2 edition of Truncation of nonlinear system expansions in the frequency domain found in the catalog.
Truncation of nonlinear system expansions in the frequency domain
S. A. Billings
by University of Sheffield, Dept. of Automatic Control and Systems Engineering in Sheffield
Written in English
|Statement||S.A. Billings and Zi-Qiang Lang.|
|Series||Research report / University of Sheffield. Department of Automatic Control and Systems Engineering -- no.633, Research report (University of Sheffield. Department of Automatic Control and Systems Engineering) -- no.633.|
extension of transfer-matrix frequency domain methods to the case of nonlinear structures . Importantly, it has also been recently demonstrated that the combination of perturbation theory, coupled-mode theory (CMT), and ﬁnite-difference-time-domain (FDTD) methods permits an efﬁcient characterization of many nonlinear PhC-based devices . The nonlinear out-of-plane vibration characteristics can be potentially harnessed in a DE vibration-driven system. the DER vibrated out-of-plane. The membrane expansion frequency was twice the excitation frequency, which was similar to the in-plane case. Time-domain and frequency-domain diagrams of displacement response under excitation.
[A] Jing X. J., , Nonlinear influence in the frequency domain: Alternating series, Systems and Control Letters, 60 (5), , —This for the first time presents a unique point of view — alternative series– into nonlinear influence in dynamic systems and reveals the beauty of nonlinear effect in the frequency domain. Studying nonlinear systems in the frequency domain therefore complements time domain analysis and often provides a deep insight into both the structure and properties of the system that are just not apparent from the analysis of purely temporal models. Examples are used to illustrate the ideas throughout.
used in linear system theory. These expansions are used in every branch of nonlinear system theory: identification summarized in his book. The functions h (, ,)n1 2 nτττare called the Volterra kernels of therefore analysed and designed in the frequency domain. For such weakly nonlinear circuits (having, say, distortion. As shown in Fig. , a compression of the signal in one domain results in an expansion in the other, and vice continuous signals, if X(f) is the Fourier Transform of x(t), then 1/k × X(f/k) is the Fourier Transform of x(kt), where k is the parameter controlling the expansion or contraction. If an event happens faster (it is compressed in time), it must be composed of .
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And the truncation of nonlinear system expansions in the frequency domain involves determining a truncated expression = E such that the effects of the system nonlinearities above the Nth-order can be neglected. Obviously this truncated expression depends upon the contribution of each Y (jo), 1 s n.
A systematic frequency domain method for nonlinear analysis and design based on Volterra series expansion, which is of both theoretical and application significance to all those researchers related to nonlinear systems.
A very novel insight into nonlinear dynamics in the frequency domain, which is very different from all the other existing commonly-used methods. The truncation of Volterra series expansions is studied using the output frequency characteristics of nonlinear systems to develop a new algorithm for determining the terms to include in a Volterra series : S.A.
Billings and Zi Qiang Lang. 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 results enable a representation of the frequency domain characteristics of nonlinear systems by means of a series of Bode diagram like plots that can be used for nonlinear system frequency analyses for various purposes including, for example, condition monitoring, fault diagnosis, and nonlinear modal analysis Xia et al.
(), Zhang et al. The Cited by: 8. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description.
But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed.
Billings SA, Lang ZQ () Truncation of nonlinear system expansions in the frequency domain. Int J Control 68(5)– CrossRef zbMATH MathSciNet Google Scholar Jing XJ, Lang ZQ, Billings SA (a) New bound characteristics of NARX model in the frequency domain.
from book Frequency Domain Analysis and Design of Nonlinear Systems Based on Volterra Series Expansion: A Parametric Characteristic Approach (pp) Output Frequency Characteristics of.
PDF | Expressions for the output frequency characteristics of nonlinear systems are derived for both multitone and general inputs to provide a natural |. Demonstration of Nonlinear Frequency Domain Methods solution W that drives this system of equations to zero for all wave numbers, but at any iteration in the solution process the unsteady MCMULLEN, JAMESON, AND ALONSO residual I^ k will be ﬁnite: I^.
Modeling Nonlinear Systems by Volterra Series Luigi Carassale, 1; and Ahsan Kareem, 2 Abstract: The Volterra-series expansion is widely employed to represent the input-output relationship of nonlinear dynamical systems. This representation is based on the Volterra frequency-response functions VFRFs, which can either be estimated from observed data or.
the frequency domain. Combined with a frequency domain model for the system acoustics with modal coupling, limit cycle amplitudes can be predicted.
Note that Fig. 1 indicates also how the CFD time series data can be used to identify a nonlinear heat source model for a time domain Galerkin model in terms of a neural network.
This alternative is. Hnis the frequency domain Volterra kernel. Why study the nonlinear system in frequency domain. Frequency domain Volterra kernels are needed to calculate the distortion.
HD 2, HD 3, IM 3, h nn (,)τ 1 Lτ is: eg. the n-dimensional Fourier transform for an nth order Volterra kernel Fourier transform: time domain Volterra Æfrequency. The advantage of identification of a nonlinear system in the frequency domain is disturbance or noise rejection due to selective choosing of only significant signal frequency data and ignoring noises spectrum.
In the section, we review input-output modeling with emphasis on. Frequency domain analysis of nonlinear systems: general theory Abstract: A unified study of the applications of Volterra functional series to nonlinear-system analysis is presented with special emphasis on frequency-domain results which either have not been published before, or where rigour had been lacking.
However, most of the previous work has been numerical time-domain development and frequency-domain analysis for the linear framework. This paper focuses on the frequency-domain analysis of the nonlinear ADRC behavior using the describing function method and characterizes the effect of the fal nonlinearity parameter on the performance of the.
in the time domain. In the frequency domain, Pichler et al. () used linear regression-based metamodels to represent the frequency response functions of linear structures. In particular, the same strategy was recently used with PCEs by Yang et al.
() and Jacquelin et al. System of nonlinear ODEs becomes a system of nonlinear algebraic equations in the frequency domain. Solving Nonlinear Algebraic Equations.
Nonlinear algebraic equations are solved using the Newton-Raphson algorithm (Newton's method) as follows. Convert the problem to a sequence of systems of linear equations. and a 3-DOF discrete system, but no comparison with experiments is presented.
Chong and Imregun  present a frequency domain nonlinear modal identification method. The method assumes well-separated modes, where a particular mode of interest is not impacted by neighboring modes.
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. 1) The discovery that each of the DPSSs, once passed through a nonlinear Volterra MIMO system, can be approximated by a quadratic generalized frequency response Volterra system representation  in the frequency domain, and by a linearly-transformed version of the input in the time domain.For a high spatial frequency grafting, the entire response is contained in the even-order nonlinear components.
Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.New magnitude bounds of the frequency response functions for the Nonlinear AutoRegressive model with eXogenous input (NARX) are investigated by exploiting the symmetry of the nth-order generalized frequency response function (GFRF) in its n frequency variables.
The new magnitude bound of the nth-order symmetric GFRF is frequency-dependent, and is a .