Bridge Influence Line Identification with Vehicle-Induced Static Transmissibility Functions

This chapter presents a novel methodology for extracting influence lines in beam-like structures subjected to moving loads by leveraging the theoretical equivalence between static transmissibility in the spatial domain and frequency-domain influence line ratios. The proposed approach formulates the problem within a Bayesian inference framework, effectively accounting for measurement uncertainties and model discrepancies through a complex-valued probabilistic model of prediction errors. Closed-form solutions are derived for both the FFT coefficients and their spatial-domain counterparts via inverse FFT, facilitating efficient computation of the most probable estimates and posterior uncertainty quantification of influence lines. Key methodological contributions include circumventing ill-posed inverse problems through direct frequency-domain parameterization, obviating dependence on moving load characteristics by utilizing static transmissibility alongside pre-calibrated reference influence lines, and improving computational efficiency via matrix-free operations relative to traditional spatial-domain techniques. Numerical validations confirm the framework’s accuracy in reconstructing influence lines while rigorously quantifying associated uncertainties, with applications demonstrating robustness to noise and modeling inaccuracies.