## 2 Methodology
### Numerical Model  
In this study, a finite element model (FEM) was used to obtain training and test data for the ANN. If measured data are available, a more realistic prediction will be possible, but as mentioned in Section 1, measuring displacement is not easy. The motivation for this study is developing another method to predict displacement. Therefore, an FEM verified with experimental values was used as an alternative. It is assumed that the results analyzed from the verified FEM correspond to the actual data. In order to carry out the finite element analysis (FEA), a simple supported slab-and-girder bridge was selected. The span of the slab was set to 36 m and the width of the slab to 15 m (Figure 1a). It is assumed that the bridge carried four lanes of traffic, two in each direction. I-shaped steel girders were used (Figure 1b). The unit weight of the concrete slab is 2300 kgf/m\({}^{3}\) and the modulus of elasticity is 30 GPa. Also, the unit weight of the steel girder is 8000 kgf/m\({}^{3}\) and the modulus of elasticity is 200 GPa. For the loads applied to the bridge, only the vehicle load was considered. Dynamic analysis was performed assuming that all materials are within the elastic range and are homogeneous and isotropic. The commercial program ABAQUS for FEM was used. Three-dimensional solid elements were used for the bottom slab of the bridge, and three-dimensional shell elements were used for the girders. In order to analyze the dynamic behavior due to the passing of the vehicle load over the bridge, it is modeled as shown in Figure 2. At both ends of the bridge, approach portions were modeled to minimize any numerical problems that might occur between the bridge and the entrance as a vehicle moved onto the bridge. The numerical model used was verified by comparing it to experimental values under static and dynamic loads [41; 42; 43]. The behavior of bridges is affected by these factors, such as vehicle weight, length, suspension, and natural period. Because these interfere with each other in a complex manner, it is difficult to construct a model that considers all variables. Therefore, in this study, it is assumed that the vehicles are limited to three types--passenger cars, buses, and trucks--and that they move at constant speeds. The dynamic performance of structures can be affected by various factors such as loading type, geometry, and so on [44]. In this paper, the dynamic interaction between the bridge and the moving vehicles can have relevant effects. To express these interactions, FE model based on the vehicle model proposed by [PERSON] and [PERSON] [44] was used. The vehicle model includes the mass, spring, and damper which have different dynamic behavior with bridge. The specifications of the models used for cars, buses, and trucks were used those proposed by [PERSON] and [PERSON] [45], [PERSON] et al. [46], and [PERSON] [47]. Figure 1: Dimensions of bridge (unit: mm). Statistics were also introduced to generalize the measured headway values of the vehicles. The traffic situation was generalized using Pearson Type III theory assuming the most general intermediate flow of traffic [48]. Pearson Type III theory is a generalized function of the gamma distribution and is often used to describe traffic conditions [49]. The Pearson Type III probability density function at arbitrary headway \(t\) is given by Equation (1). \[f(t)=\frac{\lambda}{\Gamma(K)}[\lambda(t-\alpha)]^{K-1}e^{-\lambda(t-\alpha)} \tag{1}\]  
where \(\lambda\) is the flow rate and can be calculated using the mean value (\(\mu\)) of the measured headway, \(\alpha\), and \(K;\alpha\) is the minimum expected headway; and \(K\) is the shape factor that can be calculated using \(\mu\), \(\alpha\), and the standard deviation (\(\sigma\)) of the measured headway.