## 1 Introduction  
The insulator is the most important link in transmission line equipment [1; 2; 3; 4]; the stability of the insulator's insulation performance seriously affects the safe operation of the power grid, and the regular deterioration detection of insulator strings is particularly critical [5; 6]. At present, the most common detection methods of degraded insulators are infrared detection methods, ultraviolet detection methods, and electric field detection methods [7]. In the infrared detection method, zero-value insulators basically generate no heat, so it is impossible to judge a significant difference between zero-value insulators and normal insulators. Only the heating of low-value insulators can be used for judgment [8; 9]. In the ultraviolet detection method, the corona discharge of insulators can be detected by ultraviolet methods. It is impossible to judge the situation without corona discharge [10; 11]. In addition, infrared and ultraviolet detection methods easily suffer from adverse effects of environmental factors [12; 13; 14], such as temperature and the humidity of the air, which make it more difficult for insulator strings in transmission lines to obtain accurate detection results, thus causing misjudgment and becoming a hazard for transmission line safety. The electric field detection method is used to detect degraded insulators by judging the space electric field waveform of insulator strings. Under typical conditions, the space electric field curve of insulators is a curve similar to a U shape. Whether the insulator strings are degraded can be detected by observing its space electric field waveform [15; 16]. In the case of de-graded insulators among insulator strings, the electric field distribution of insulators will change, resulting in distortion [17; 18; 19]. The literature [20] has conducted research on the electric field strength of insulator strings with different positions and numbers of degraded insulators by the finite element method. According to the results, the degradation of insulators at a high-voltage end has the greatest influence on the electric field of insulators. Another work [21] established an electric field simulation model of 110 kV porcelain suspension insulators and conducted a space electric field experiment of insulators to prove that the live detection of degraded insulators can be completed through the measurement of the space electric field. The literature [22] has also explored the space electric field distribution characteristics of suspension insulator strings and indicated that degraded insulators can be located by analyzing the change of the axial electric field of insulator strings. According to the electric field characteristics of insulators, electric field detection methods of insulators under typical conditions are of the contact type and contactless type [23]. Most electric field detection devices for contact insulators are climbing tower robots, but they are expensive and time-consuming, with a threat to personal safety [24; 25]. The contactless detection method of insulators has very high application prospects. Researchers [26] have built an inspection platform of UAV for both the airborne end and the ground end of the UAV and detected a conduction defect of the composite insulator mandrel. Others have [27] developed a space electric field detection device and a zero-value insulator detection algorithm, and the proposed method can effectively identify zero-value insulators. At the actual site, due to the influence of regional climate characteristics, extreme terrain tower erection, insulator string weight, etc., there may be differences in the electric field characteristics of insulators, which also poses a challenge to the detection method of space electric field of insulators.