## 1 Introduction
[20] used an ANN as a damage detection method to evaluate the performance of the Hilbert-Huang transform based on fully integrated empirical mode decomposition and adaptive noise technology. The experimental results show that the method can accurately identify and extract the damage features of the signal, which indicates that the CEEMDAN-HT-ANN model has excellent ability and robustness in locating damage location and dividing damage severity. [PERSON] et al. [21; 22] proposed a structural damage identification method based on an improved whale intelligent optimization algorithm. This method takes the modal parameters as the identification factor, and several numerical examples are used to show that the method can accurately identify the damage location and severity of different structures and can effectively improve the efficiency of damage identification. [PERSON] et al. [23] proposed a new damage identification method that combines ANN and CS algorithms. In numerical examples, various single intelligent algorithms are used to identify structural damage, which shows that this method is superior to other single intelligent algorithms and has higher computational efficiency. [PERSON] et al. [24] proposed a two-stage damage detection method. The damage index based on modal strain energy is used for damage detection and location in the first stage. In the second stage, an ANN quantifies the damage degree. The results show that this method accurately predicts steel girder bridges' damage location and damage size. The above research shows that structural damage identification is a process from preliminary location to damage quantification [25]. Generally speaking, the bridge is invariably subjectively divided for structural damage identification. Then, the element's damage is preset, and an appropriate method is selected for identification and verification according to the relationship between the characteristic damage parameters and the actual damage [26; 27; 28]. These studies have solved the problem of structural damage identification to some extent. Nevertheless, there is a problem in these treatments; it is assumed that the location of the damage is precisely an element in the finite element model (FEM), and the location of the damage corresponds one-to-one to the element division form of the FEM. However, this is an ideal and exceptional condition. In practice, the bridge structure is damaged due to the train's impact, a lack of material strength, and the interplay of material faults and environmental conditions. Because these factors are unpredictable, the location and magnitude of these damages are uncertain and cannot be established without a professional evaluation. As a result, the damage location is not guaranteed to correspond one-to-one to the element division form of the FEM, and it is necessary to consider the difference between them. In order to solve the problem, a multi-times damage location method based on variable-length elements and an improved genetic algorithm (IGA) is proposed. The convergence speed and recognition effect of the algorithm are studied. The effects of noise, the number of measuring points, and train speed on the recognition rate are discussed. First, a slightly larger length element is used to divide the bridge. Then, the appropriate damage step size and range are selected for rough identification to lock the scope of the bridge damage location. Finally, half of the length is used to subdivide these possible damage locations, the range of variables is limited, and then, the IGA is used to identify them. This process is repeated until the desired accuracy is achieved.