Alternating direction method for structure-persevering finite element model updating problem

The problem of finding the optimal approximation to the discrete stiffness matrix modeled by the finite element method is considered in this paper. Desired properties of the updated matrix, including symmetry, positive semidefiniteness and structure connectivity, are imposed as side constraints. Besides these, the optimal approximate matrix should be the least-squares solution to the dynamics equation. To the best of the author’s knowledge, the optimal matrix approximation problem containing all these constraints simultaneously has not been proposed in the literature earlier. Alternating direction method is first applied to this constrained minimization problem. Numerical examples are performed to illustrate the efficiency of the proposed method.