# Possibility of Bridge Inspection through Drive-By Vehicles
## 1 Background and Literature Review
However, the MOSS can only be extracted when the vehicle has a much higher frequency than that of the bridge and the speed of the vehicle cannot be faster than 2 m/s. [PERSON] and [PERSON] conducted a study on how to extract mode shapes using multiple vehicles [9]. They simulated the vehicle-bridge interaction (VBI) model as a 2D beam with two quarter-vehicles. Singular Value Decomposition (SVD) was applied to the power spectral density matrix to obtain the mode shapes. This method can extract modes easily from the acceleration history of two moving vehicles. However, the results are two-point modes of each segment, which may not be fine enough to identify a bridge's damage. [PERSON] and [PERSON] explored this method in the detection of damages [10]. In order to improve this method, several laser vibrometers were added to the two-axle vehicle. The vibrometer can detect the relative velocity between vehicle and road, through which vehicle body acceleration history and the bridge velocity at the contact point can be extracted. Furthermore, the segment number can be increased by decreasing time spacing between signals with multi-laser vibrometers. According to the case study, the damage location can be identified from the extracted MOSS compared with the undamaged MOSS. The speed of the test vehicle can be increased to 8 m/s. If there is noise, small damages can still be detected. This may not work with multiple cracks, however. [PERSON] and his team also adopted the multiple axle VBI model to extract the frequency and modal property [11]. They used the residual response of moving vehicles to extract bridge properties. The residual response is the vertical displacement difference of two moving vehicles. The vehicles pass the bridge with a time difference. Furthermore, the residual response is calculated from the difference between the two vehicle's vertical displacements at the same location. It is found that it is more efficient to use the residual response than the single axle response to identify mode properties. More bridge frequencies and their mode shape squares can be extracted from the residual responses. In another [PERSON] research [12], he used the two-vehicle models to test the residual response method. One model still uses the single-degree-of-freedom vehicles, while another model uses a five-axle truck model. The results show that the multi-DOF model has better performance for extracting mode shapes. The residual response method shows another possible way of monitoring bridge property. Much research was conducted recently to look at ways of making the drive-by inspection more practical [13; 14; 15]. [PERSON] and his collaborators [16; 17; 18] researched wavelet entropy and the Hilbert transform method of the vehicle acceleration history to improve the bridge frequency extraction accuracy at normal vehicle operational speeds. [PERSON] and his collaborators [19; 20] adopted numerical modeling and Kalman filter method to test drive-by damage detection in cable-stayed bridges. Successful detection, localization, and assessment of damage in the cables are obtained using a realistic range of vehicle parameters without any bridge response measurement. [PERSON] et al. [21] extended the drive-by inspection using smartphones instead of fixed accelerometers. However, the fundamental questions such as the initial conditions for performing correct VBI analysis and STFT transformation for damage identification of multi-span bridges under realistic road surface conditions and vehicle damping are not fully understood, which were researched in this study.