System Identification of a Nonlinear One-Degree-of-Freedom Vibrating System

In this paper, the modeling of a nonlinear one-degree-of-freedom mechanical system is investigated with nonlinear system identification methods. To this end, a nonlinear mechanical system with a cubic law for its stiffness characteristics is formulated using MATLAB/SIMULINK software. To identify the nonlinear properties of the mechanical system at hand, the Nonlinear ARX model is studied as the identification method. The nonlinear ARX model consists of linear and nonlinear output functions. More specifically, Feed Forward Network and Sigmoid Network functions are studied as nonlinear output functions of the Nonlinear ARX model to investigate the nonlinear dynamics of the mechanical system of interest. Numerical experiments show that the nonlinear mathematical models of the mechanical system are identified successfully.