# An Interface Pressure Detection Method of Cable Silicone Rubber-XLPE Based on Nonlinear Ultrasound
## 1 Introduction  
With the continuous deepening of China's urbanization process, the scale of urban power grid cable equipment is constantly increasing. According to statistics, in addition to external damage, 70% of cable faults are caused by cable accessory faults [1]. The silicone rubber cross-linked polyethylene (XLPE) composite interface between the cable accessories and the body is a high incidence of cable line faults due to the concentration of stress in the electric field and the occurrence of partial discharge, leading to insulation breakdown [2]. Studies have shown that the interface pressure distribution between cable accessories and the body is between 0.10 MPa and 0.25 MPa to ensure the stable operation of the cable line [3]. The main methods for detecting the pressure at the interface between the cable attachment and the body are the sensor method [4; 5; 6; 7] and the finite element analysis method [8; 9; 10]. The built-in sensor method is to pre-install a pressure sensor between the cable attachment and the body, and the sensor detects the pressure change at the interface and outputs the result. As this method not only requires a high-pressure sensor size specification, but also destroys the insulation characteristics between the cable attachment and the body, it is not applicable to the interface pressure measurement of cable attachments with voltage levels above 10 kV. The external fiber optic curvature sensor method is based on the outer curvature-radial displacement interface pressure relationship model of the cable accessory calibrated fiber optic sensor, which is tangentially applied to the outer layer of the accessory along the outer diameter to measure the curvature and thus obtain the interface pressure value. However, this method has only been studied for 10 kV cable accessories,and the repeatability and stability of the sensor measurements are still in the laboratory optimization stage. The finite element analysis method uses simulation software to create a three-dimensional model of the cable joint to analyze the effect of overfill, temperature, and other factors on the interface pressure. Although the finite element analysis is a simple method, there are errors between the simulation parameters and the actual cable, and the simulation results need to be compared with the test results for verification. In summary, the existing methods for testing the interface pressure of cable accessories have their own limitations, so there is an urgent need to introduce a new method to test the interface pressure of cable accessories in the field of cable transportation and inspection. In recent years, nonlinear ultrasound techniques have been increasingly applied to stress detection. Scholars have built stress detection platforms based on nonlinear ultrasound have conducted a large number of studies on interface adhesion [11], aluminum alloy surface stress [12], aluminum plate pre-stress [13], metal material internal stress [14; 15], metal plate residual stress [16], and metal contact interface stress [17]. [PERSON] et al. [18] combined the LCR wave method with nonlinear ultrasound techniques to evaluate the internal stresses in metallic materials under pre-stress loading conditions. The pre-stress within the metal was also detected along three directions, respectively. The experimental results showed that the second-order relative nonlinear coefficients monotonically increased with stress, and the normalized relationship was consistent with a simplified dislocation model, verifying the reliability of the method. [PERSON] et al. [15; 19] found that when tensile stress is applied to a metallic material, it affects the ultrasonic nonlinear properties in addition to the propagation velocity of the ultrasonic waves inside. [PERSON] et al. [20] used ultrasonic methods to detect stresses in concrete, taking into account the third-order elastic constants, providing an effective method for concrete stress detection. [PERSON] et al.