Estimating modal scale factors based on vehicle-induced variation of bridge frequencies

This paper presents a formulation for estimating scale factors based on the vehicle-induced variation of bridge frequencies. The scale factors of mass-normalized mode shapes are formulated to avoid dealing with randomly-scaled mode shapes from output-only modal tests. To this end, the variations of higher-order bridge frequencies and mode shapes during vehicle passage are firstly investigated, in which the synchrosqueezing transform and multi-ridge exaction algorithm are adopted in signal processing to precisely track the instantaneous frequencies in a vehicle-bridge interaction system. Various practical conditions such as pavement irregularity, bridge damping, measurement noise, vehicle speed, and bridge boundary conditions are investigated in the parametric study. The robustness of the formulation for estimating scale factors is demonstrated through the extracted time-varying bridge frequencies and mode shapes with higher-order modes included. The efficacy of using the proposed formulation is explored numerically and experimentally in signal processing for practical applications.