Proper orthogonal decomposition for model updating of non-linear mechanical systems

Proper orthogonal decomposition (POD), also known as Karhunen}Loeve (K}L)
decomposition, is emerging as a useful experimental tool in dynamics and vibrations. The
POD is a means of extracting spatial information from a set of time-series data available on
a domain. The use of (K}L) transform is of great help in non-linear settings where traditional
linear techniques such as modal-testing and power-spectrum analyses cannot be applied.
These decomposition can be used as an orthogonal basis for e$cient representation of the
ensemble. The POM have been interpreted mainly as empirical system modes and the
application of POD to measured displacements of a discrete structure with a known mass
matrix leads to an estimation of the normal modes. We investigate the use of the proper
orthogonal modes of displacements for the identi"cation of parameters of non-linear
dynamical structures with an optimisation procedure based on the di!erence between the
experimental and simulated POM. A numerical example of a beam with a local non-linear
component will illustrate the method. (C) 2001 Academic Press