Accelerated generalized minimax-concave sparse regularization for impact force reconstruction and localization

Impact force identification has always been of significance for structure health monitoring especially on the applications involving composite materials. As a typical inverse problem, impact force reconstruction and localization is undoubtedly a challenging task. The well-known ℓ₁ sparse regularization has a tendency to underestimate the amplitude of impact forces. To alleviate this limitation, we propose an accelerated generalized minimax-concave (AGMC) for sparse regularization that employs a non-convex generalized minimax-concave (GMC) penalty as the regularizer and incorporates an acceleration technique to expedite the attainment of the global minimum. Compared with the classic ℓ₁-norm penalty, the GMC penalty can not only induce sparsity in the estimation, but also maintain the convexity of the cost function, so that the global optimal solution can be obtained through convex optimization algorithms. This method is applied to solve the impact force identification problem with unknown force locations to simultaneously reconstruct and localize impact forces in the under-determined case utilizing a limited number of sensors. Meanwhile, K-sparsity criterion is used to adaptively select regularization parameters by taking advantage of the sparse prior knowledge on impact forces. Simulations and experiments are conducted on a composite plate to verify the computational efficiency and robustness of the AGMC method in terms of impact force reconstruction and localization, particularly in the presence of noise. Results demonstrate that the proposed AGMC method achieves faster convergence and provides more accurate and sparse reconstruction and localization of impact forces compared to other state-of-the-art sparse regularization methods.