Impact force identification on composite panels using fully overlapping group sparsity based on Lp-norm regularization

Impact force identification is of great importance for composite structural health monitoring due to the poor impact resistance of composite materials. Convex sparse regularization method based on L 1 -norm tends to underestimate the amplitude of the impact force. This paper proposes a novel method using fully overlapping group sparsity based on L p -norm regularization (FOGS L p ) for impact force identification, which can localize the impact force and reconstruct its time history simultaneously with limited measurements in under-determined cases. The FOGS L p method takes more sparse prior information into account by combining the non-convex L p -norm ([Formula: see text]) and fully overlapping group sparsity to promote sparse solutions, thus improving the accuracy of the reconstructed impact force. An accelerated grouped shrinkage-thresholding algorithm is employed to solve the non-convex optimization problem under the majorization-minimization framework. The Nesterov’s acceleration strategy is modified to accommodate the requirements of non-convex optimization. Simulations and experiments are conducted on composite panels to validate the effectiveness of the FOGS L p method. Results demonstrate the efficiency and robustness of the FOGS L p method to localize the impact force and reconstruct its time history simultaneously while 25 potential impact points are monitored using two sensors. Compared with L 1 -norm, L p -norm, and L 2,1 -norm regularization methods, the proposed method performs best in both simulations and experiments.