# Frequency Domain Analysis And Design Of Nonlinear Systems Based On Volterra Series Expansion Pdf

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- Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion
- Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion
- Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion
- frequency-response functions

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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Jing , Xingjian, Lang , Ziqiang. 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.

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

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Front Matter Pages i-xv. Pages Output Frequency Characteristics of Nonlinear Systems.

Parametric Characteristic Analysis. Nonlinear Characteristic Output Spectrum. Summary and Overview. Back Matter Pages 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.

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.

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. Buy options.

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

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In this work, a novel approach in determining the first- and second-order frequency-domain Volterra kernels for weakly nonlinear partial differential equations PDEs with a forcing term in semidiscrete form based on the application of the harmonic probing method is presented. This represents a formal extension of the linearized frequency-domain LFD methods to a nonlinear framework, leading to a so-called LFD method for a second-order functional series expansion method. The method allows for the representation of weak nonlinearities by solving two input-independent linear algebraic systems of equations in the frequency domain, and thus circumvents the solution of the nonlinear PDE by numerical integration for each different input, representing a nonlinear reduced-order model ROM for the physical phenomena. The general form of the equations is derived, and several applications are discussed. The proposed method overcomes two constraints present in other methods for the solution of nonlinear PDEs, namely, the consideration of exclusively periodic solutions as in the harmonic balance method and the dependency of the kernels with the input signal as in the Volterra kernel identification methods. Google Scholar.

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

The system can't perform the operation now. Try again later. Citations per year. Duplicate citations. The following articles are merged in Scholar.

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Show all documents New results on the generalized frequency response functions of nonlinear volterra systems described by NARX model computation of the GFRFs can not explicitly reveal the analytical relationship between system time domain model parameters and system frequency response functions in a straightforward manner. In order to solve these problems, the parametric characteristics of the GFRFs for nonlinear Volterra systems described by a NARX model were studied in Jing et al , which effectively builds up a mapping from the model parameters to the parametric characteristics of the GFRFs and provides an explicit expression for the analytical relationship between the GFRFs and the system time-domain model parameters.

### frequency-response functions

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In this study, the discrete-time Volterra series are used to update parameters in a nonlinear finite element model. The main idea of the Volterra series is to describe the discrete-time output of a nonlinear system using multidimensional convolutions between the Volterra kernels represented in a Kautz orthogonal basis and the excitations. A metric based on the residue between the experimental and the numerical Volterra kernels is used to identify the parameters of the numerical model. First, the identification of the linear parameters is performed using a metric based only on the first order Volterra kernels.

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Front Matter Pages i-xv. Pages

In this work, a novel approach in determining the first- and second-order frequency-domain Volterra kernels for weakly nonlinear partial differential equations PDEs with a forcing term in semidiscrete form based on the application of the harmonic probing method is presented. This represents a formal extension of the linearized frequency-domain LFD methods to a nonlinear framework, leading to a so-called LFD method for a second-order functional series expansion method. The method allows for the representation of weak nonlinearities by solving two input-independent linear algebraic systems of equations in the frequency domain, and thus circumvents the solution of the nonlinear PDE by numerical integration for each different input, representing a nonlinear reduced-order model ROM for the physical phenomena. The general form of the equations is derived, and several applications are discussed.

The system can't perform the operation now. Try again later. Citations per year. Duplicate citations. The following articles are merged in Scholar.

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Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion. A Parametric Characteristic Approach Part of the Understanding Complex Systems book series (UCS). Download book PDF Pages PDF · Parametric Convergence Bounds of Volterra-Type Nonlinear Systems.