## 1 Introduction
[23] proposed a life safety assessment method by calculating the fragility under combined wind and earthquake loads, which can calculate the collapse probability of the tower under different wind loads. [PERSON] et al. [24] introduced a fragility surface for assessing a transmission tower-line system under combined ice and wind loads, and analyzed the effects of wind direction and material properties on fragility. The results indicated that wind direction had a significant impact on the bearing capacity of the tower-line system. [PERSON] et al. [25] analyzed the meteorological parameters in the region where a 400 Kv transmission line was located, studying the interactions between maximum wind speed, maximum ice thickness, and temperature, and calculated the fragility curve of the transmission line under different combined ice and wind loads. Although the fragility analysis method can evaluate the failure probability of transmission lines under different combined ice and wind loads, the studies mentioned above ignored the randomness and occurrence probabilities of ice loads and wind loads [26]. Therefore, to more accurately assess the failure probability of tower-line systems under combined ice and wind loads, it is necessary to consider the joint probability distribution between ice loads and wind loads. The Copula function joint distribution theory, which considers the correlation between variables, is widely used for constructing multivariate joint probability distributions [27]. [PERSON] et al. [28] employed the Copula function to develop a joint probability distribution of ice thickness and wind speed, and predicted the failure probability of transmission lines utilizing the extreme learning machine method, but ignored the correlation between wind speed and wind direction. [PERSON] et al. [29] established joint probability distributions of ice thickness and wind speed, wind speed and wind direction through Copula function. Subsequently, they combined these distributions with the fragility analysis method to propose a failure probability analysis approach that considersthe joint probability of ice and wind loads, and assessed the failure probability of the tower-line system. Nonetheless, their work utilized the static analysis method, neglecting the fluctuating nature of wind. The natural wind speed is composed of mean wind speed and fluctuating wind speed. The mean wind speed remains relatively constant and can be considered a static load. However, the fluctuating wind speed varies continuously over time, thereby inducing dynamic responses of the structures. Existing studies have indicated that the fluctuating effect of wind can lead to significant variations in the mechanical response of structures [30]. Therefore, it is necessary to conduct a dynamic analysis of the tower-line system under combined ice and wind loads considering the fluctuating effect of wind load. The aforementioned studies on the failure probability of transmission lines under combined ice and wind loads have employed certain models, in which the material parameters and geometric dimensions of the structure are treated as constant. However, during the processes of material manufacturing, transportation, and installation of structural components, there may be deviations in the material strength and geometric dimensions from the designed values [31; 32]. [PERSON] et al. [33; 34; 35] established uncertain finite element models (FEMs) of the transmission tower-line system using the Latin Hypercube Sampling method (LHS), and analyzed the vulnerability of transmission tower under wind loads. The results showed that the influence of material uncertainty on fragility is more significant than that of geometric uncertainty. [PERSON] and [PERSON] [36] studied the influence of the structural uncertainty on the dynamic response of the transmission tower subjected to conductor breakage. The results showed that the yield strength of the diagonal member and the geometric size of the member had a significant effect on the results. [PERSON] et al.