Exploring Time-Varying Characteristics in Drive-By Bridge Frequency Extraction with the Second-Order Synchrosqueezing Transform

Recently, due to low cost and convenience, the concept of estimating the bridge's first natural frequency through indirect measurements of a passing vehicle has gained increasing attention-known as drive-by bridge structural health monitoring. As the vehicle acts as a moving mass added to the bridge, this system is nonstationary with time-varying characteristics. Most related studies assume constant bridge and vehicle frequencies of vehicle-bridge interaction (VBI), which is only appropriate when the VBI effect is negligible. When the vehicle mass is significant compared with the bridge mass, often a feature of railway bridges, the interaction effect cannot be ignored. Therefore, this paper presents a nonlinear time-frequency analysis approach to examine the time-varying nature of frequencies in the VBI system using the second-order synchrosqueezing transform. In comparison to the classical linear approaches, such as wavelet transform and short-time Fourier transform, the proposed method can significantly improve the energy concentration of the time-frequency representations, resulting in a clear pattern to show how the frequencies change. In addition, an indicator is proposed to automatically select the parameters with the proposed approach to obtain suitable results. Both numerical simulation and laboratory experiments are carried out to investigate the feasibility of the proposed approach. It is found that due to the time-varying nature of VBI, the frequencies of both vehicles and bridges are time-varying. Therefore, the extracted drive-by bridge frequency should be distinguished from that found using direct (on-bridge free vibration) measurements.