## 3 Results and Discussion  
### Basic Experiment Analysis and Results  
In order to select the sensor and impact position, which can grasp the dynamic behavior of the porcelain insulator, four experimental conditions were set up, as listed in Table 2; the hammer and sensor positions and the FRF results are shown in Figure 3. It was found that the natural mode obtained from Type 2 was the most visible, and its average value through the five experiments was also the most consistent. Figure 2: Experimental setup for frequency response function measurement of porcelain insulator. (a) Impact hammer; (b) accelerometer; (c) signal conditioner; (d) DAQ; (e) data visualization. In order to ensure data reliability, an accelerometer was installed in the porcelain part; thereafter, as indicated for type 2, the side of the porcelain part was struck with an impact hammer. Figure 4 shows a graph of the frequency response of the mean and five experimental results at the same location. At frequencies less than 5 kHz, the five experimental and average values agreed. At frequencies greater than 5 kHz, the natural frequencies were identical; however, the waveforms among the natural modes were slightly different. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Impact** & **Sensor** \\ \hline Type 1 & Porcelain & Cap \\ \hline Type 2 & Porcelain & Porcelain \\ \hline Type 3 & Cap & Cap \\ \hline Type 4 & Cap & Porcelain \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Type according to impact hammer and sensor position. Figure 3: Frequency response function (FRF) results according to impact and sensor position. After confirming the consistency of experimental results, the frequency response of the intact insulator was analyzed. As mentioned above, porcelain insulators used in the 154 kV transmission towers in Korea are combined with cristobalite and alumina materials; thus, basic analysis was necessary to distinguish between the two materials. The frequency response of the intact porcelain insulator of the two materials is shown in Figure 5; four natural modes appeared below 5 kHz, and four appeared between 5 and 10 kHz in both materials. In the first mode, the alumina exhibited a frequency of approximately 100 Hz higher than that in cristobalite; the frequency difference gradually increased in the subsequent modes. Accordingly, the two materials could be distinguished based on the difference in positions among the natural modes, as shown by the basic frequency response graph. Porcelain insulators undergo several manual processes during manufacture that may introduce uncertainties; uncertainties are also introduced by cement and porcelain materials. Because specimens are manufactured in different locations, installation sites, and service periods, the natural frequencies may change. Accordingly, experiments were conducted to set the frequency range of the natural modes of the intact porcelain insulators before measuring and comparing them with those of damaged insulators. Table 3 shows min, max, frequency average, standard deviation values by the peaks of the natural modes (modes 1-4) of the cristobalite and alumina insulators. It can be observed that there are differences in the natural mode frequencies among the 15 intact insulators. In the case of cristobalite, the minimum and maximum differences of 100 and 190 Hz were generated, respectively; for alumina, the minimum and maximum differences were 80 and 140 Hz, respectively. Similar differences were observed in natural modes 4-8. Figure 5: Natural frequency of FRF results according to material.