## 1 Introduction  
Contact resistance is a key factor affecting the electrical contact performance of contact groups, and failures caused by high contact resistance account for the majority of statistical cases of switch failures [1, 2]. According to [PERSON]'s theory of electrical contact, the contact resistance is not only composed of the resistance of the metal base but also includes the resistance of the film layer and the constriction resistance [3, 4]. At the microscale, the three-dimensional morphological characteristics of contact surfaces have a significant impact on electrical contact performance. According to ISO 25178-2:2021 [5], surface topography is a general term that encompasses various characteristics of a surface, including its geometric shape, texture, roughness, waviness, and more. Among these, surface roughness is an important subset of surface morphological characteristics, typically used to describe the irregularities on a surface at the microscale. Calculating the surface contact area through using roughness joint surfaces and constructing a micro-asperity model is an effective method for analyzing the electrical contact performance of contact groups. [PERSON] et al. [6] constructed a micro-asperity distribution model based on the principles of G-W statistics. This model is based on assumptions about the distribution pattern of micro-asperities and explores the correlation between the number of micro-asperities and the actual contact area. The heights of micro-asperities on a rough surface do not necessarily follow a Gaussian distribution but exhibit chaotic and disordered characteristics. In statistical models, the standard deviation of roughness parameters of the microsurface is affected by the accuracy of the measuring instrument, and traditional statistical methods cannot uniquely characterize the micro-morphology of rough surfaces. [PERSON] et al. [7; 8] discussed geometric modeling techniques for anisotropic rough surfaces and analyzed the relationship between the number of asperities, deformation height, and contact area in the contact interface of rough surfaces with the W-M function possessing fractal characteristics. A three-dimensional rough surface contact resistance model was constructed using the W-M function [3; 9], considered the random distribution characteristics of contact spots and the interaction between spots [10]. [PERSON] et al. [11] used fractal dimension and multi-scale parameters, specifically relative area (Srel), relative length (RL), area-scale fractal complexity (Asfc), and length-scale fractal complexity (Lsfc), to describe the micro wear on the surface after contact with worn surface and worn tool surface. [PERSON] et al. [12] proposed a fractal contact model of rough surfaces (isotropic and non-Gaussian), which revealed the influences of topography and material properties on the contact characteristics. Contact resistance is one of the important parameters characterizing the electrical contact performance of contacts [9; 10; 11; 12; 13]. [PERSON] et al. [13] analyzed the peak time series of moving contact resistance of contacts based on chaos theory and verified the effectiveness of chaos prediction. [PERSON] et al. [14] analyzed the factors influencing the contact resistance changes in railway relay contacts and the relationships between these factors. Contact failure has a crucial impact on the reliability of switching electrical appliances. Existing studies on the intrinsic failure mechanisms of switching electrical appliances have not clearly identified the relationship between the surface morphology characteristics of contacts and the types of failure, nor have they deeply investigated the correlation between morphological parameters and failure mechanisms. Therefore, the analysis of the micro-morphology of the contact surfaces of the contact group is crucial [15; 16; 17]. The contact surface models constructed in existing studies mainly focus on single contact surface [18; 19; 20].