Optimal matrix pencil approximation problem in structural dynamic model updating

The problem of finding the least change adjustment to a given matrix pencil is considered in this paper. Desired matrix properties including satisfaction of characteristic equation, symmetry, positive semidefiniteness, and sparsity are imposed as side constraints to form the optimal matrix pencil approximation problem. Such a problem is related to the frequently encountered engineering problem of a structural modification on the dynamic behavior of a structure. Alternating direction method is applied to this constrained minimization problem. Numerical results are included to illustrate the performance and application of the proposed method.