.10%). The x-axis coordinates were multiplied by the largest variance, PC1 (kurtosis), and the y-axis coordinates were multiplied by the second largest variance, PC2 (average); these were two-dimensionally plotted, as shown in Figure 10.  
The two-dimensional graph analysis of all data using the largest PC1 and PC2 showed that three out of the four damaged porcelain data exhibited considerable differences from other data in the negative direction of PC1. However, this two-dimensional classification was ambiguous depending on the damage of the cap, internal damage, and material. Therefore, the analysis was performed, as shown in Figure 11, using the third vector for further analysis. Figure 10: 2D plot using extracted two eigenvectors from time data. One set of porcelain damage data that was close to the normal cluster range on a two-dimensional graph differed in the normal cluster range and z-axis direction; this allowed for differentiation in the three-dimensional graph. Moreover, it was found that instead of the intact cristobalite data, the intact alumina data were distributed upward in the z-axis direction. However, cap damage and internal damage data were still within the normal data distribution. The principal component analysis using the time data showed that porcelain damage and material were distinguishable in the three-dimensional graph; however, it was difficult to distinguish between gold and internal damage. To distinguish between these two, new characteristics were derived and analyzed from the frequency domain. The characteristic extraction of frequency response was based on the frequency response data shown in Figures 6-8. The real and imaginary values were set to be the basic values according to the procedure in Figure 12; each of the two values extracted five characteristics for a total of 10 features. Figure 11: 2D and 3D plots using two and three eigenvectors extracted from time data.