Truncated Transfer Matrix-Based Regularization for Impact Force Localization and Reconstruction

Civil infrastructure, such as bridges and buildings, is susceptible to damage from unforeseen low-speed impacts during service. Impact force identification from dynamic response measurements is essential for structural health monitoring and structural design. Force identification is an ill-posed inverse problem, and the regularization technique is widely used to solve this problem using a full transfer matrix. However, existing regularization techniques are not suitable for large-scale practical structures due to the high computational cost for the inverse calculation of a high-dimensional transfer matrix, and impact excitation locations are often unknown in practice. To address these challenges, a novel two-step truncated transfer matrix-based impact force identification method is proposed in this study. In the first step, a sparse regularization-based technique is developed to determine unknown force locations using modal superposition. In the second step, the full transfer matrix is truncated by time windows corresponding to short durations of impact excitations, and a Tikhonov regularization-based technique is adopted to reconstruct the time history of impact forces. The proposed method is verified numerically on a simply supported beam and experimentally on a 10 m steel-concrete composite bridge deck. The results show that the proposed method could determine the impact locations and reconstruct the time history of impact forces accurately. Compared with existing Tikhonov and sparse regularization methods, the proposed method demonstrates superior accuracy and computational efficiency for impact force identification. The robustness of the proposed method to noise level and the number of modes and sensors is investigated. Experimental studies for both single-force and multiple-force localization and identification are conducted. The results indicate that the proposed method is efficient and accurate in identifying impact forces.