Proper Orthogonal Decomposition for Model Updating of Nonlinear Mechanical Systems

Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve 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 Karhunen-Loeve (K-L) transform is of great help in nonlinear 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 efficient representation of the ensemble. The Proper Orthogonal Modes (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 identification of parameters of nonlinear dynamical structures with an optimization procedure based on the difference between the experimental and simulated POM. A numerical example of a beam with a local nonlinear component will illustrate the method.