• Korean Journal of Optics and Photonics
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• v.23 no.6
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• pp.246-250
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• 2012

We derive analytical expressions for the output spectral density and the noise power $P_{\beta}$ in noise loading analysis using Volterra kernels to characterize fiber nonlinearities. The bandwidth of the input noise source has little effect on $P_{\beta}$, but the power of the input noise source and the dispersion parameter value of the fiber have a significant effect on $P_{\beta}$. The Volterra method predicts ${\Delta}P_{\beta}[dB]$ = 30 dB/decade, which agrees very accurately over a wide range of fiber parameters compared with the numerical results by the split-step Fourier method. Therefore the Volterra method could be useful to predict the performance of a dense WDM system when we plan to upgrade fiber or increase signal power.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.161-164
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• 1996

The authors have recently proposed a new method for identifying Volterra kernels of nonlinear control systems by use of M-sequence and correlation technique. A specially chosen M-sequence is added to the nonlinear system to be identified, and the crosscorrelation function between the input and output is calculated. Then every crosssection of Volterra kernels up to 3rd order appears at a specified delay time point in the crosscorrelation. This method is applied to a saturation-type nonlinear feedback control system of mechanical-electrical servo system having torque saturation nonlinearity. Simulation experiments show that we can obtain Volterra kernels of saturation-type nonlinear system, and a good agreement is observed between the observed output and the calculated one from the measured Volterra kernels.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1443-1448
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• 2003

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impounded by linear models due to the lack of a similarly accepted nonlinear modelling or data based technique. The authors have recently developed a new method for obtaining Volterra kernels of up to third order by use of pseudorandom M-sequence. By use of this method, nonparametric NMPC is derived in discrete-time using multi-dimensional convolution between plant data and Volterra kernel measurements. This approach is applied to an industrial polymerisation process using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.26.3-26
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• 2001

Van de Vusse reactor is known as a highly nonlinear chemical process and has been considered by a number of researchers as a benchmark problem for nonlinear chemical process. Various identification methods for nonlinear system are also verified by applying these methods to Van de Vusse reactor. From the point of view of identification, only the Volterra kernel of second order has been obtained until now. In this paper, the authors show that Volterra kernels of nonlinear Van de Vusse reactor of up to 3rd order are obtained by use of M-sequence correlation method. A pseudo-random M-sequence is applied to Van de Vusse reactor as an input and its output is measured. Taking the cross correlation function between the input and the output, we obtain up to 3rd order Volterra kernels, which is ...

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.221-224
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• 2005

The authors have recently developed a method for identification of Volterra kernels of nonlinear systems by using M-sequence and correlation technique. In this paper, we apply the proposed method to identification of a robot manipulator which has two degrees of freedom. From the results of the experiment, the nonlinear characteristics of the robot manipulator can be identified by the proposed method.

• Journal of Mechanical Science and Technology
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• v.20 no.2
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• pp.205-211
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• 2006

Among other critical conditions in rotor systems the large non-linear vibration excited by bearing non-linearity causes the rotor failure. For reducing this catastrophic failure and predictive detection of this phenomenon the analysis of orthotropic bearing non-linearity in rotor system using higher order frequency response functions (HFRFs) is conducted and is shown to be theoretically feasible as that of non-rotating structures. The complex HFRFs based on the Volterra series are newly developed for the process and investigated their features by using the simple forms of the FRFs associated with the forward and the backward modes.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.915-927
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• 2000

This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.12
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• pp.2315-2325
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• 2011

We propose a novel reduced-state maximum-likelihood sequence detection (MLSD) structure using the Viterbi algorithm based on the second-order Volterra kernel modeling nonlinear distortion due to square law detection of multipath channels commonly occurring in chromatic dispersion (CD) or polarization mode dispersion (PMD) in optical communication systems. While all existing MLSD methods for square-law detection receivers are based on direct computation of branch metrics, the proposed algorithm provides an efficient and structured way to implement reduced-state MLSD with almost the same complexity of a MLSD for linear channels. As a result, the proposed algorithm reduces the number of parameters to be estimated and the complexity of computation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.93-102
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• 2020

The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.