A statistical influence line identification method using Bayesian regularization and a polynomial interpolating function

As inherent characteristics of bridge structures, influence lines have been successfully applied in the fields of model updating, damage detection, and condition evaluation. The fast and accurate identification of a bridge influence line (BIL) is the premise and foundation of the above applications. BIL identification can be regarded as a typically ill-posed problem for which it is usually necessary to establish a regularization model to identify the model parameters and reconstruct the BIL. In this study, a BIL identification method that can automatically determine the regularization coefficient and quantify the uncertainties of BIL identification results is proposed. To accommodate the uncertainties involved in the measurements as well as the modeling error, an interpolation function-aided influence line model is embedded into the Bayesian framework with Gaussian prior distribution. The most probable values (MPVs) and variance of the interpolation function coefficients are derived analytically and then further used to infer the posterior probability density function of the influence line. Numerical example of a concrete continuous beam and field test for a box girder bridge show the accuracy, efficiency and qualitative evaluation of the proposed method. The results indicate that Bayesian regularization can be used to select the optimal regularization coefficient more accurately and effectively than traditional methods. More importantly, the uncertainty quantification for the influence line can qualitatively reflect the accuracy of the results as well as the effects of the parameters of the BIL identification model.