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2015 | OriginalPaper | Chapter

8. Determination of Nonlinear Output Spectrum Based on Its Parametric Characteristics: Some Theoretical Issues

Authors : Xingjian Jing, Ziqiang Lang

Published in: Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion

Publisher: Springer International Publishing

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Abstract

This chapter shows that, the analytical parametric relationship described by the OFRF of any polynomial structure in terms of any model parameters of interest for Volterra systems described by a NDE model can be determined explicitly up to any high order by using a simple Least Square method from some simulation or experimental data, and every specific component of the OFRF can also be determined effectively. Moreover, the main result established is not only applicable for the OFRF based method, but also has significance for the determination of any analytical parametric relationship of this kind of system polynomial functions by using numerical methods.

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previous chapter The Parametric Characteristics Based Output Spectrum Analysis

next chapter Nonlinear Characteristic Output Spectrum

Chen Y, Jing X, Cheng L (2013) Frequency domain analysis and design of nonlinear vehicle suspension systems, Chapter 12. In: Liu H, Gao H, Li P (eds) Handbook of vehicle suspension control systems. IET control book series. ISBN: 978-1-84919-633-8

Jing XJ, Lang ZQ (2009a) On the generalized frequency response functions of Volterra systems. Trans ASME J Dyn Syst Meas Control 131(6)

Jing XJ, Lang ZQ, Billings SA, Tomlinson GR (2006) The parametric characteristic of frequency response functions for nonlinear systems. Int J Control 79(12):1552–1564CrossRefMATHMathSciNet

Jing XJ, Lang ZQ, Billings SA (2007a) New bound characteristics of NARX model in the frequency domain. Int J Control 80(1):140–149CrossRefMATHMathSciNet

Jing XJ, Lang ZQ, Billings SA (2008e) Mapping from parametric characteristics to generalized frequency response functions of nonlinear systems. Int J Control 81(7):1071–1088CrossRefMATHMathSciNet

Jing XJ, Lang ZQ, Billings SA (2009d) Determination of the analytical parametric relationship for output spectrum of Volterra systems based on its parametric characteristics. J Math Anal Appl 351:694–706CrossRefMATHMathSciNet

Title: Determination of Nonlinear Output Spectrum Based on Its Parametric Characteristics: Some Theoretical Issues
Authors: Xingjian Jing
Ziqiang Lang
Publisher: Springer International Publishing
Book: Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion
Print ISBN: 978-3-319-12390-5

Electronic ISBN: 978-3-319-12391-2

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-12391-2_8