The Convergence of the Volterra Series Representation of Nonlinear Systems

2021 ◽  
pp. 69-94
Author(s):  
Yunpeng Zhu
Keyword(s):  
Nonlinear Systems ◽  
Volterra Series ◽  
Series Representation

scholarly journals Identification of Nonlinear Systems: Volterra Series Simplification

10.14311/976 ◽  
2007 ◽  
Vol 47 (4-5) ◽  
Author(s):  
A. Novák
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Transfer Function ◽  
Linear System ◽  
Impulse Response ◽  
Volterra Series ◽  
Series Representation ◽  
Multimedia Systems ◽  
Audio Amplifier ◽  
Enormous Number

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown. 

Instantaneous Identification of Polynomial Nonlinearity Based on Volterra Series Representation

2005 ◽  
Vol 293-294 ◽  
pp. 703-710 ◽  
Author(s):  
Giacomo V. Demarie ◽  
Rosario Ceravolo ◽  
Alessandro de Stefano
Keyword(s):  
Structural Engineering ◽  
Volterra Series ◽  
Series Representation ◽  
Consistent Estimate ◽  
Short Time Fourier Transform ◽  
Dynamic Identification ◽  
Polynomial Nonlinearity ◽  
Definition Of ◽  
Short Time

In structural engineering applications a sufficient quantity of experimental data to be able to achieve a consistent estimate of nonlinear quantities is seldom available: this applies in particular when the structures are to be tested in situ. This report discusses the definition of instantaneous estimators to be used in the dynamic identification of invariant nonlinear systems on the basis of Short-Time Fourier Transform representation of excitation and system’s response and within the framework of a Volterra series representation of the input/output relationship. An estimation of the parameters of a dynamic system can be worked out from the evolution of such instantaneous estimators.

On Convergence of Volterra Series Expansion of a Class of Nonlinear Systems

2017 ◽  
Vol 19 (3) ◽  
pp. 1089-1102 ◽  
Author(s):  
Xingjian Jing ◽  
Zhenlong Xiao
Keyword(s):  
Nonlinear Systems ◽  
Series Expansion ◽  
Volterra Series

On Random Field Discretization in Stochastic Finite Elements

1998 ◽  
Vol 65 (2) ◽  
pp. 320-327 ◽  
Author(s):  
B. A. Zeldin ◽  
P. D. Spanos
Keyword(s):  
Random Field ◽  
Volterra Series ◽  
Interpolation Method ◽  
Series Representation ◽  
Stochastic Mechanics ◽  
Discretization Methods ◽  
Nonlinear Input ◽  
Midpoint Method ◽  
Stochastic Finite Elements ◽  
Theoretical Developments

Several traditional methods for discretizing random fields in stochastic mechanics applications are considered; they are the midpoint method, the interpolation method, and the local averaging method. A simple and computationally convenient criterion for estimating the accuracy of these discretization methods is developed. Also, the Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems. The theoretical developments are elucidated by a numerical example involving a beam problem.

Sign in / Sign up

Export Citation Format

Share Document