## 1 Introduction  
The cable-stayed bridge is a kind of long-span bridge widely used worldwide. Generally, the designed service life of these long-span bridges could be 100 years [1]. During the service period, bridges must bear the traffic load, wind load, earthquake, and other alternating loads but also be affected by environmental erosion. For example, the humid atmospheric environment and corrosive media in the air will promote the corrosion of bridge components [2]. Long-term environmental erosion and alternating load will inevitably lead to the accumulation of local fatigue damage to the structure, which will reduce the ability of the bridge structure to resist sudden extreme load and even lead to the sudden failure of the bridge structure in the service process. The damaged state of the cable-stayed cable, which is the main force transfer member of the superstructure of the cable-stayed bridge, will directly affect the safety of the cable-stayed bridge in service. At the moment, researchers worldwide are interested in the unique problem of cable fracture. Through long-term investigation, [PERSON] and [PERSON] [3] found that cables are the most vulnerable component in cable-supported bridges. Although strict protective measures are taken during the design of the cable, improper technology and aging of protective materials during construction and service can also lead to protection failure, allowing corrosive media and moist air from the environment to enter the cable body. Under the combined action of environmental erosion and alternating stress, cables will suffer corrosion fatigue damage and become the most sensitive component in cable-supported bridges [4; 5]. According to the investigation of active cable-supported bridges worldwide, many bridges have serious cable corrosion fatigue problems, and several serious cable-breaking accidents have occurred [6; 7; 8; 9; 10]. The service of these sick cables was generally less than 20 years, far from reaching the expected service life [11]. Due to long-term environmental erosion and alternating load, corrosion fatigue failure has become one of the typical failure modes of cable-stayed bridge structures, which is far more than the combination of alternating stress and corrosive medium alone. It is a severe failure mode [12; 13]. [PERSON] [14] and [PERSON] [15] et al. first used control voltage technology and fatigue fracture analysis method to analyze the damage evolution mechanism during metal corrosion fatigue. [PERSON] and [PERSON] [16] proposed that in the process of corrosion fatigue crack initiation and propagation, there is a competitive relationship between mechanical fatigue and electrochemical action. That is, the rate of corrosion fatigue crack initiation and propagation depends on which of these two factors is dominant. This competitive model later became one of the important theories for studying corrosion fatigue: [PERSON] and [PERSON] [17], [PERSON] et al. [18], and [PERSON] and [PERSON] [19] analyzed the corrosion distribution rule of cable section by detecting the old cables of the bridge. In terms of cable safety evaluation, [PERSON] et al. [20], [PERSON] [21], and [PERSON] et al. [22] used the Monte Carlo method, extreme value distribution method, and random field method to evaluate the safety of bridge cables. However, due to the lack of analysis on the deterioration process of cables, this evaluation method based only on probability and statistics theory cannot predict the change in cable security over time. However, it can only evaluate the cable security state at the current time point. [PERSON] et al. [23]. proposed the bearing capacity evaluation model of parallel steel wire cables and the time-varying failure probability model of corrosion based on the assumption of uniform corrosion of steel wire. As the main part of a cable-stayed bridge that transfers force, the stay cable can get damaged or even break due to natural factors such as wear and tear and corrosion, as well as accidental loads, such as car accidents and fires.