## 1 Introduction  
Owing to modern industrial development, mechanical system automation, and global warming, power demand is increasing; high transmission voltage is required to supply a large amount of power stably. This demands a high level of insulation for transmission lines. Porcelain insulators play an important role in determining reliability and safety in the transmission sector, such as mechanically fixing transmission lines and transmission towers and securing insulating gaps between transmission lines and transmission towers through electrical insulation [1, 2]. In Korea, since 2000, many efforts have been made to apply polymer insulators, which are cheaper to manufacture and install than porcelain insulators, and have excellent durability and pollution resistance. They are also lightweight and easy to handle and manufacture owing to their variable design [3, 4]. However, because of frequent accidents due to the breakage of polymer insulators, porcelain insulators are used, as they have excellent mechanical properties at very high voltage transmissions, such as 154 and 345 kV, and they can be used for a long period of time. Currently, approximately 9.8 million porcelain insulators are installed in Korea, and 5.1 million are imported from Japan's NGK, accounting for approximately 52% of the total. Of these, approximately 1.24 million porcelain insulators with 154 kV transmission lines are used, and approximately 0.8 million insulators have exceeded their service life (30 years), which accounts for 65% of the total [5]. The insulator does not immediately suffer from performance deterioration or mechanical damage after it exceeds its service life. However, depending on the usage environment, the aging of porcelain insulators due to continuous stress and deterioration may accumulate and lead to their sudden breakage, resulting in the cut off or falling of the power line [6]. Furthermore, power failure accidents caused by problems related to porcelain insulators cause considerable damage, and this entails human and physical damage leading to economic losses. Thus, it is necessary to develop inspection techniques to prevent accidents by verifying porcelain insulators in a reliable manner and replacing them beforehand. Most techniques for identifying insulator damage focus on evaluating the electrical insulation performance of the insulator from an electrical standpoint. Common methods include the insulation resistance measurement method, the electric field measurement method, the partial discharge measurement method, and the HI-Pot test [7; 8; 9; 10], and recently, infrared scanning, the aerial image analysis method, and 3D-CT have been studied for measuring mechanical damage [11; 12; 13]. However, the above measurement methods are highly influenced by the results of the measurements along with temperature, humidity, and solar flux. Given that most methods focus only on the electrical damage and breakdown of porcelain parts, the mechanical damage of porcelain insulators nearing the end of their life cycle is difficult to identify. In addition, the infrared camera and imaging methods, which can measure the mechanical damage, can detect the breakage of the insulator disc, but they are affected by ambient temperature and brightness. Using these methods, it is difficult to detect defects such as cracks and voids shown in Figure 1. The 3D-CT method can identify internal damage to porcelain insulators, but it is difficult and expensive. In this study, the frequency response function (FRF) method was applied, which was simple to measure, was less affected by the surrounding environment, and could identify mechanical damage.