## 1 Introduction  
Electricity demand is increasing rapidly owing to modern industrial development, mechanical system automation, global warming, and increasing demand for electric vehicles. To reliably supply such a large amount of power, high transmission voltage is required, and thus, a transmission line with high insulation is required. The insulator mechanically fixes the transmission line to the transmission tower and plays an important role in determining the reliability and safety of the transmission line, such as securing an insulation gap between the transmission line and the transmission tower through electrical insulation [1,2]. In Korea, a significant amount of effort has been invested since the beginning of the 21 st century to apply polymer insulators that are easy to manufacture and install, have excellent durability and pollution resistance, and are light and easy to manufacture [3,4]. However, owing to frequent accidents caused by their breakage, porcelain insulators are mostly used in transmission lines of 154 kV or more. In Korea, more than 99% of porcelain insulators are used in transmission lines, and of the 9.8 million porcelain insulators installed, 5.1 million are NGK insulators, Ltd. produced in Japan, accounting for 52% of the total. Among these, more than 1.2 million porcelain insulators installed have 154 kV transmission lines, and approximately 0.8 million insulators have been used for more than 30 years. Insulators do not suffer immediate deterioration or mechanical damage when they are used for longer than their useful life [5]. However, stress accumulation and deterioration of porcelain insulators may cause a sudden breakdown of the insulator due to exposure to an environment of continual stress. This can lead to accidents in which the power line breaks or falls [6]; further, power outages caused by problems with porcelain insulators can be extensive, and can lead to economic and human injury and material damage. To prevent this, it is necessary to develop measuring equipment and inspection technology to allow reliable verification. Most techniques for detecting damage to an insulator focus on checking the insulation performance of the insulator from an electrical standpoint. Commonly used contact inspection methods in the field include the HI-Pot test, partial discharge measurement method, electric field measurement method, and insulation resistance measurement method [7, 8, 9, 10]. In addition, recently, non-contact infrared scanning and image analysis methods for measuring mechanical damage from a long distance have been studied [11, 12]. However, for the above measurement method, even if there is no physical damage, these values vary depending on the temperature, humidity, and chloride content of the atmosphere. In addition, the existing methods cannot be effective in identifying the damage of the insulator due to insensitivity to internal and external physical damage, as presented in Figure 1. In particular, internal cap defects and interfacial damage are difficult to find with visual inspection so a method of overcoming this is necessary. Therefore, it is difficult to identify mechanical damage around the broken or internal pollution of the cap on the porcelain insulator, as shown in Figure 1. In addition, as the porcelain insulator in the transmission line is coupled with the pins of other porcelain insulators, it is difficult to identify damage visually or using image analysis because a part is covered by the porcelain disc component. In this study, a frequency response function (FRF) method, which is a simple measurement that is minimally influenced by the surrounding environment and easily detects mechanical damage, is applied to detect the damage on the cap. FRF is one of the methods for confirming the dynamic behavior of an object, and displays dynamic responses such as resonance in the frequency domain for  
Figure 1: Porcelain insulator showing possible defects. a standardized input.