Partial transfer matrix-based group sparse regularisation for impact force localization and reconstruction

Existing methods for impact force identification are based on full transfer matrix. Constructing and using transfer matrices can be computationally intensive, especially for large-scale complex structures in practice. Partial transfer matrix refers to a subset of the full transfer matrix, potentially reducing computational cost and complexity. In this paper, a partial transfer matrix-based group sparse regularisation method is proposed for the impact force localization and reconstruction. Its robustness and adaptivity with respect to different subsets of full transfer matrix, noise level and number of impact forces are numerically studied using impact forces on a simply supported beam. The number of sensors for impact force identification can be significantly reduced by the proposed method and its localization and time history reconstruction can be determined even with one single sensor configuration. A 10 m long steel-concrete composite bridge model is built in the laboratory. The effectiveness of the proposed method for impact force identification is validated and compared with L₁-norm and L₂-norm regularisation methods numerically and experimentally. Results show that the proposed partial transfer matrix-based group sparse regularisation method has good robustness and identification accuracy and has better performance on the impact force localization and time history reconstruction comparing with L₁-norm and L₂-norm regularisation methods.