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

A Parametric Characteristic Approach

  • Xingjian Jing
  • Ziqiang Lang

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Xingjian Jing, Ziqiang Lang
    Pages 1-7
  3. Xingjian Jing, Ziqiang Lang
    Pages 31-52
  4. Xingjian Jing, Ziqiang Lang
    Pages 53-63
  5. Xingjian Jing, Ziqiang Lang
    Pages 113-131
  6. Xingjian Jing, Ziqiang Lang
    Pages 153-177
  7. Xingjian Jing, Ziqiang Lang
    Pages 297-320
  8. Xingjian Jing, Ziqiang Lang
    Pages 321-324
  9. Back Matter
    Pages 325-331

About this book


This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain.  The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis and design method. Based on the parametric characteristic approach, nonlinear influence in the frequency domain can be investigated with a novel insight, i.e., alternating series, which is followed by some application results in vibration control. Magnitude bounds of frequency response functions of nonlinear systems can also be studied with a parametric characteristic approach, which result in novel parametric convergence criteria for any given parametric nonlinear model whose input-output relationship allows a convergent Volterra series expansion. This book targets those readers who are working in the areas related to nonlinear analysis and design, nonlinear signal processing, nonlinear system identification, nonlinear vibration control, and so on. It particularly serves as a good reference for those who are studying frequency domain methods for nonlinear systems.


Frequency Domain Methods Nonlinear Analysis and Design Nonlinear Signal Processing Nonlinear Systems Vibration Control

Authors and affiliations

  • Xingjian Jing
    • 1
  • Ziqiang Lang
    • 2
  1. 1.The Hong Kong Polytechnic UniversityHong KongChina
  2. 2.The University of SheffieldSheffieldUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-12390-5
  • Online ISBN 978-3-319-12391-2
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site
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