Damage quantification for beam bridges based on definitive frequency-band transmissibility matrix

Quantifying damage severity is important for bridge operation and maintenance. Traditional vibration-based damage identification methods often rely on measurements of input excitation, abundant prior damage information, precise initial finite element models, and model updating, making it difficult to accurately and rapidly invert the local damage degree of bridges using only dynamic responses from a limited number of measurement points. To address these limitations, a two-step identification method, termed “localization–quantification,” based on a definitive frequency-band transmissibility function matrix is proposed in this study. First, accurate sensitive frequency bands are determined based on the relationship between the transmissibility function matrix and various mode shapes. A comprehensive index is constructed by integrating the rate of change of the transmissibility function, Gaussian curvature, and singular value decomposition to achieve damage interval identification. Subsequently, the condensed stiffness and mass matrices are obtained through static-dynamic condensation. The dynamic characteristics relationship between these matrices and the definitive frequency-band transmissibility function matrix is utilized to establish an objective function. The stiffness modification factors of the damaged units are directly inverted through least-squares optimization, ultimately enabling a quantitative estimation of the damage degree. Validation through vehicle–bridge coupling simulations and simply supported beam tests demonstrates that the method exhibits precise localization capabilities, stable quantification performance, and good engineering robustness under various uncertain factors, including vehicle speed, vehicle weight, surface roughness, and noise levels.