Structural damage detection based on iteratively reweighted l1 regularization algorithm

Abstract

Structural damage usually appears in a few sections or members only, which is sparse compared with the total elements of the entire structure. According to the sparse recovery theory, the recently developed damage detection methods employ the l1 regularization technique to exploit the sparsity condition of structural damage. However, in practice, the solution obtained by the l1 regularization is typically suboptimal. The l0 regularization technique outperforms the l1 regularization in various aspects for sparse recovery, whereas the associated nonconvex optimization problem is NP-hard and computationally infeasible. In this study, a damage detection method based on the iteratively reweighted l1 regularization algorithm is proposed. An iterative procedure is employed such that the nonconvex optimization problem of the l0 regularization can be efficiently solved through transforming it into a series of weighted l1 regularization problems. Experimental example demonstrates that the proposed damage detection method can accurately locate the sparse damage over a large number of elements. The advantage of the iteratively reweighted l1 regularization algorithm over the l1 regularization in damage detection is also demonstrated.