• East Asian mathematical journal
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• v.26 no.5
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• 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 ...

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.853-862
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• 2014

In this paper, two approximate analytical methods have been applied to forced nonlinear vibration problems to assess a high accurate analytical solution. Variational Iteration Method (VIM) and Perturbation Method (PM) are proposed and their applications are presented. The main objective of this paper is to introduce an alternative method, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Some patterns are illustrated and compared with numerical solutions to show their accuracy. The results show the proposed methods are very efficient and simple and also very accurate for solving nonlinear vibration equations.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.349-360
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• 2014

In this study, three approximate analytical methods have been proposed to prepare an accurate analytical solution for nonlinear oscillators with fractional potential. The basic idea of the approaches and their applications to nonlinear discontinuous equations have been completely presented and discussed. Some patterns are also presented to show the accuracy of the methods. Comparisons between Energy Balance Method (EBM), Variational Iteration Method (VIM) and Hamiltonian Approach (HA) shows that the proposed approaches are very close together and could be easily extend to conservative nonlinear vibrations.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.271-274
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• 1995

This paper is concerned with the problem of robust stabilization of uncertain single-input and single-output nonlinear systems. Based on the input/output linearization approach for nonlinear state feedback synthesis in conjunction with Lyapunov methods, a stabilizing state feedback controller is proposed. Compared with the controllers reported in the control literature, instead of uniform ultimate boudedness, the controller proposed in this paper can guarantee uniform asymptotic stability of nonlinear systems in the presence of uncertainties. The required information about uncertain dynamics in the system is only that the uncertainties are bounded in Euclidean norm by known functions of the system state.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.171-178
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• 2017

Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.53-60
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• 2002

It has been recognized that damage control must become a more explicit design consideration. In an effort to develop design methods based on performance it is clear that the evaluation of the inelastic response is required. The methods available to the design engineer today are nonlinear time history analyses, or monotonic static nonlinear analyses, or equivalent static analyses with simulated inelastic influences. Some codes proposed the capacity spectrum method based on the nonlinear static(pushover) analysis to determine earthquake-induced demand given the structure pushover curve. This procedure is conceptually simple but iterative and time consuming with some errors. This paper presents a nonlinear direct spectrum method to evaluate seismic Performance of structure, without iterative computations, given the structural initial elastic period and yield strength from the pushover analysis, especially for multi degree of freedom structures. The purpose of this paper is to investigate accuracy and confidence of this method from a point of view of various earthquakes and unloading stiffness degradation parameters.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.12
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• pp.1748-1755
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• 2015

A linear regression is widely used for prediction problem, but it is hard to manage an irregular nature of nonlinear system. Although nonlinear regression methods have been adopted, most of them are only fit to low and limited structure problem with small number of independent variables. However, real-world problem, such as weather prediction required complex nonlinear regression with large number of variables. GP(Genetic Programming) based evolutionary nonlinear regression method is an efficient approach to attach the challenging problem. This paper introduces the improvement of an GP based nonlinear regression method using ADF(Automatically Defined Function). It is believed ADFs allow the evolution of modular solutions and, consequently, improve the performance of the GP technique. The suggested ADF based GP nonlinear regression methods are compared with UM, MLR, and previous GP method for 3 days prediction of wind speed using MOS(Model Output Statistics) for partial South Korean regions. The UM and KLAPS data of 2007-2009, 2011-2013 years are used for experimentation.

• Journal of Electrical Engineering and Technology
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• v.10 no.4
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• pp.1843-1850
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• 2015

Controlling nonlinear systems with linear feedback control methods can lead to chaotic behaviors. Order increase in system dynamics due to integral control and control parameter variations in PID controlled nonlinear systems are studied for possible chaos regions in the closed-loop system dynamics. The Lur’e form of the feedback systems are analyzed with Routh’s stability criterion and describing function analysis for chaos prediction. Several novel chaotic systems are generated from second-order nonlinear systems including the simplest continuous-time chaotic system. Analytical and numerical results are provided to verify the existence of the chaotic dynamics.

• 전기의세계
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• v.22 no.2
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• pp.40-44
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• 1973

A method for obtaining state equation for nonlinear time-varying RLC networks is presented. The nonlinear time-varying RLC elements are decomposed by using Murata method to formulate nonlinear state equation. A nonlinear time-varying RLC network containing twin tunnel diode is solved as an example. In consequence of solving the examjple, simple methods are presented for revising the original network model so that the formulation of state equation is simplified.