Model Updating Using a Quadratic Form

Abstract

The research presented in this thesis addresses the problem of updating an analytical model using a parametric Reference Basis approach. In this method, some parameters are assumed to be accurate (e.g. natural frequencies, mode shapes and mass matrix), while others are adjusted so that the eigenvalue equation is satisfied. Updating is done with the use of principal submatrices, and the method seeks the best parameters multiplying these matrices. This is a departure from classical model reference, and is closer to the formulation of sensitivity methods. The submatrices allow updating of the stiffness matrix with certain freedom while preserving connectivity. Closed form solution can be achieved through multiple ways; two different approaches, denoted as the Quadratic Compression Method (QCM) and the Full Vector Method (FVM), are described in this paper. It is shown that the QCM possesses superior robustness properties with respect to noise in the data. This fact, as well as the simplicity offered by QCM, is demonstrated theoretically and experimentally. The experiments are presented to show the advantage of the QCM in the updating process.