Influence line estimation of bridge based on Elastic Net and vehicle-induced response

Abstract

Influence lines (ILs) of the bridge have great potential in structural damage detection, model updating and bridge weigh-in-motion system. To address the prolonged traffic closure and low efficiency during the field tests, a regularization technique using Elastic Net and vehicle-induced response is proposed for IL estimation. Firstly, a portable camera and a multi-resolution deep feature framework are used to obtain the displacement response induced by the vehicle. Secondly, the mathematical model for IL estimation is established based on load matrix and measured response. Finally, due to the ill-posed of the inverse problem for specific vehicle configurations, the Elastic Net that integrates with both L1 and L2 norms is adopted to establish the objective function for IL estimation. This combination allows for training a sparse model where few of the weights are non-zero, while still maintaining the regularization properties like stability. The estimation of the IL is simulated by a simply supported beam, and the results show that the estimated IL is highly consistent with the reference one under different noise and vehicle loads, with minimum overall relative error (ORE) and peak relative error (PRE) of 0.16% and 0.40%. Furthermore, the accuracy and feasibility of the proposed method are verified with the laboratory tests on a scaled suspension bridge under the moving vehicle. It is shown that the results estimated under various moving load conditions indicate decent agreement with the ground truth acquired by the static method, with minimum ORE and PRE of 3.60% and 0.81%. Several issues concerning the practical applications of the IL estimation are also discussed, such as noise, vehicle weight and moving speed.