Volterra Polynomials Research Articles

MIMO Volterra polynomial equalizer for PDM ultrahigh-order QAM signals

In this work, we proposed and experimentally demonstrated a multiple-input multiple-output (MIMO) Volterra polynomial equalizer (MVPE), in a probabilistic shaping (PS) polarization-division multiplexed (PDM) 4096-quadrature amplitude modulation (QAM) coherent optical transmission system. In comparison with the conventional single-input single-output (SISO) Volterra nonlinear equalizers (VNLEs), the proposed MVPE can equalize the in-phase (I) and quadrature (Q) components in both the X and Y polarizations simultaneously and effectively alleviate nonlinear distortions. In the PS-PDM-4096-QAM experiment, the normalized generalized mutual information (NGMI) reached the threshold of DVB-S2 low-density parity-check (LDPC) codes with a 20% overhead. Compared to the SISO VNLE scheme, the MVPE scheme improves receiver sensitivity by approximately 2.8 dB while maintaining nearly similar computational complexity.

A Note About Numerical Range of Some Volterra Polynomials

A Note About Numerical Range of Some Volterra Polynomials

Integral Models in the Form of Volterra Polynomials and Continued Fractions in the Problem of Identifying Input Signals

The paper discusses the prospect of using a combined model based on finite segments (polynomials) of the Volterra integral power series. We consider a case when the problem of identifying the Volterra kernels is solved. The predictive properties of the classic Volterra polynomial are improved by adding a linear part in the form of an equivalent continued fraction. This technique allows us to distinguish an additional parameter—the connection coefficient α, which is effective in adapting the constructed integral model to changes in technical parameters at the input of a dynamic system. In addition, this technique allows us to take into account the case of perturbing the kernel of the linear term of the Volterra polynomial in the metric C[0,T] by a given value δ, implying the ideas of Volterra regularizing procedures. The problem of choosing the connection coefficient is solved using a special extremal problem. The developed algorithms are used to solve the problem of identifying input signals of test dynamic systems, among which, in addition to mathematical ones, thermal power engineering devices are used.

Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems

In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. The advantage of the presented approach is to obtain explicit formulas for calculating the transient responses (Volterra kernels), which determine the unique solution of the Volterra integral equations of the first kind with two variable integration limits. The numerical method proposed in the paper for solving the corresponding equations includes the use of smoothing splines. An important result is that the constructed identification algorithm has a low methodological error.

An Approach to Stabilizing the Dynamic Loads of a Wind Turbine Generator Based on the Control of the Blades Setting Angle

This study deals with the problem of modeling nonlinear dynamic systems of the ”input-output” type using Volterra polynomials in the case of vector input signals. The study focuses on the effect of the blade rotation angle and the wind speed on the rotational speed of the wind turbine elements. The paper presents the results of a simulation experiment. The basic issue of applicability of the developed procedure of numerical modeling, which involves the estimation of the maximum length of the time segment [0, T] is scrutinized.

Формулы обращения для трехмерного интегрального уравнения Вольтерра I рода с предысторией

The article is devoted to solving one class of Volterra equations of the first kind with variable upper and lower limits. These equations were introduced in connection with the problem of identifying asymmetric kernels for constructing integral models of nonlinear dynamical systems of ”input-output” type in the form of Volterra polynomials. To solve the identification problem, previously introduced test signals with duration h (grid sampling step) are used in the form of a linear combination of Heaviside functions. The article demonstrates a method for obtaining the desired solution, which develops the step method for the one-dimensional case. Matching conditions are established that ensure the desired smoothness of the solution.

Inversion formulas and their finite-dimensional analogs for multidimensional Volterra equations of the first kind

The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric kernels for constructing integral models of nonlinear dynamical systems of the “input-output” type in the form of Volterra polynomials. The case when the input perturbation of the system is a vector function of time is considered. To solve the identification problem, previously introduced test signals of duration h (mesh step) are used in the form of linear combinations of Heaviside functions with deviating arguments. The paper demonstrates a method for obtaining the desired solution, developing a method of steps for a one-dimensional case. The matching conditions providing the desired smoothness of the solution are established. The mesh analogs of the studied integral equations based on the formulas of middle rectangles are considered.

Studying the complexity of identification of Volterra kernels for the case of a vector input signal of arbitrary dimension

The work discusses the technique for constructing an integral model of a nonlinear dynamic system with a vector input based on Volterra polynomials as applied to a section of the steam-water path of the power unit of the Nazarovo power station. The complexity of the applying the technique presented in the work is analyzed, and the number of initial data required to build a mathematical model in the case of a vector input disturbance with an arbitrary dimension is calculated.

Assessment of digital predistortion methods for DFB‐SSMF radio‐over‐fiber links linearization

AbstractThis letter presents a comparative evaluation between three different behavioral models to perform digital predistortion (DPD) that enhances the linearity of radio‐over‐fiber (RoF)‐based front haul links for the mobile network. In particular, the intention is to jump out of the volterra box and propose models based on segmentation approach. Especially the decomposed vector rotation (DVR) model is compared to volterra polynomials such as memory and generalized memory polynomial (GMP) architectures. DPD is employed to RoF links that are based on distributed feedback laser emitting at 1310 nm, and standard single‐mode fiber for long‐term evolution 20‐MHz signal with 256‐QAM modulation format. The effectiveness of the digital predistortion methodology is investigated for varying input powers in terms of normalized mean square error, adjacent channel power ratio, and error vector magnitude. The experimental results demonstrate that DVR achieves elevated linearization when compared to memory polynomial and GMP models.

