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.

Robustness of nonlinear parameter identification in the presence of process noise using control-based continuation

“…Goharoodi [12] and Marchesiello [13] perform nonlinear subspace identification by a timedomain study of the system response for a given excitation. A similar approach is followed by Narayanan [14] using multi-harmonic excitation. Noel and Kerschen carry out a similar identification of nonlinear subspaces in the frequency domain [15] reducing the computational burden of the method [16].…”

A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

“…For example, in the work of Yuan and Feeny (220) , the identification scheme relies on the extraction of unstable periodic orbits in a chaotic response and the use of the harmonic balance method for determining the system parameters based on the extracted periodic orbit. Prompted by observations that a chaotic signal may be used to probe a nonlinear system (221) , the feasibility of using a chaotic excitation to drive the system to be identified has been explored by Narayanan and co-workers (222) . Noting that a periodically forced nonlinear system does not always exhibit a chaotic response, a motivation to use a chaotic excitation has been to ensure that the driven system exhibits features of a chaotic response irrespective of the linear or nonlinear nature of the system.…”

Parametric identification of nonlinear systems using multiple trials

“…A review of the parametric identification using HB method [10] is given in this section. Let us consider vibratory systems governed by nonlinear ordinary differential equations and subjected to harmonic force excitation.…”

“…An interpretation can be given for Equation (10) in terms of errors in forces. Let the system with the identified parameters be forced through the original periodic trajectory.…”