Frequency domain analysis and identification of block-oriented nonlinear systems

• Published in: Journal of sound and vibration Vol. 330; no. 22; pp. 5427 - 5442
• Main Author: Jing, Xingjian
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 24.10.2011; Elsevier
• Subjects: Algorithms; Blocking; Dynamical systems; Exact sciences and technology; Frequency response functions; Fundamental areas of phenomenology (including applications); Mathematical models; Measurement and testing methods; Nonlinear dynamics; Nonlinearity; Physics; Solid mechanics; Structural and continuum mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Frequency dependence; Vibration; Generalized function; Frequency domain method; Modeling; Processing control; Polynomial function; Response function; Experimental design; Non linear model; Signal processing; Frequency response; System identification; Non linear effect; Analytical function
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2011.06.015

Block-oriented nonlinear models including Wiener models, Hammerstein models and Wiener–Hammerstein models, etc. have been extensively applied in practice for system identification, signal processing and control. In this study, analytical frequency response functions including generalized frequency response functions (GFRFs) and nonlinear output spectrum of block-oriented nonlinear systems are developed, which can demonstrate clearly the relationship between frequency response functions and model parameters, and also the dependence of frequency response functions on the linear part of the model. The nonlinear part of these models can be a more general multivariate polynomial function. These fundamental results provide a significant insight into the analysis and design of block-oriented nonlinear systems. Effective algorithms are therefore proposed for the estimation of nonlinear output spectrum and for parametric or nonparametric identification of nonlinear systems. Compared with some existing frequency domain identification methods, the new estimation algorithms do not necessarily require model structure information, not need the invertibility of the nonlinearity and not restrict to harmonic inputs. Simulation examples are given to illustrate these new results. ► Frequency response functions are developed for block-oriented nonlinear systems. ► Effective algorithms are proposed for the estimation of nonlinear output spectrum. ► A general procedure is given for frequency domain identification of block-oriented models. ► The new estimation algorithms do not need some restrictive requirements on the system. ► Examples are given to demonstrate these new results and the potential applications.