Parameter identification of nolinear mechanical systems using POD

Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve decomposition, or principal components analysis (PCA), is emerging as a useful experimental tool in dynamics and vibrations. The POD is a statistical pattern analysis technique for finding the dominant structures in an ensemble of spatially distributed data. These structures 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. They have been shown to represent the optimal distributions of kinetic energy or power, and the proper orthogonal values indicate the power associated with these principal distributions. 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.