Identification of Parametric Finite Element Models Using Experimental Modal Data

摘要

A general parametric form of a dynamic finite-element model of a linear elasticstructure with small deformations is presented, with the model consisting of a set of scalar parameters multiplying element kernel matrices. The parameters of the finite-element model can represent stiffness and inertia properties, as well as axial forces if linearized buckling is assumed. Optimization of an orthogonality-based objective functional is employed to estimate parameters, using nondestructively measured experimental eigenpair data, allowing for the finite dimensional, unnormalized, sparse, truncated, and inaccurate natures of experimental modal data. The method enables the use of incomplete eigenvectors, i.e., modes shapes with sparsely measured displacements. Although not vital to the parameter identification method, a procedure for combining modal data from numerous separate experiments is discussed, with the purpose of improving accuracy of the parameters. Given a sufficient number of completely measured eigenvectors with associated eigenvalues, an optimum set of parameters of the finite-element model are obtainable by solution of a linear set of equations. Some simple parameter constraint (e.g. known total mass) is used, without any explicit a priori parameter values. Arbitrary weighting factors are included in the method to take advantage of a priori knowledge of error distributions. The accuracy of the estimated parameters is shown to be function of the accuracy of the experimental modal data employed, independent of any a priori parameter estimates. The effects of missing modal data, especially lower frequency modes, is numerically demonstrated; better parameter accuracy is found with higher frequency modes despite missing lower frequency modes.