## 1 Introduction  
The current transportation market, driven by a steady increase in global, is growing rapidly driven by a steady increase in the global economy, especially in developing countries [1]. There is an urgent demand for constructing highways and railways in mountainous and cross-sea areas, where long-span bridges are widely built or in construction [2]. Cable-supported bridges, including cable-stayed bridges and suspension bridges, are widely used in highways crossing gorges, rivers, and gulfs, due to their superior structural mechanical property and beautiful appearance [3]. A cable-supportedbridge is usually the key junction of a highway or a railway demanding a higher safety margin. However, long-span bridges suffer from harsh environmental effects and complex loading conditions, such as heavy traffic loading, significant wind load effects, severe corrosion effects, and other natural disasters [4, 5, 6]. Subsequently, these effects may result in changes in the structural-mechanical behavior, which may alter the dynamic characteristics and resistance of the bridge during its lifetime. Due to the structural flexibility of cable-supported bridges, wind load and seismic effect are critical factors affecting bridge safety [7, 8]. Furthermore, the steadily growing traffic load and environmental corrosion effects can lead to bridge safety degradation [9, 10]. Therefore, it's critical to ensure the structural safety of cable-supported bridges in harsh environments. Cable-supported bridges have one or more pylons and flexible decks supported by prestressed cables. The cables are critical components to support girder gravity and moving vehicle loads [11]. However, cables are subjected to corrosion under the coupling effect of fatigue loading and environmental corrosion. As a result, cable corrosion can lead to strength degradation, which can result in cable rupture or even collapse of the bridge. A research conducted by [PERSON] et al. [12] revealed that more than half of the stay cables of an in-service cable-stayed bridge were severely corroded, demanding prompt replacement. Cable-supported bridges are associated with numerous uncertainties, such as material performance behaviors, cross-sectional dimensions, and various external loads. These uncertainties make the safety analysis of cable-supported bridges more complex for two main reasons. First, the structural mechanical behavior is highly nonlinear. Second, the bridge structure is statically indeterminate, which may lead to a failure sequence of more complicated systems. System reliability theory is a powerful tool for the estimation of the life-cycle safety of cable-supported bridges accounting for uncertainties [13, 14]. For a statically indeterminate structure, the scenario of a component failure may not result in safety issues. For example, the rupture of a stay cable may not affect the safety and serviceability of a cable-stayed bridge. However, a progressive failure of critical components may result in safety problems or even a bridge collapse event. The system reliability theory can be employed to search for potential failure sequences and identify sensitive components or parameters, which is beneficial for design optimization. There are two critical problems in structural system reliability evaluation. First and foremost, long-span bridges have a higher indeterminate degree that makes the structural performance functions more complicated. Thus, it is important to accurately and efficiently approximate the limit state function by utilizing an adequate approach. In this regard, there are several commonly used approaches, such as the artificial neural network (ANN) and the respond surface method (RSM). With the rapid development of artificial intelligence (AI), the application of AI-based approaches in structural reliability analysis is becoming increasingly popular. [PERSON] et al. [15] proposed a least squares support vector regression (LS-SVR) for structural reliability analysis with high efficiency and accuracy. [PERSON] et al.