Model Update Using Modal Contribution to Static Flexibility Error

Abstract

A new technique for the parametric correction of full-order analytical stiffness matrices from reduced-order modal measurements is presented. The proposed algorithm corrects model parameters by minimizing a matrix residual formed at measurement degrees of freedom only. The residual is the difference between the measured modal contribution to the static flexibility matrix and the corresponding analytical modal contribution to the static flexibility matrix. Analytical expressions are developed for the flexibility matrix error residual gradient in terms of modal sensitivities found via Nelson's method. By utilizing a flexibility-based matrix error residual, the effect of poorly modeled inertia properties on stiffness parameter estimates is greatly reduced. Unlike technlques that utilize only static data, this technique is suitable for use on unconstrained structures. In addition, the method avoids the problems of mode selection, determining modal correspondence, and eigenvector expansion or model reduction. Numerical simulation results are presented for Kabe's model as well as a finite element model of a welded frame structure.