Model updating based on incomplete modal data

The objective of model updating is to improve the accuracy of a dynamic model based on the correlation between the measured data and the analytical (finite element) model. In this paper, we intend to update the mass and stiffness matrices of an analytical model when only modal frequencies or spatially incomplete modal data are available. While the proposed method is systematic in nature, it also preserves the initial configuration of the analytical model, and physical equality and/or inequality constraints can be easily incorporated into the solution procedure. Numerical examples associated with a simple 5-DoF (degree of freedom) mass-spring system are chosen to illustrate the detailed procedure and the effectiveness of the proposed method. Numerical scenarios ranging from the updating for stiffness terms only to that for all mass and stiffness terms based on various kinds of incomplete modal data are studied. The obtained model updating results are excellent when the measured modal data are noise-free. Uncertainty studies are also conducted based on simulations of corrupted modal data, but a thorough theoretical analysis of the noise effect on the proposed method is still needed.