Novel formula for determining bridge damping ratio from two wheels of a scanning vehicle by wavelet transform

A novel formula is derived for determining the bridge damping ratio from the correlation of the front and rear wheels of a test vehicle using the modal components extracted by the wavelet transform (WT). Firstly, closed-form solutions are derived for the dynamic responses of the bridge under a moving two-axle vehicle. Next, to remove the masking effect by vehicle's frequencies, the wheel-bridge contact responses back-calculated from the vehicle responses are used in analysis. Then, the WT is employed to obtain the instantaneous amplitudes of the component responses of the two contact points. Finally, using the correlation between the two contact points, a novel formula is derived for the bridge damping ratio. The above derivations are validated by numerical simulations. Through the theoretical analysis and numerical simulations, the following conclusions are made: (1) the spatial correlation of the front and rear contact points is utilized to derive the bridge damping formula using the WT; (2) for multi-span bridges, the RANdom SAmple Consensus (RANSAC) can beneficially downplay the data points with large deviations near the internal supports in fitting the bridge damping ratio; (3) the first span can be reliably used to calculate the damping ratio of multi-span bridges, especially in the presence of pavement roughness; and (4) the formula has been attested to be robust against various levels of vehicle and bridge damping.