• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1901-1906
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• 1995

The frequency response functions of systems incorporating a non-linear cubic stiffness subject to sinusoidal excitation are derived using the Volterra series and the convergence characteristics investigated. It is shown that the series representation of the frequency response functions converges only when the sinewave input amplitude is within a certain range. Within the range of convergence the frequency response function based on the Volterra series approaches the analytical one as more higher order frequency response function terms are included. Proposed is a criterion for the studies systems to predict approximately the range of sinewave input amplitude for which the series representation of the frequency response functions converges.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.867-872
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• 1999

In this paper we study the stability theorems for nonlinear Fredholm-Volterra integral equations system.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.553-556
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• 2000

This paper proposes an adaptive linearization method of Volterra nonlinear systems using DWT(Discrete Wavelet Transform)and an LMS-type predistorter. In particular, the proposed wavelet transform-domain lineatization method leads to diagonalization of the input vector auto-correlation matrix which yields improvement of the convergence rate of the corresponding transform-domain LMS algorithm. Furthermore, the adaptive Volterra predistorter followed by a corresponding weakly Volterra nonlinear system(here. a TWT amplifier model in a satellite communication system) is utilized to compensate for the distortion in the output. Also,12-PSK and 4-QAM are applied as the input to the nonlinear system to be tested. Some simulation results show that the proposed linearization approach has better performance than DCT-based or conventional normalized LMS algorithms do.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.12
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• pp.793-798
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• 2004

In this paper, the problem of adaptively identifying time-varying nonlinear systems is considered. For that purpose, the discrete time-varying Volterra series is employed as a system model, and the filtered weighted least squares (FWLS) algorithm, developed for adaptive identification of linear time-varying systems, is utilized for the adaptive identification of time-varying quadratic Volterra systems. To demonstrate the performance of the proposed approach, some simulation results are provided. Note that the FWLS algorithm, decomposing the conventional weighted basis function (WBF) algorithm into a cascade of two (i.e., estimation and filtering) procedures, leads to fast parameter tracking with low computational burden, and the proposed approach can be easily extended to the adaptive identification of time-varying higher-order Volterra systems.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.981-982
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• 2008

In this paper, Kalman-LMS algorithm is further extended to nonlinear system identification, whereby Kalman-LMSalgorithm and third-order Volterra filer are utilized.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.12
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• pp.1173-1177
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• 2015

This paper deals with estimating the acid concentration of pickling process using the Volterra inputs. To estimate the acid concentration, the whole pickling process is represented by the grey box model consists of the white box dealing with known system and the black box dealing with unknown system. Because there is a possibility of nonlinear term in the unknown system, the Volterra series are used to estimate the acid concentration. For the white box modeling, the acid tank solution level and concentration equations are used, and for the black box modeling, the acid concentration is estimated using the Volterra Least Mean Squares (LMS) algorithm and Least Squares (LS) algorithm. The LMS algorithm has the advantage of the simple structure and the low computation, and the LS algorithm has the advantage of lowest error. The simulation results compared to the measured data are included.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.131-145
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• 1991

The purpose of this paper is to prove the approximate controllability results, which were shown in [4] for the abstract semilinear control system, here, for the delay volterra system in the case of trajectories.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.7C
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• pp.627-634
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• 2007

When a higher-order modulation scheme (16QAM or 64QAM) is applied to the communications system using the nonlinear high power amplifier (HPA), the performance can be degraded by the nonlinear distortion of the HPA. The nonlinear distortion can be compensated by the adaptive nonlinear Volterra equalizer using the low-complexity LMS algorithm at the receiver. However, the LMS algorithm shows very slow convergence performance. So, in this paper, the parallel M-band discrete wavelet transformed LMS algorithm is proposed in order to improve the convergence speed. Throughout the computer simulations, it is shown that the convergence performance of the proposed method is superior to that of the conventional time-domain and transform-domain LMS algorithms.