Generalized Discrete Estimating Method for Moving Force Identification on a Simply Supported Beam Bridge

Abstract

Moving forces are one of the major loads acting on bridge decks, and moving force identification (MFI) is essential for bridge safety. However, there are two shortcomings in existing MFI methods. First, time discrete sampling for the force leads to ill-posedness in MFI. Second, identifying moving forces by means of a fixed frequency and a single type of force dictionary cannot fully and sparsely represent these forces. To address these issues, basis functions containing a trigonometric function and variable-frequency rectangular function are used to sparsely express the force, and the Duhamel integral is used to avoid ill-posed reduction of time discrete sampling for the force. A generalized discrete estimating method (GDEM) is proposed to identify moving forces. The l1-norm regularization method in a sparse solution is introduced to transform the force identification problem into an l1-norm regularization solution problem. The fast-iterative shrinkage threshold algorithm (FISTA) is used to solve the l1-norm regularization problem, and the coefficient of the basis functions is obtained by combining the Bayesian criteria to identify the force. To validate the GDEM, the single and double time-varying forces on a simply supported beam are identified by numerical simulation. The results illustrate that the GDEM can accurately identify moving forces with strong robustness and performs better than the dictionary method. The response combinations of MFI are also discussed.