## 6 Conclusions  
This study modifies the influence line area method by integrating its absolute values while accounting for the distribution of uniformly distributed loads on the bridge, which can mitigate the effect of noise. A moving load identification method that considers uniformly distributed load noise is derived. In practice, the displacement data when the truck or heavy vehicle passes the bridge are relatively easy to obtain. By using Equation (7) or Equation (5), the vehicle load will be identified. The following conclusions are drawn from the simulation analysis validation:  
Figure 18: The comparison of the identification results and the measurement data.  
For cases with noise subject to the moving load: The three methods, including IL, AIL, and AIL-Modified, can all identify moving loads effectively. The wheelbase and moving speed have little impact on the identification methods.
2. The IL method is highly sensitive to the location of monitoring points, while the AIL and AIL-Modified methods are less dependent on the location of the monitoring points.
3. For cases with uniformly distributed load noise subject to the bridge, the IL method becomes nearly unreliable. The AIL method performs within acceptable error margins, and the AIL-Modified method provides more accurate identification results.
4. The application of the proposed method to the bridge demonstrates its feasibility and potential for implementation in similar bridge structures. However, the effectiveness of this method is highly dependent on the accuracy of input data. Therefore, further research is necessary to assess its applicability to other types of bridges. And the location of the displacement sensors also has a significant effect.
5. The accurate moving load identification is fundamentally crucial to fatigue life models that help to assess the remaining life of bridge structures. This underpins the predictive and preventative maintenance regime that is cost-effective and eco-friendly.  
Conceptualization, L.D., P.L., T.H. and S.K.; Methodology, L.D., P.L. and T.H.; Validation, L.D., P.L. and T.H.; Formal analysis, L.D., P.L. and T.H.; Investigation, L.D., P.L. and T.H.; Data curation, L.D. and P.L.; Writing--original draft, L.D., P.L. and T.H.; Writing--review & editing, L.D., P.L., T.H. and S.K.; Supervision, S.K.; Funding acquisition, L.D., P.L. and T.H. All authors have read and agreed to the published version of the manuscript.  
The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant No. 52078486) and the Key Project for Scientific and Technological Cooperation Scheme of Jiangxi Province (Grant No. 20223 BBH80002). This article is in part based upon work from COST Action (FABER--Fatigue Benchmark Repository, CA23109), supported by COST (European Cooperation in Science and Technology).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The moving load conditions are critical information for remaining fatigue life prediction. This article forms a part of the load condition identification based upon work from COST Action (FABER--Fatigue Benchmark Repository, CA23109), supported by COST (European Cooperation in Science and Technology).