An optimization technique for damped model updating with measured data satisfying quadratic orthogonality constraint

A two-stage optimization procedure for matrix updating of a damped finite element model in structural dynamics is proposed. In Stage I, the measured data is updated to satisfy a recently established orthogonality relation between the eigenvectors of a quadratic matrix pencil associated with the model. This updated data is then used in Stage II to update the stiffness matrix so that (i) the updated model reproduces the measured data, and (ii) the symmetry of the original model is preserved. The results of the paper generalize some well known and recent results in several ways. Our contribution also includes mathematically proved results to demonstrate that Stage I is essential to obtain a symmetric updated matrix KK in Stage II, unless, of course, the measured eigenvector matrix is such that the orthogonality constraint has been already satisfied, which is extremely unlikely to happen in practice.