Parametric Identification of Nonlinear Systems Using Chaotic Excitation

Abstract

The use of a time series, which is the chaotic response of a nonlinear system, as an excitation for the parametric identification of single-degree-of-freedom nonlinear systems is explored in this paper. It is assumed that the system response consists of several unstable periodic orbits, similar to the input, and hence a Fourier series based technique is used to extract these nearly periodic orbits. Criteria to extract these orbits are developed and a least-squares problem for the identification of system parameters is formulated and solved. The effectiveness of this method is illustrated on a system with quadratic damping and a system with Duffing nonlinearity.