The matrix pencil nearness problem in structural dynamic model updating

Abstract

This paper considers the problem of finding the least change adjustment to a given matrix pencil. The desired matrix properties, including satisfaction of the characteristic equation, symmetry, positive semidefiniteness, and sparsity, are imposed as side constraints to form the optimal matrix pencil approximation problem. This problem is related to the frequently encountered engineering problem of a structural modification to the dynamic behavior of a structure. Conditions ensuring the feasible region of the matrix pencil nearness problem are analyzed using a matrix decomposition technique. An unconstrained minimization formulation is presented in terms of the Lagrangian multiplier method and solved by a subgradient algorithm. Numerical results are included to illustrate the performance and application of the proposed method.

Updating structured matrix pencils with no spillover effect on unmeasured spectral data and deflating pair

“…Analytical expressions of the updating matrices are also obtained for undamped models in [41] and [40] by treating the MUP as a residual minimization problem and matrix pencil nearness problem respectively. An optimization approach is also considered in [7] to obtain the updates.…”