## 3 Finite Element Modulation and Damage Detection
### Stationary Vehicle Location  
The premise of the study is that the movable vehicle can be stationed at any location on the bridge. Therefore, the vehicle can be stationed at several locations until the damage existence and location are confirmed.  
The first location of the vehicle is chosen to be at mid-span and the damage is located from 7.5 m to 8.5 m from the left side of the bridge. The IA of the high frequency IMF is shown in Figure 5. The IA amplitude shows irregularity around the stationary vehicle and damage locations. Irregularities around the stationary vehicle location occur because added mass is considered as damage [46]. Knowing where the car is parked, it noticed that the damage occurs around the point of 8 m from the left side of the bridge.  
As there are some other minor irregularities such as between the vehicle at mid-span and the damage location, it is important to park the vehicle at different locations to examine the true location of the damage. Therefore, the movable vehicle is stationed now far from the damage, at 20 m from the left side of the bridge. Figure 6 shows the IA of the IMF of the stationary vehicle located far from the damage. It still shows irregularities around the vehicle and damage locations. This again indicates that the damage location is correctly identified at 8 m from the left side of the bridge.  
When the vehicle is parked at mid-span (12.5 m away from the left side) and when it is located at 20 m away from the left side of the bridge, the IA results still show the correct location of the damage. Now, we have an idea where the location of the damage is. To further investigate the detection process, the vehicle is stationed at the detected damage location. Figure 7 shows the IA of the contact-point response of the vehicle when it is  
Figure 5: IA of the contact-point response of a stationary vehicle parked at mid-span.  
Figure 6: IA of the contact-point response of a stationary vehicle parked far from the location of the damage.  
stationed at the damage location (8 m from the left side of the bridge). In this figure, there is only one peak, which is at the location of the damage and vehicle, unlike Figures 5 and 6. This confirms the findings in Figures 5 and 6.  
Finally, although this method does not rely on previous information from the healthy bridge, it is worth showing what the IA of the healthy bridge would look like. Figure 8 compares the IA results of a stationary vehicle parked at mid-span from the damaged and undamaged bridges. It is noticed that for the healthy state bridge, the irregularities only occur at the vehicle location. It is important to note that irregularities happen at the end and beginning to the bridge due to the boundary conditions [39]. Therefore, even a healthy bridge would have irregularities at the boundaries of the bridge. This is considered one of the disadvantages of the proposed method. If the damage is near the boundary condition, it is difficult to detect such damage. The authors notice that from the beginning of the bridge until 6 m, the irregularities do not represent damage, but the boundary condition of the bridge.