# Possibility of Bridge Inspection through Drive-By Vehicles
## 1 Background and Literature Review  
With the massive amount of infrastructure built in US, the timely assessment of these infrastructures becomes critical to the public's safety. Due to the high cost and time-consuming direct condition assessment methods, such as closing traffic for sensor installation and monitoring, indirect bridge monitoring has become a promising method to manage transportation infrastructure conditions. The idea of indirect bridge assessment that uses a passing vehicle to detect dynamic bridge properties was initiated by [PERSON] et al. in 2004 [1]. They built a numerical model of a bridge vehicle system and studied the possibility of extracting bridge frequencies from vehicles' responses. [PERSON] and [PERSON] [2] further proposed a finite element model and verified the accuracy of the concept. The results clearly showed four frequencies in the acceleration spectrum: vehicle frequency, driving frequency, and two shifted bridge frequencies. However, the theoretical model is still a little far from applicable in practice because the model does not consider vehicle damping and multi-span effects of the bridge. In another [PERSON] and [PERSON] research [3], they studied more about the relationship of vehicle-bridge systems. In contrast to the previous model, the response of the bridge concentrates on its first vibration mode. The reason is that the vehicle, which acts as a moving force, cannot transfer much energy to trigger higher modes of a heavier bridge. Through comparison of the displacement, velocity, and acceleration responses of the bridge under five different vehicle speeds, it was found that the acceleration response is more sensitive on extracting bridge frequencies. Another tested parameter is the damping of the vehicle. It was found that the damping will decrease the amplitude of the acceleration spectrum, which may cause difficulty in identifying bridge frequencies. [PERSON] and [PERSON] further conducted a parametric study on this indirect method [4]. In this work, a more complicated response function was derived to describe the vehicle-bridge system and concluded that the initial vehicle/bridge acceleration amplitude ratio is important in identifying the bridge frequency. The smaller the ratio, the greater the probability of successfully identifying the bridge frequencies is. [PERSON] et al. also had another study to build the mode shape from a passing vehicle [5]. In this study, the bridge response's instantaneous amplitude history can be regarded as a mode shape. However, the bridge's vibration amplitude is always captured in absolute value, and the sign of the mode values needs to be decided first. [PERSON] performed a simulation of extracting bridge frequency using vehicles under different conditions [6]. In this study, a 3D vehicle and bridge finite element models were built using MSc/NASTRAN software. In the simulation, the first natural frequency of the bridge is not found in various vehicle speeds. [PERSON] conducted a further study on extracting bridge frequency and damping [7]. The model adopted was a 2D half vehicle and bridge model simulated in MATLAB. Three different length bridges with five different damping conditions were simulated. By increasing the bridge length, the power spectrum (higher amplitude) will shift to higher frequencies. If damping and the road roughness were considered, the acceleration spectra itself sometimes could not show the bridge frequency due to energy dissipation caused by damping and road roughness. However, the power spectrum's sensitivity at all frequencies with respect to damping level changes can still show the bridge frequency. [PERSON] and his team performed a damage detection study based on the bridge mode shapes [8]. In their study, the Short-Time Fourier Transformation (STFT) acceleration spectrum's amplitude is approximately proportional to the mode shape square (MOSS). Furthermore, the mode shape square can show obvious differences between damage and undamaged parts.