Group sparse regularization for impact force identification in time domain

Abstract

Impact force identification remains a challenging inverse problem, where a small error in structural responses may lead to a large deviation in the actual solution. Recently, sparse regularization has attracted a lot of interest in the field of force identification. However, the standard sparse regularization method for force identification does not consider the intrinsic structure of impact force, i.e., the nonzero elements occur in groups, called group sparsity. In this paper, by exploiting the group sparse structure of impact force time history, we develop a general group sparse regularization method based on minimizing mixed l2,1-norm for the inverse problem of impact force identification. First, the number and size of groups including a complete profile of impact force are determined for penalizing the sum of the l2-norm of groups associated with the pulse profile of impact force. Second, a general group sparse optimization model based on the mixed l2,1-norm penalty for impact force identification is constructed in time domain, leading to a non-smooth convex optimization problem. Third, given the transfer function and the impact response, an accelerated gradient descent method is developed to solve such a group sparse regularization model. Finally, experiments including identification of single and consecutive impact forces are conducted on a clamped-free thin plate to illustrate the effectiveness and applicability of the proposed approach. Experimental results demonstrate that the classical Tikhonov regularization methods can only identify the single impact force from weakly noisy responses; the group sparse regularization method can efficiently identify both single and consecutive impact forces from heavily noisy responses, and has a slightly better improvement of the peak force amplitude than the standard sparse regularization method.