## 3 Results and Discussion
### Frequency Response Analysis Results  
A frequency response analysis of damaged cristobalite specimens was conducted to distinguish between normal and damaged specimens.  
In the case of a damaged insulator, the frequency of the natural mode may change because of change in mass, inner voids, non-adhesion of interface, or cracked porcelain; the magnitude of the response energy may change because of variation in attenuation. Accordingly, the specimens were analyzed according to damage type.  
The frequency response graphs of intact and defective porcelain insulators are presented in Figure 6. The frequency response of the damaged and cracked porcelain samples was significantly different compared with that of the intact sample. The broken porcelain discs (A-1, A-2, A-3) lost eight natural mode characteristics that were observed in the intact specimens; they dissipated most of the energy within the 5 kHz frequency. In the porcelain disc with crack (A-4), all natural modes disappeared, and a new mode occurred at low frequencies. In the case of damaged porcelain, porcelain disc cracking was judged to have a greater effect on resonance than the broken porcelain disc.  
Figure 6: Defective porcelain samples and FRF result. A-1, A-2, A-3: Broken porcelain discs; A-4: Porcelain disc with crack.  
The frequency response of cap damage shown Figure 7 was maintained in the eight natural modes observed in the intact frequency response. However, a new mode occurred near the 1 kHz frequency; this mode appeared in all three cap-damaged specimens. In addition, the second and third modes moved to a lower frequency, which was found to be significantly outside the original mode range of the previous set.  
The internally damaged specimen was fabricated by placing a normal ceramic insulator in insulating oil and then applying a commercial frequency voltage. This applied voltage was raised as quickly as possible to the insulated failure voltage between 175 and 190 kV (minimum and maximum, respectively) as confirmed by an instrument that measured the voltage [28].  
A frequency response graph was plotted for each of the three test specimens that had been subjected to the commercial frequency voltage test but with no apparent damage to the appearance of the insulator, as shown in Figure 8.  
The FRF of C-1 and C-2 exhibited eight unique modes, a new mode occurred near 1 kHz, and a second mode moved to a lower frequency. This result is the same as the FRF result of the cap damage test specimen; it is deduced that the two test specimens were damaged inside the cap.  
Different from these two cases, no new mode occurred in the case of C-3 test specimens. However, the second and third modes moved the most to the lower frequencies, and the mode near the 5 kHz frequency disappeared. Because the disappearance of the natural mode was similar to that in the FRF result of porcelain damage, it was expected that considerable damage had occurred inside the porcelain.  
In the frequency response graph, several peaks, waveforms, and frequency range analyses of natural modes were conducted; characteristics such as extinction, generation, and movement of natural modes were found to vary depending on the type of damage, and internal damage could be estimated by contrasting their characteristics.  
Figure 7: Cap defective samples and FRF results.