Journal ArticleDOI
Technical communique: Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model
TLDR
New magnitude bounds of frequency response functions for nonlinear Volterra systems described by NARX model are established and provide a significant insight into the magnitude based analysis and synthesis of nonlinear systems in the frequency domain.About:
This article is published in Automatica.The article was published on 2008-03-01. It has received 27 citations till now. The article focuses on the topics: Frequency response & Frequency domain.read more
Citations
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Journal ArticleDOI
Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review
TL;DR: In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts derived from the VOLTERRA series, including the general frequency response function (GFRF), the nonlinear output frequency response functions (NOFRF) and associated frequency response (AFRF), and a detailed review is then given on the applications of Volterras in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
Journal ArticleDOI
Frequency domain analysis and identification of block-oriented nonlinear systems
TL;DR: In this article, analytical frequency response functions including generalized frequency response function (GFRF) and nonlinear output spectrum of block-oriented nonlinear systems are developed, which can demonstrate clearly the relationship between frequency response and model parameters, and also the dependence of frequency response on the linear part of the model.
Journal ArticleDOI
Computation of Convergence Bounds for Volterra Series of Linear-Analytic Single-Input Systems
Thomas Hélie,Béatrice Laroche +1 more
TL;DR: The singular inversion theorem is used to obtain the main result of the paper, namely, an easily computable bound of the convergence radius of the Volterra series.
Journal ArticleDOI
Fault diagnosis of complex system based on nonlinear frequency spectrum fusion
TL;DR: In this article, a fault detection and diagnosis approach for nonlinear complex systems by combining nonlinear frequency spectrum characteristics and evidence theory is proposed, which is based on the evidence theory.
Journal ArticleDOI
Parameterized Convergence Bounds for Volterra Series Expansion of NARX Models
TL;DR: Evaluation of the convergence bound in the frequency domain for Volterra series expansion of nonlinear systems described by NARX models is studied and new convergence criteria are developed for harmonic inputs and then extended to multi-tone and general input cases.
References
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Journal ArticleDOI
Fading memory and the problem of approximating nonlinear operators with Volterra series
Stephen Boyd,Leon O. Chua +1 more
TL;DR: In this article, it was shown that any time-invariant continuous nonlinear operator with fading memory can be approximated by a Volterra series operator, and that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map.
Journal ArticleDOI
Representations of non-linear systems: the NARMAX model
Sheng Chen,Stephen A. Billings +1 more
TL;DR: In this paper, it is shown that the NARMAX (Non-linear AutoRegressive Moving Average with eXogenous inputs) model is a general and natural representation of non-linear systems and contains, as special cases, several existing nonlinear models.
Journal ArticleDOI
The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs
E. Bedrosian,S.O. Rice +1 more
TL;DR: Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented.
Continuous nonlinear systems
TL;DR: In this paper, a thesis submitted to M.I.T. Dept. of Electrical Engineering, July 24, 1959, is described, based on which the following paper is presented:
Related Papers (5)
Fading memory and the problem of approximating nonlinear operators with Volterra series
Stephen Boyd,Leon O. Chua +1 more