Identification nonlinear dynamic systems based on Volterra polynomials with using polyharmonic test signals

Предложен метод построения аппроксимационной модели Вольтерра нелинейных динамических систем в частотной области с использованием тестовых полигармонических сигналов различной амплитуды. Вычислительный метод идентификации основан на использовании метода наименьших квадратов с регуляризацией и выборе оптимальной величины шага по амплитуде тестовых сигналов. Исследуется точность и вычислительная устойчивость метода идентификации в виде многомерных амплитудно- и фазо-частотных характеристик. Метод повышает точность и стабильность результатов идентификации. Ил.: 2. Библиогр.: 18 назв. Ключевые слова : нелинейные динамические системы; аппроксимационная модель Вольтера; тестовые полигармонические сигналы; метод наименьших квадратов с регуляризацией.

Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials

We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.

Quadratic and cubic Volterra polynomials: identification and application

Quadratic and cubic Volterra polynomials: identification and application

Quadratic and cubic Volterra polynomials: identification and application

Работа выполнена при частичной финансовой поддержке Российского фонда фундаментальных исследований (грант №15-01-01425а) и Программы фундаментальных исследований Сибирского отделения РАН (проект № АААА-А17-117030310446-6).

Automatic Control Systems Modeling by Volterra Polynomials

Automatic Control Systems Modeling by Volterra Polynomials

Application of neural network and genetic algorithm in identification of a model of a variable mass underwater vehicle

This paper is one of the few works in identification of a model of a Variable Mass Underwater Vehicles (VMUVs) with six degrees of freedom. Since, the mass of fuel changes during the operation, the mass and the center of mass of these vehicles also change and therefore the VMUV has nonlinear-time varying model. In order to obtain a model of the VMUV, an identification procedure is done by using an especial neural network. In this network, which is called the Volterra neural network, the basis functions are Volterra polynomials. Also, genetic algorithm (GA) is used with neural network to structure selection of these nonlinear polynomials. Computer simulations, Monte Carlo and cross-correlation analyses are done by considering admissible levels of noises in the underwater vehicles instrumentations (rate gyros) and the results show the efficiency of the presented approach.

A New Algorithm for Construction of Quadratic Volterra Model for a Non-Stationary Dynamic System

The research is dedicated to the integro-power Volterra series application in the description of nonlinear dynamic input-output systems. The paper presents a new algorithm for the identification of Volterra polynomial of the second degree for non-stationary dynamic systems which allow an active experiment using test sets of input signals. A horizontal - axis wind turbine is used for a test case study. The quadratic Volterra polynomials are constructed. They describe the nonlinear dynamics of the angular velocity of the wind turbine components depending on the blade lean angle and wind speed. The practical identification of Volterra kernels was carried out with respect to some random stationary state of a modeled system.

Estimating the characteristics of randomized dynamic data models (the Entropy-Robust Approach)

We propose a new approach to finding dependencies between small volumes of input and output data based on randomized dynamic models and density estimation for the distributions of their parameters. Randomized dynamic models are defined by functional Volterra polynomials. To construct robust nonparametric estimation procedures, we develop an entropybased approach that employs functionals of generalized informational Boltzmann and Fermi entropies.

New Methods of Entropy-Robust Estimation for Randomized Models under Limited Data

The paper presents a new approach to restoration characteristics randomized models under small amounts of input and output data. This approach proceeds from involving randomized static and dynamic models and estimating the probabilistic characteristics of their parameters. We consider static and dynamic models described by Volterra polynomials. The procedures of robust parametric and non-parametric estimation are constructed by exploiting the entropy concept based on the generalized informational Boltzmann’s and Fermi’s entropies.

Modeling heat exchangers by quadratic Volterra polynomials

Different procedures based on special families of piecewise constant test inputs and intended for identification of the quadratic Volterra polynomials were compared as applied to the problem of automatic control of the nonlinear dynamic system. The results of computer-based experiments for the reference heat exchange model were presented.

Modeling of Nonlinear Dynamic Systems with Volterra Polynomials

The paper presents a review of the studies that were conducted at Energy Systems Institute (ESI) SB RAS in the field of mathematical modeling of nonlinear input-output dynamic systems with Volterra polynomials. The first part presents an original approach to identification of the Volterra kernels. The approach is based on setting special multi-parameter families of piecewise constant test input signals. It also includes a description of the respective software; presents illustrative calculations on the example of a reference dynamic system as well as results of computer modeling of real heat exchange processes. The second part of the review is devoted to the Volterra polynomial equations of the first kind. Studies of such equations were pioneered and have been carried out in the past decade by the laboratory of ill-posed problems at ESI SB RAS. A special focus in the paper is made on the importance of the Lambert function for the theory of these equations.