Model Correction via Compatible Element Method

Abstract

The theoretical derivation proposed in this paper uses a specific pseudoinverse technique baesd on an incomplete set of measured modes to satisfy the orthogonality condition. Unlike others, this method demonstrates that the updated model derived from the special pseudoinverse technique does exist in the complete modal space and satisfy the eigenequation. There are three basic, compatible, model characteristics in the updated model: (1) Both low‐order and high‐order modes of the updated model correspond to the measured modes and the analytical high‐order modes of the original finite element model, respectively; (2) the distortion (such as negative eigenvalues) of eigenpairs obtained from the modified model can be eliminated by controlling the high‐order modes of the updated model; and (3) the updated matrices retain the properties of the original finite element matrices, including the banded‐state matrix using the element approach. The derivation of modification formulas in this paper is only based on the orthogonality conditions; therefore, the formulas are much simpler than other procedures.