Multi-vehicle responses for high-resolution bridge mode shape identification integrating Kalman filter and compressive sensing

Abstract

This study introduces a three-step procedure for identifying high-resolution bridge mode shapes using responses from a limited number of test vehicles. First, contact-point displacements are retrieved from the vehicle responses using the generalized Kalman filter with unknown input algorithm. Second, the sparse bridge response matrix, populated with contact-point displacements, is completed using the spatial compressive sensing theory. Third, high-resolution mode shapes are extracted by applying singular value decomposition in the completed response matrix. An illustrative example shows that the first two mode shapes of a 60-m bridge can be well identified using the responses of eight test vehicles, achieving a spatial resolution of 0.5 m. The performance of the procedure is further evaluated by considering practical factors, including bridge boundary conditions, environmental noises, and the number of test vehicles. Additionally, the subtraction strategy has successfully removed the effect of pavement irregularity for mode shape construction. The capability of the procedure for accurately and effectively identifying the high-resolution bridge mode shapes is therefore demonstrated.