A novel state space method for force identification based on the Galerkin weak formulation

• An novel state space method based on the Galerkin weak formulation is developed.
• The proposed method is accurate enough.
• The proposed method is capable for the case of discontinuous loading.
• A refined version is developed for the case of large noise.

A novel force identification method in state space based on the Galerkin weak formulation is proposed. Using the time function interpolations of both displacement and force, the equation of motion of structural system in state space based on the principle of weighted momentum is formulated. The method is more suitable for the cases of large time step and discontinuous loading compared with the conventional state space method and the explicit Newmark method. Additionally, the proposed method is extended to a refined version for the case of high noise level by dividing the time step into several smaller time substeps.