## 1 Introduction  
The rapid urbanization process in China has intensified the environmental and traffic-related repercussions of bridge construction, where associated indirect costs frequently surpass direct construction expenses [1, 2]. To address these challenges, the bridge engineering sector has increasingly embraced industrialized approaches centered on factory-based prefabrication and on-site modular assembly [3, 4, 5]. This methodology effectively shortens on-site construction duration while alleviating socioeconomic disruptions. While these methods offer efficiency, they rely heavily on precise segmental assembly, where any failure in connections leads to costly rework and delays. Among various bridge types, self-anchored suspension (SAS) bridges are increasingly employed as iconic urban structures. This preference arises from their harmonious blend of architectural elegance and material-efficient design, which fulfills both esthetic and functional demands of modern infrastructure [6; 7; 8]. However, the construction of SAS bridges poses considerable challenges, especially during the spatial transformation of the main cable configuration. One of the most critical issues in SAS bridge construction is preventing hanger bending damage during the spatial configuration transformation of the main cable [9]. The tensioning process of hangers involves complex interactions between the main cable, tower, and the girder system. Since the hangers are pre-fabricated and installed before the cables reach their final tensioned state, they are highly susceptible to angle deviation and bending damage. Furthermore, discrepancies between the free-hanging cable state (FHC) and fully-loaded cable state (FLC) exacerbate the risks associated with hanger installation. These risks are further compounded by construction errors and environmental factors, which can cause unpredictable disturbances during the process [10; 11]. Addressing these challenges requires effective assembly fault tolerance, which is essential for maintaining structural safety. However, practical engineering applications face constraints such as time, technology, and investment. Leveraging the self-shape-finding and rebalancing properties of flexible cable systems can enhance hanger tolerance and improve adaptability to construction errors, reducing scheduling and cost pressures. However, fault tolerance in assembly involves complex, interrelated factors--such as structural reliability, cable shape optimization, and local damage resistance--that are difficult to isolate and address using conventional methods [12]. While existing methods, such as interval optimization based on reliability analysis, offer potential solutions, they have limitations [13; 14]. [PERSON] et al. [15] proposed an interval optimization method considering tolerance design, which can determine the optimal design scheme and the maximum allowable manufacturing error range. [PERSON] et al. [16] focused on the industrialized construction of SAS bridges and proposed an inverse analysis method for assembly fault-tolerant intervals based on the geometric nonlinearity redundancy of cable systems, which guides the fault tolerance range of hanger tensioning. Existing methods typically rely on passive fault-tolerant mechanisms, which address errors after they occur [17]. However, these methods lack adaptability to real-time disturbances and fail to account for unforeseen issues that may arise during construction. To address these limitations, there is a growing need for an active fault-tolerant control method that can dynamically monitor and compensate for construction errors as they occur. Notably, research in the aviation and mechanical engineering fields provides valuable insights for this approach [18; 19; 20]. For example, [PERSON] et al. [21] proposed an online active fault-tolerant control method for sensor faults in morphing aircraft, demonstrating the effectiveness of dynamic fault compensation in real-time control processes. Similarly, [PERSON]. [PERSON] et al.