Novel recursive formula for removing damping distortion effect on bridge mode shape restoration using a two-axle scanning vehicle

Mode shapes recovered for bridges are often distorted by bridge damping when using the vehicle scanning method (VSM). To remedy such an effect, a novel recursive formula utilizing the spatial correlation between the front and rear contact points of a two-axle scanning vehicle is theoretically established. For a bridge subjected to a two-axle moving test vehicle, the dynamic response of the system is first derived in closed form. The vehicle-bridge contact response is used as a substitute for the vehicle response in signal processing, since it is free of the masking effect posed by vehicle frequencies. Using either the Hilbert transform (HT) or wavelet transform (WT), instantaneous amplitudes are extracted for the component response of the bridge of concern. Further, recursive formula that accounts for the spatial correlation between the two contact points is established to recover the undistorted bridge mode shapes. The following are the conclusions: (1) The distortion effect of damping on bridge mode shapes can be effectively removed by the recursive formula against various factors; (2) the WT is more effective in recovering undistorted bridge mode shapes than the HT; and (3) the proposed formula works well for restoring the mode shapes of bridges with rough pavement, by adding an accompanying truck during the vehicle scanning.