A semi-analytical method for moving force identification of bridge structures based on the discrete cosine transform and FEM

Abstract

A semi-analytical method is proposed for moving force identification (MFI) based on the finite element model of the bridge structures. The moving force can be expanded by a set of cosine basis functions based on the discrete cosine transform (DCT) in the time domain. By constructing the segmented continuous mode shape of the bridge deck, the analytical relationship between the measured acceleration responses and the basis coefficients is derived using the Duhamel integral, which is not affected by the time step. The weighted l1-norm regularization method is used to solve the basis coefficients to improve the accuracy and noise immunity for identification. For complex bridge structures, the relationship between the responses and the moving forces can be analytically characterized by only knowing node modes of the bridge deck elements. Thus the identification can be carried out effectively. In numerical simulations, the effects of measured locations, noise levels, mode numbers, and moving speeds on the recognition accuracy are discussed under different models. The effectiveness, applicability, and robustness of the proposed method are verified.