2 edition of **Mearsurement of the Volterra kernels of a nonlinear system of finite order.** found in the catalog.

Mearsurement of the Volterra kernels of a nonlinear system of finite order.

Teddy HUANG

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Published
**1965** by Massachusetts Institute of Technology, Department of Electrical Engineering in Cambridge (Mass.) .

Written in English

**Edition Notes**

Submitted...in partial fulfillment of the requirements for the degree of Master of Science.

ID Numbers | |
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Open Library | OL21655167M |

Volterra series expansion [2]. The functions h 0, h 1, h 2,,h n are known as the Volterra kernels of the system. In general, h n is the n th order kernel of the series that completely characterizesthe nth order nonlinearity of the system.

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The Volterra series is a model for non-linear behavior similar to the Taylor differs from the Taylor series in its ability to capture 'memory' effects.

The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of this system depends strictly on the input at that particular time. The response of a finite memory, causal, and nonlinear system can be described by the Volterra functional series, in which each term captures the influence of higher-order interactions between Author: John Van Opstal.

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 by: developed (e.g., Wu and Kareem ). The identification of Volterra series kernels (es-pecially higher-order kernels) is a critical issue to establish the Volterra series based non-linear analysis framework.

This research focuses on the systematical comparison of vari-ous identification schemes for the truncated Volterra system. Fig. 6 Second-order Volterra kernel of example system Fig.

7 Section through third-order Volterra kernel with third axis fixed T able 3: Levels of components of output fr om simulated.

A method of measuring the Volterra kernels of a finite-order non-linear system is presented. The kernels are obtained individually as a multi-dimensional impulse response. memory nonlinear system having a finite-order Volterra series representation can be allel cascade identification is applied to measure accurately the kernels of nonlinear of the Wiener or.

pp Schetzen,M().Measurement of kernels of a nonlinear system of Finite Order, Int.l. Control. voU. pp Sussman,H.J(). Existence and Uniqueness of Minimal Realizations of Nonlinear Systems. New methods of controlling nonlinear system represented by discrete Volterra functional series are proposed.

These methods make it possible to eliminate the effect of disturbance on the desired output by using. explicit input terminals, whose values can be easily set. Measurement of the kernels of a non-linear system of finite order.

By M. Schetzen. Abstract. Measurement of Volterra kernels of finite order nonlinear syste Topics: ELECTRONICS. Year: OAI identifier: oai: The behavior of a nonlinear dynamic system under arbitrary excitation can be represented by the Volterra series if the Volterra kernels of different orders are known.

This study presents a methodology for a direct estimation of the Volterra kernel coefficients up to the second-order using prepared data obtained by running a time-domain analysis.

first Volterra kernel and the higher-order Volterra kernels (i.e. the second and the third Volterra kernels). Both input signals are used to update the 3D nonlinear finite element model. Finally, a middle level of amplitude force generated by the chirp input signal as well as a low, a middle and a.

We consider the representation and identification of nonlinear systems through the use of parallel cascades of alternating dynamic linear and static nonlinear elements.

Building on the work of Palm and others, we show that any discrete-time finite-memory nonlinear system having a finite-order Volterra series representation can be exactly represented by a finite number of parallel LN cascade paths.

This is a result of a large number of measurements being required in order to produce an adequate estimate, due to overparameterization issues. is the n th order Volterra kernel (or the n-th-order impulse response of the non-linear system M.

Isaksson, Multitone design for third order MIMO Volterra kernels, in: IEEE MTT-S. Nonlinear systems with convergent Volterra series representations will be considered.

New definitions of stability and stabilizability, and the H ∞ norm for nonlinear systems will be given via the Laplace transform of the corresponding Volterra kernel. Second-order and bilinear systems are used as examples to deal with the stability in detail.

mines the kernels of a nonlinear system that can be represented as a Volterra filter. It makes use of the general Wiener model of a nonlinear system as shown in Fig.

1 [7]. This decomposes the nonlinearity into a parallel set of linear filters which comprise all of the time-varying part of the model, termed the memory of the system.

is the lth-order Volterra kernel, or lth-order nonlinear impulse response. The Volterra series is an extension of the linear convolution integral. Most of the earlier identification algorithms assumed that just the first two, linear and quadratic, Volterra kernels are present and used special inputs such as Gaussian white noise and correlation methods to identify the two Volterra kernels.

Representation, identification, and modeling are investigated for nonlinear biomedical systems. We begin by considering the conditions under which a nonlinear system can be represented or accurately approximated by a Volterra series (or functional expansion).

Next, we examine system identification through estimating the kernels in a Volterra functional expansion approximation for the system. nonlinear systems. Nonparametric identification methods are those that measure Wiener kernels or Volterra kernels, since an output of a nonlinear system can be described by the convolution integral of Wiener or Volterra kernels and the system input.

Section 1 highlights the representation methods of nonlinear systems by kernels including mutual. The nonlinear behavior is modeled using a finite number of the Volterra kernels of the plant and the desired input-output map of the closed-loop system.

The control design takes place in the frequency domain and is realized as an interconnected set of linear systems. IDENTIFICATION OF A NONLINEAR SYSTEM BUDURA GEORGETA1, BOTOCA CORINA2 Key words: Identification, nonlinear system, Wiener kernels estimation, signal reconstruction.

The nonlinear system identification based on the Volterra model is applicable only for systems whose order is known and finite.

