## 1 Introduction
### Literature Review  
At present, the prevailing approach for project-level bridge maintenance decision making is multi-objective decision making. In the context of multi-objective decision-making methods, [PERSON] et al. [7] proposed a maintenance multi-objective decision-making method for single-span highway bridge deck panels. However, their study did not provide specific maintenance measures. Based on the multi-objective particle swarm optimization algorithm, [PERSON] et al. [8] carried out a multi-objective optimization of an RC bridge superstructure based on the reinforcement years, failure probabilities of the main beam and bridge panels, and the FRP volume used for reinforcement. [PERSON] et al. [9] introduced the applicability index, established a table corresponding to the repair methods for typical types of bridge deck diseases, and divided maintenance measures into four maintenance activity levels (daily maintenance, repair, reinforcement, and replacement). The multi-objective function consisted of a restoration effect, applicability, and maintenance cost, and it was optimized by a genetic algorithm. In [PERSON]'s study, maintenance measures were divided into four activity levels: routine maintenance, repair, strengthening, and replacement. The multi-objective function comprised restoration effectiveness, applicability, and maintenance cost. Genetic algorithm optimization was employed to determine the appropriate measures for each bridge deck panel element. Furthermore, a multi-objective decision model was constructed, thereby optimizing the maintenance priorities for each bridge deck panel element and helping with the allocation ratio of funds. Cost-effectiveness analysis in bridge maintenance encompasses an estimation of the maintenance measure costs that are incurred during the maintenance process and the assessment of benefits generated after maintenance. In the current research on bridge maintenance decision making, many studies have not specifically focused on the cost estimation of measures at the element and defect level. [PERSON] et al. [10] defined cost estimation in bridge maintenance as the process of estimating the expenses associated with a specific maintenance strategy, which considers both the general category and detailed measures of the maintenance approach. This estimation is based on the bridge maintenance and repair quotas. The maintenance cost estimation comprises two parts: base price and workload. However, the study's defined scope of maintenance work was relatively broad, and the cost estimation process for maintenance work was not presented in detail. Some researchers have focused on specific defect types and measures, whereby they quantified the cost of measures based on the volume of materials used. For instance, [PERSON] et al. [8], in their research on lifecycle decision optimizations of the superstructure of RC bridges, considered a single maintenance measure (FRP strengthening), and its cost was quantified by the total volume of FRP material required. In the field of bridge engineering, there is a need to further specify and present the cost estimation process for maintenance work, which is achieved by considering specific defect types, measures, and the material volumes used. [PERSON] et al. [11] defined it such that each maintenance operation involves replacing 10% of the original materials, and the maintenance cost is calculated based on the volume of material replacement. However, the cost of maintenance measures not only includes material costs, but also encompasses expenses related to labor, machinery, and other factors such as regional rates. Therefore, quantifying the cost solely based on material volume may not be entirely accurate. Scholars both domestically and internationally have different definitions of bridge maintenance benefits. For example, [PERSON] et al. [8] used the cumulative time-dependent failure probability as a measure of lifecycle benefits. [PERSON] et al.