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 (FOGSL(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 FOGSL(p) method takes more sparse prior information into account by combining the non-convex L-p-norm ( 0 < p < 1 ) 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 FOGSL(p) method. Results demonstrate the efficiency and robustness of the FOGSL(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,L-1-norm regularization methods, the proposed method performs best in both simulations and experiments.