## 5 Conclusions  
In order to study the influence on the recognition effect when there is a difference between the element division form of the FEM and the actual damage location, a multi-times location damage method based on variable-length elements and an improved genetic algorithm is proposed. First of all, the selection, crossover, and mutation operators in the traditional genetic algorithm are improved, and catastrophe and neighborhood search mechanisms are introduced to enhance the local optimization ability of the local algorithm. The test function verifies the performance of the improved genetic algorithm. Then, the time-varying equation of train-rail-bridge coupling is established, and the objective function is constructed using the bridge's dynamic response under trainload. Finally, an example is used to perform multiple independent repeated calculations for different damage conditions, and the stability and convergence rate of the algorithm is statistically analyzed. Moreover, the effects of noise, the number of measuring points, and train speed on the identification results are discussed. From this study, the following conclusions can be drawn:  
1. The sum of the search space of this algorithm is less than that of the traditional one-time recognition method, and the computational efficiency is improved. With the increase in the number of damaged units, the number of the former slowly increases, while the number of the latter exponentially increases. As far as an example is concerned, the traditional method is 6.7 times that of the algorithm.
2. The algorithm converges quickly. The number of iterations required for the first appearance of the optimal solution \(ANS\) is mostly between 8 and 14, which is on the low side. Under the action of the optimal holding strategy operator, the algorithm can converge quickly.
3. There is a specific relationship between noise, number of measuring points, train speed, and recognition rate. The recognition rate has an \"S\" curve relationship with noise, a positive correlation with the number of measuring points, and a negative correlation with train speed.
4. Even if there is a difference between the damage location and the element division form of the FEM, the damage location can be correctly located, but the quantitative result of the damage degree will be affected. Under the given suggested value, the recognition effect of the algorithm is good and can reach more than 95%.  
Figure 20: Relationship between \(v\) and \(IR_{\rm Z}\).  
**Author Contributions:** Conceptualization, H.Y. and W.Z.; methodology, W.Z.; software, W.Z.; validation, H.Y.; formal analysis, H.Y.; investigation, A.Z.; resources, H.Y.; data curation, H.Y.; writing--original draft preparation, H.Y.; writing--review and editing, W.Z.; visualization, N.W.; supervision, W.Z.; project administration, Z.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant numbers 51708429, 52178301; the Open Projects Foundation of State Key Laboratory for Health and Safety of Bridge Structures, grant number 2017-04-GF; the Plan of Outstanding Young and Middle-aged Scientific and Technological Innovation Team in Universities of Hubei Province, grant number T2020010; the 13 th Graduate Education Innovation Fund Project of Wuhan Institute of Technology, grant number CX2021120.  
The data presented in this study are available on request from the corresponding author.  
All authors declare no conflict of interest about the representation or interpretation of reported research results.