Impact force identification on composite panels using fully overlapping group sparsity based on L_p-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 L₁-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 ((Formula presented.)) 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 L₁-norm, L_p-norm, and L_2,1-norm regularization methods, the proposed method performs best in both simulations and experiments.