Relationship Between the Structure and Performance of Identified Nonlinear Polynomial Models

The effect of the structure of identified nonlinear polynomial models on the dynamical behaviour of such models is investigated. In particular, the effects of the sampling rate, the number of process terms and the order of the models is studied and input design is also considered. Bifurcation diagrams and Poincare sections are used to assess global and local dynamical behaviour of the identified models which were estimated from data generated by the Duffing-Ueda equation. In several of the examples which are provided to illustrate the main points of the paper, the identified models are compared to the original system over a wide range of parameter values for which the Duffing-Ueda equation exhibits regular oscillations, period-doubling cascades, pitchfork bifurcations and chaos.