## 1 Introduction  
Bridges play a vital role in modern cities and have far-reaching implications for the efficiency and sustainability of urban transport. When ambient temperatures are low, fog, rain, and snow can cause bridges and bridge cables to freeze. As the temperature warms, they will fall onto the roads, seriously threatening pedestrians and road safety [1, 2, 3, 4]. And the ice accretion to the variation of bridge properties (mainly mass) can lead to false alarms if a monitoring system is installed [5]. At the same time, bridge pylon crossbeams have a larger surface region compared to bridge cables, and the risk of freezing is more significant [6]. The main objects of current research on bridge ice melting are bridge deck structures and bridge cables. Their ice-melting methods are mainly divided into four categories: laying carbon fiber heating cables inside the bridge deck [7, 8]; laying thermal exchange pipes inside the bridge deck (using thermal pumps to transfer thermal from the thermal source to the roadway through circulating fluids) [9, 10]; removing the ice buildup by human resources, but this method is inefficient and dangerous to work at high altitudes [11, 12, 13]; and applying a hydrophobic coating on the surface of the bridge structure to prevent icing, but with a concise service life [14, 15, 16, 17]. Among them, burying carbon fiber heating cablesand thermal exchange pipes is the method of melting ice which uses thermal energy [18]. However, due to the high position of the bridge pylon crossbeams, the total trip of laying the thermal exchange pipe is too long and leads to too much thermal loss, and the effect of melting ice is poor. Ice melting by carbon fiber electric heating is not affected by the environment and deployment location and is highly applicable. And there are already engineering applications that use carbon fiber heaters to melt ice and snow. At present, scholars have applied carbon fiber heating wires to bridge cables [19], road pavements [20], tunnels [21], and airport pavements [22]. The research results show that the carbon fiber heating wire can achieve the effect of melting snow and melting ice in practical engineering. At present, there are no examples of carbon fiber release wires applied to bridge pylon crossbeams, only numerical simulations of this aspect [6]. Therefore, this paper chooses to use carbon fiber electric heating as the suspension bridge pylon crossbeam structure of the ice-melting program. On the other hand, it is essential to consider the ice-melting efficiency of the approach, namely the energy usage of the system, to minimize energy wastage during the ice-melting process [23]. [PERSON] et al. [7; 24] studied the energy utilization of bridge deck structures and developed an automatic snow-melting system (AS-EHP) that utilizes cable heating and snow melting. Their findings indicate that a shallower burial depth of the cables leads to improved energy utilization in bridge deck structures. AS-EHP's design and operation strategy is proposed by studying the energy of three factors: pipe burial spacing, burial depth, and wind speed. [PERSON] et al. [25; 26] developed a model that combines thermodynamics and mass transfer to analyze hydraulically heated pavements. They also proposed an optimal operation strategy for these pavements. Additionally, they created a numerical model that combines thermodynamics and economics to evaluate a hydraulic snow-melting pavement system. This model was compared with data from the Beijing Daxing International Airport, providing recommendations for the system's operation strategy. [PERSON] et al. [27] conducted field experiments and numerical simulations to investigate the temperature and energy distribution at various pavement depths. Their research aimed to give empirical references for enhancing the energy efficiency of snow and ice melting on airport pavements. However, all of the above studies have been conducted on bridge decks, pavements, and airport runways.