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

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- frequency-response functions
- 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

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## frequency-response functions

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

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Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra ISBN ; Digitally watermarked, DRM-free; Included format: PDF, input-output relationship allows a convergent Volterra series expansion.

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

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.

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. The nth-order GFRF can directly be determined as an n-degree polynomial function of the first order GFRF according to its parametric characteristic by using this new mapping function.

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

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.

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. Then the nonlinear parameters are identified through a metric based on the higher-order kernels.

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Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. In this paper, parametric convergence bounds for Volterra series expansion of nonlinear systems described by a SIMO nonlinear auto-regressive with exogenous inputs model are studied in the frequency domain, which can clearly indicate the parametric range in which a given nonlinear system has a convergent Volterra series expansion, referred to as parametric bound of convergence PBoC. With the resulting PBoC of characteristic parameters, nonlinear systems with a nonlinear multiobjective performance MOP function can then be analyzed in the frequency domain using a nonlinear characteristic output spectrum method based on the Volterra series expansion.

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