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摘要
Sparse model updating problems, considered in this paper, focus on updating the constructed second-order finite element model under the sparsity constraint, that is, the updated model should have the desired eigenvalues and eigenvectors, and preserve the symmetry, positive semi-definiteness, and sparsity of the original model. In the process of performing model updating, sparsity of the model, which implies the inner connectivity and other physical properties of the updated system, plays a critically important role in the model updating problems. However, very few results in the earlier literature have paid attention to this important constraint due to the difficulty associated with it. In this paper, an alternating projection method, which is versatile enough to solve a huge class of sparse model updating problems, is presented. A distinct practical feature of this method is that it is easy to design and develop because, in the process of applying this method, one only needs to alternatively find the optimal solutions of some matrix approximation problems arising naturally from the requirement of practical application. And our numerical results demonstrate that alternating projection is an effective tool for sparse model updating problems.
