Bridge Modal Identification using Single Moving Sensor under Random Traffic Loading

This paper explores the feasibility of utilizing the response recorded by a single moving sensor to identify the modal parameters of a bridge system under different loading conditions, such as known excitation and unknown random traffic-induced vibrations. The sensor traverses the bridge and captures its dynamic response (acceleration). The natural frequencies and damping ratios are identified using the moving sensor data in the frequency domain. In the case of known inputs, these parameters are then used to obtain the mode shapes, expressed as a linear combination of basic orthonormal polynomials (BOPs), with the coefficients of the BOPs in the linear combinations obtained via optimization. A statistical formulation is proposed to estimate the mode shapes in the case of unknown random traffic-induced vibrations, including the effect of road roughness. It is shown that the absolute value of the mode shapes are proportional to the ensemble standard deviation (SD) of the modal responses. This approach requires the sensor to traverse the bridge multiple times, with the mode shapes identified in both the time domain using variances, and in frequency domain through the evolutionary power spectrum of these responses. The random traffic loading is modeled such that vehicle arrival times follow a Poisson distribution, while the mass and velocity of the vehicles are assumed to follow uniform distributions. To incorporate the effect of road roughness, modeled as a homogeneous random field, a vehicle-bridge-interaction (VBI) model is utilized. Numerical validation under the different loading conditions demonstrates that a single moving sensor can be used to identify the modal parameters quite accurately, with high spatial resolution of the identified mode shapes, offering a cost-effective and efficient alternative for bridge health monitoring.