Nonlinear characteristics of damaged bridges under moving loads using parameter optimization variational mode decomposition

Investigation on the dynamic characteristics of bridges for structural condition assessment is challenging when nonlinear breathing cracks in the bridge and nonstationary vehicle-bridge interaction are considered. Variational mode decomposition (VMD) method has been widely used to analyze the nonlinear time-series, but its performance is highly dependent on the parameter setting, i.e., the number of modes and the penalty factor. A new method based on the parameter optimization VMD is proposed to extract the nonlinear dynamic characteristics from responses of bridge under moving vehicle loads in this paper. The Chicken Swarm Optimization algorithm is used to optimize the VMD parameters to improve the decomposition and characterization. A general breathing crack model is introduced to simulate the bridge damage. The acceleration response of bridge considering the cracks is decomposed by the proposed method. The instantaneous frequency (IF) is then obtained from the time–frequency representation of the bridge-related response component using the ridge detection. Numerical simulations are performed to investigate the effect of the crack location and extent on the IFs for structural damage detection. The effect of the vehicle–bridge interaction is also discussed. The method is further verified using the laboratory experimental results of a concrete bridge model under the vehicle load. The nonstationary and nonlinear dynamic properties of the bridge model with different damage scenarios are successfully identified. The results show that the extracted IF clearly reveals the behaviour of breathing crack that can be a potential indicator of the damage in the bridge.