Adaptive Homotopy Sparse Regularization for Impact Force Reconstruction with Coupling-Aware Uncertainties

Impact force reconstruction from structural responses is an important inverse problem for systems in which direct force measurement is impractical. This study proposes an adaptive homotopy sparse regularization method for impact force reconstruction with coupling-aware uncertainties. First, a short-support basis adaptive homotopy [Formula: see text]-norm formulation is introduced to reconstruct the impact force under deterministic conditions. A short-support basis representation is established to describe the local temporal structure of impact loads, preventing adjacent force components from being merged. The adaptive homotopy [Formula: see text]-norm method is then applied to enhance the sparsity of the reconstructed forces. Second, a coupling-aware uncertainty approach is developed to estimate the bounds of the reconstructed impact forces while accounting for strong coupling among uncertain parameters. A finite element numerical example on a finite element spacecraft model verifies that the proposed algorithm can accurately estimate the bounds of the reconstructed impact forces under two impact conditions in a small-sample setting. The proposed method provides a practical approach for impact force reconstruction under uncertain conditions.