Non-linear curve fitting for modal analysis

Abstract

This paper discusses deficiencies of techniques widely adopted for curve fitting in modal analysis applications. A new Direct Simultaneous Modal Approximation (DSMA) method is introduced that can significantly improve the accuracy of eigenvalues and eigenvector reconstructed from experimental measurements on real structures. The method employs a Newton iteration technique to approximate simultaneously all eigenvalues and eigenvectors of the structure concerned. A major advantage of the method is that it minimises the non-linear function of weighted global least square error for all available data, enabling accurate reconstruction of modal parameters even when this data contains significant levels of noise and/or when modes are very closely spaced. The concept of the DSMA algorithm can be transferred to other disciplines with non-linear curve fitting requirements where estimation of a large number of parameters is required.