A lot of practical applications need the. We show that Volterra kernels of order > 1 occurring in the series expansion of the solution operator A are continuous functions, and establish recurrence relations between the kernels allowing their explicit calculation.

A practical tensor calculus is provided for the finite-dimensional case. Volterra and Wiener series provide a general representation for a wide class of nonlinear systems. In this paper we derive rigorous results concerning (a) the conditions under which a nonlinear functional admits a Volterra-like integral representation, (b) the class of systems that admit a Wiener representation and the meaning of such a representation, (c) some sufficient conditions providing.

the th-order time-domain Volterra kernel of the system; each kernel is bounded and a symmetrical function of its arguments. The set of kernels describes the dynamic characteristics of the nonlinear system. Equations (2) and (3) can be interpreted as an extension of the well-known linear convolution integral, which describes the time-domain.

The uniform recurrent arithmetical formula of each order frequency-domain kernel was given, the Volterra frequency-domain kernel acquisition method was discussed, and the fault diagnosis method based on recurrent neural network was showed. A fault diagnosis illustration verified this method.

A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way.

Algorithms based on the functional expansions of Wiener and Volterra, the identification of block-oriented and bilinear systems, the selection of input signals, structure detection, parameter. finite. rWhen the nonlinear system order is unknown, adaptive methods and algorithms are widely used for the Volterra kernel estimation.

The accuracy of the Volterra kernels will determine the accuracy of the system model and the accuracy Mof the inverse system used for compensation. The speed of kernel estimation process is also important. This system can be represented to any desired degree of accuracy by a finite series of the form (5).

This equation is known as the Volterra series expansion. The h 0,h1,h 2,h n are known as the Volterra kernels of the system [2] [3]. The kernelh 0 is called the impulse response of the system, h 1 is the first order kernel, h 2 is.

Nonlinear System Model and Output Cumulants Analysis. We focus on the identification of a second-order Volterra-Hammerstein model with finite memory as it is given in: where is the input of the system, assumed to be a stationary zero mean Gaussian white random process with.

stands for the model order. () A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels. International Journal of Computer Mathematics, () A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model.

addition we investigate the annoying case when the kernel of (E) is degener-ate and some of our theorems either become trivial or do not apply. We conclude by presenting the result one gets when one applies, e.g., Theorem to a first order, nonlinear system. InStephen Boyd came up with a way to measure the Volterra kernels.

InNiclas Bjorsell showed how to measure Volterra kernels for A-to-D converters. But, I have not been able to find anything on adaptive systems using the Volterra model where the kernels are derived from the input/output relationship. In this paper, we study a class of fractional nonlinear second order Volterra integro-differential type of singularly perturbed problems with fractional order.

We divide the problem into two subproblems. The first subproblems is the reduced problem when ϵ = 0. The second subproblems is fractional Volterra integro-differential problem.

We use the finite difference method to solve the first. The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensional boundary layers. Our aim is to study the nonlinear properties of the wavefield through a Volterra series equation.

The kernels of the Volterra expansion, which contain relevant physical information about the system, are estimated. Volterra kernels samples of order (k =1,2) with a specified. discreteness (V. k) and moments of Volterra kernels.

k () r. of different orders. r, r = 0,3) (M. Diagonal sections moments of Volterra kernels. Proposed the universal approach to forming a of diagnostic features sets, which consists in using of Volterra kernels. to identify kernels of Volterra decomposition from the measurements of the input output data series and to identify Volterra model of the unknown dynamical system.

[5] Most importantly, the measurement of the Volterra kernels is required in the identification of nonlinear systems based on the Volterra series model. The Volterra series. first-order Volterra kernel is evaluated for m -- 1: M(Sl) K1 (Sl) - -- (7) L(SI) Note that the nonlinear terms in Eq.

1 do not contribute to K1 (i.e., the first-order Volterra kernel of the system represents strictly the linear portion of the nonlinear dif- ferential equation, as expected).

When the linear and time-invariant assumptions are valid, measuring the impulse response of a system is an ideal way to capture its properties such that output with any input can be computed with convolution.

Nonlinear systems with memory, for example musical instruments and vacuum tube, require an approach such as Volterra series. Measurement technique can capture the information of the.

tem (non-linear system with memory). The non-linear block is then described by the cascade of a purely-linear dynamic system with a virtually non-finite memory and of a non-linear one associated with finite, relatively short memory effects (Fig.2).

The first block of such a cascade is simply characterized. The First-Order Operator -- 3. Second-Order Volterra Systems -- 4. The Second-Order Kernel Transform -- 5. Higher-Order Volterra Systems -- 6. Higher-Order Kernel Transforms -- 7.

The pth-Order Inverse -- 8. The Application of Volterra Theory to Nonlinear System Analysis -- 9. Motivational Basis for the Wiener Theory of Nonlinear Systems -. () Extrapolation for solving a system of weakly singular nonlinear Volterra integral equations of the second kind.

International Journal of Computer Mathematics() Quasi-wavelet based numerical method for fourth-order partial integro-differential equations with a weakly singular kernel.() A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel.

Journal of Computational and Applied Mathematics() High-Order Methods for Volterra Integral Equations with General Weak Singularities. 3 is sufficiently well-behaved so that it has the stationary and causal representation. where functions g k are called the Volterra kernel. The right-hand side of Eq.

8 is generically called the Volterra expansion, and it plays an important role in the nonlinear system theory (13, ). There is a continuous-time version of Eq.