Updating Structural System Parameters Using Frequency Response Data

New approaches are developed that use two sets of measured frequency response data to update the analytical system mass and stiffness parameters in order to improve the agreement between the dynamical behaviors of the analytical and actual systems. Taking the differences between the measured frequency response and the analytical predictions, the resulting matrix equations are first manipulated to isolate the mass correction matrix of the system, after which the stiffness matrix can be adjusted. Rearranging the system correction matrices into vector forms, the connectivity information can be enforced, thereby preserving the physical configuration of the system and reducing the sizes of the least-squares problems that need to be solved. Solution techniques to perform the model update are introduced, and the numerical issues associated with solving overdetermined and underdetermined least-squares problems are investigated. Heuristic criteria are given for determining the minimum number of frequency response data points that need to be measured in order to ensure sufficiently accurate updated mass and stiffness matrices, and numerical experiments are presented to validate the proposed model updating techniques based on using the frequency response data.