Nonlinear identification of systems with parametric excitation

In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification (HBNID) and IHBNID are also studied and compared by using numerical simulation. The effectiveness of the IHBNID is verified through the Mathieu-Duffing equation as an example. With the aid of the new method, the derivation procedure of the incremental harmonic balance method is simplified. The system responses can be represented by the Fourier series expansion in complex form. By keeping several lower-order primary harmonic coefficients to be constant, some of the higher-order harmonic coefficients can be self-adaptive in accordance with the residual errors. The results show that the IHBNID is highly efficient for computation, and excels the HBNID in terms of computation accuracy and noise resistance.