Non-parametric identification method of GFRFs for MIMO nonlinear system excited by multitone signal

We propose a novel non-parametric method to identify generalized frequency response functions (GFRFs) for multi-input multi-output (MIMO) nonlinear systems in this paper. Firstly, the formula to calculate GFRFs is derived in terms of the corresponding output frequency properties of GFRFs of the MIMO nonlinear system excited by a single-tone signal. Secondly, to improve the efficiency of the non-parametric identification method, we utilize the multitone excitation to drive the MIMO nonlinear system, and propose a searching algorithm of the frequency base of multitone excitation. Finally, the general procedure of identifying GFRFs of MIMO nonlinear system excited by the multitone excitation is summarized. The proposed non-parametric identification method is suitable for application as it only depends on input–output data of the MIMO nonlinear system and avoids time-consuming study of its complicated physical mechanisms. Moreover, the proposed non-parametric identification method is proved to be effective by the precisely identifying GFRFs of a two-input two-output nonlinear system.