## 6 Conclusions and Discussion  
This research introduces a novel method for identifying train axle loads considering dynamic amplification effects, utilizing a hybrid approach combining strain influence line theory and mathematical optimization. The methodology was applied to an in-service simply supported composite beam bridge within an urban rail transit system. A dedicated strain field measurement scheme was developed and implemented, facilitating comprehensive data acquisition. Numerical modeling and validation were integral parts of this study, particularly in establishing and verifying the strain influence lines at measurement points across the bridge. Statistical analyses were performed on the distribution patterns of train axle loads within urban rail transit scenarios. According to the above comprehensive analysis, the following conclusions can be drawn:  
(1) The axle load characteristics of forward AC03-type trains on Shanghai Metro Line 3 exhibit distinct statistical distributions: locomotives follow a logarithmic normal distribution model, whereas middle train carriages conform to a normal distribution model. Specifically, the statistical mean value of axle load of locomotives is 9.64 t, while it is 10.77 t for middle train carriages. The axle load of locomotives and middle train carriages has the same variance with values of 0.8. (2) The axle loads of locomotives and middle train carriages for reverse AC03 type trains on Shanghai Metro Line 3 both follow normal distribution models. The statistical findings indicate that both locomotives and middle train carriages of reverse trains have similar mean axle loads of around 10.5 t. However, there is a notable difference in variance, with locomotives exhibiting higher variability (variance of 1.36) compared to middle train carriages (variance of 0.8). (3) The developed method for identifying train axle loads, which considers dynamic amplification effects through a hybrid approach combining strain influence line theory and mathematical optimization, proves effective in monitoring train loads and assessing their impact on structural integrity. Although the train axle load identification method developed in the study is based on a simply supported beam bridge and applied to AC03 type train, the methodology itself has strong scalability due to the universality of the two inside basic principles of strain influence line theory and mathematical optimization techniques. For different bridge types, such as continuous beam bridges, arch bridges, and cable-stayed bridges, it is only necessary to calculate strain influence lines of measurement points in a targeted manner to update the coefficient matrix \(\mathbf{I}(x)\) (Equation (4)). For different trains, only the axle load matrix \(\mathbf{P}\) needs to be adjusted according to the specific train configuration. Currently, due to limitations in measurement data size, the analysis of train axle load distribution is restricted to locomotives and middle train carriages. Moving forward, an ongoing collection of strain responses at measurement points on the simply supported composite beam bridge will be conducted to expand the sample data size. This expansion aims to establish comprehensive axle load distribution models for each carriage type on Shanghai Metro Line 3. In the near future, based on the developed method and artificial intelligence technology, the intelligent identification and overload warning system for train axle loads will be designed and installed on the simply supported composite beam bridge on Shanghai Metro Line 3. By accurately determining train axle loads and providing timely overload warnings, engineers can effectively assess the bridge's response to dynamic loading conditions, therefore enhancing the safety and longevity of existing bridge structures. Methodology, H.S. ; Software, H.S. ; Validation, J.X. ; Formal analysis, H.T. ; Investigation, X.P. ; Resources, J.X. and H.T. ; Data curation, X.P. ; Writing--original draft, X.P. ; Writing--review & editing, H.S. ; Visualization, J.X. and H.T.