A novel strategy for response and force reconstruction under impact excitation

Force and response amplitude are vital to mechanical product life-time. However, these data are always difficult, even impossible, to measure directly. Therefore, we propose a reconstruction strategy based on the subspace identification (SI) algorithm and fast iterative shrinkage-thresholding (FIST) algorithm to reconstruct impact-force and response at desired location. For the reconstruction strategy, reconstruction equations are built by a state-space model, and SI algorithm is utilized to estimate coefficient matrices of the state-space model to form transfer matrices. And then, considering ill-condition of transfer matrix and sparsity of impact-force, FIST algorithm is employed to solve sparse regularization model by minimizing the l₁-norm. Numerical and experimental studies indicate that the proposed reconstruction strategy can be used to accurately reconstruct force and response under impact excitation, and compared with typical l₂-norm regularization methods, FIST algorithm is more efficient and accurate in both single-time impact and consecutive impact cases.