Impact force identification via sparse regularization with generalized minimax-concave penalty

As a typical inverse problem, impact force identification tends to be a challenge owing to its ill-posedness. Recently, the sparse characteristic of the impact force in time domain are taken into consideration to convert the ill-posed problem into a sparse recovery task. The classic way to obtain sparse approximate solutions of impact force is to use the L1-norm regularization. However, underestimating the exact solution inevitably happens when applying the L1-norm regularization to impact force identification. In this paper, a novel sparse regularization method with generalized minimax-concave (GMC) penalty is proposed to deal with the impact force identification problem. Even if the GMC penalty turns out to be a nonconvex regularizer to promote sparsity in the sparse estimation, it retains the convexity of the sparsity-regularized least squares cost function and the global optimal solution can be found by convex optimization. Additionally, an approach to adaptively set regularization parameters is presented. Finally, simulations and experiments are conducted to verify the performances of the proposed method, and the results are compared with those of the L1-norm regularization method. Results demonstrate that the nonconvex sparse regularization based on GMC can produce more accurate estimations for impact force identification.