Flexibility Matrix Reconstruction and Mode Shape Identification for Girder Bridge Based on Displacement Influence Line

To address the limitations of low resolution and sensor dependency in environmental vibration-based bridge modal identification, this study proposes a deflection influence line-driven flexibility matrix reconstruction method for modal shape extraction. Displacement responses under moving vehicle loads are first processed using variational mode decomposition to extract quasi-static components, and Tikhonov regularization is employed to enhance the stability of influence line identification under noise. The reconstructed displacement influence lines are then used to formulate the flexibility matrix, from which mode shapes are efficiently identified via eigenvalue decomposition. Theoretical derivations establish the mathematical foundation of the method, while numerical simulations verify its accuracy and robustness under different noise levels. Experimental validation on a scaled three-span continuous girder bridge model further confirms its practical feasibility. Comparative analysis demonstrates that the proposed approach successfully reconstructs flexibility matrices from measured deflection influence lines, while the eigenvalue decomposition-derived modal shapes satisfy engineering accuracy requirements for rapid bridge performance evaluation. This methodology establishes a novel paradigm for contactless modal identification, demonstrating promising practical applicability for rapid bridge condition assessment.