• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2006.06a
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• pp.67-72
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• 2006

적응신호처리 분야에서 LMS(Least Mean Square) 알고리즘은 수식이 간단하고, 적은 계산 량으로 인해 널리 사용되고 있지만, 시간영역의 적응알고리즘은 입력신호의 고유치 분포 폭이 넓게 분포할 때는 수렴속도가 느려지는 단점이 있다. 본 논문에서는 적응 신호처리의 수렴속도를 향상 시키고 복잡한 계산 량을 줄이는 새로운 fast running FIR 필터 구조를 제안한다. 그리고 제안한 알고리즘을 가변스텝 사이즈 웨이블렛 기반 적응 알고리즘에 적용한다. 실제로 합성 음성을 사용하여 적응 잡음 제거기에 적용하여 컴퓨터 시뮬레이션을 통해 제안한 알고리즘과 기존 알고리즘과의 성능을 비교한다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.359-369
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• 1999

The paper describes the study of concurrent subspace optimization(CSSO) for coupled multidisciplinary design optimization (MDO) techniques in mechanical systems. This method is a solution to large scale coupled multidisciplinary system, wherein the original problem is decomposed into a set of smaller, more tractable subproblems. Key elements in CSSO are consisted of global sensitivity equation(GSE), subspace optimization (SSO), optimum sensitivity analysis(OSA), and coordination optimization problem(COP) so as to inquiry valanced design solutions finally, Automatic differentiation has an ability to provide a robust sensitivity solution, and have shown the numerical numerical effectiveness over finite difference schemes wherein the perturbed step size in design variable is required. The present paper will develop the automatic differentiation based concurrent subspace optimization(AD-CSSO) in MDO. An automatic differentiation tool in FORTRAN(ADIFOR) will be employed to evaluate sensitivities. The use of exact function derivatives in GSE, OSA and COP makes Possible to enhance the numerical accuracy during the iterative design process. The paper discusses how much influence on final optimal design compared with traditional all-in-one approach, finite difference based CSSO and AD-CSSO applying coupled design variables.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.183-184
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• 2007

As the mobile communication service is widely used, the demand for wireless repeaters is rapidly increasing because of the easiness of extending service areas. But wireless repeaters has a problem that the output of the transmit antenna is partially fed back to the receive antenna, which results in feedback interference. In this paper, we investigate the performance of adaptive variable step-size NLMS-based algorithms for cancelling the interference signals in the W-CDMA system under time-varying multipath channels. The criteria for comparison are tracking capability, convergence speed, and complexity.

• Proceedings of the KIEE Conference
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• 2009.04b
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• pp.263-265
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• 2009

In order to improve the output efficiency of the PV system, we adopt maximum power point tracking(MPPT) techniques. This paper analyzes a two-mode MPPT method based on the variable step size incremental conductance method and constant voltage MPPT method. Compared with the conventional MPPT method, the proposed method can effectively improve the MPPT speed and maximize the efficiency with the irradiation and temperature changing. In this paper, a theoretical analysis is provided and feasibility of this method is proved by simulation.

• Journal of Korean Society of Water and Wastewater
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• v.13 no.3
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• pp.42-55
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• 1999

A mathematical model for biological nutrient removal in a sequencing batch reactor process, which is based on the IAWQ Activated Sludge Model No. 2 with a few modifications, has been developed. Twenty water quality components and twenty three kinetic equations are incorporated in the model. The model is structured in the matrix form based on the law of mass conservation using stoichiometry and kinetic equations. Stoichiometric coefficients and kinetic parameters included in the model equations are chosen from the literature. A multistep predictor-corrector algorithm of variable step-size is adopted for solving the vector nonlinear ordinary differential equations. The simulation for experimental results is conducted to evaluate the validity of the model and to calibrate coefficients and parameters. The simulation using the model well represents the experimental results from laboratory. The mathematical model developed in this study may be utilized for the design and operation of a sequencing batch reactor process under the steady and unsteady-state at various environmental conditions.

• Proceedings of the Korea Multimedia Society Conference
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• 2004.05a
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• pp.179-182
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• 2004

무선통신분야에서 LMS5(Least Mean Square) 알고리즘은 식이 간단하고 계산량이 비교적 적기 때문에 널리 사용되고 있다. 그러나 시간영역에서 처리할 경우 입력신호의 고유치 변동폭이 넓게 분포되어 수렴속도가 저하하는 문제점이 있다. 이를 해결하기 위하여 신호를 FFT(Fast Fourier Trasnform)나 DCT(Discrete Cosine Transform)로 변환하여 신호간의 상관도를 제거함으로써 시간영역에서 LMS알고리즘을 적용할 때 보다 수렴속도를 크게 향강시킬 수 있다. 본 논문에서는 수렴속도 향상을 위해 시간영역의 적응 알고리즘을 직교변환인 고속웨이브렛(wavelet)변환을 이용하여 변환영역에서 수행하며, 짧은 필터계수를 가지는 DWT(Discrete Wavelet Transform)특성에 맞는 Fast running FIR 알고리즘을 이용하여 WTLMS(Wavelet Transform LMS)적응알고리즘을 통신시스템에 적용한다. 적응 알고리즘의 성능향상을 위하여 시간에 따라 적응상수의 크기를 가변시켜 수렴 초기에는 큰 적응상수로 따른 수렴이 가능하도록 하고 점차 적응상수의 크기를 줄여서 misadjustment도 줄이는 방법의 적응 알고리즘을 제안하였다. 제안한 알고리즘을 실제로 적응잡음제거기(adaptive noise canceler)에 적용하여 컴퓨터 시뮬레이션을 하였으며, 각 알고리즘들의 계산량, 수렴속도를 이용하여 각각 비교, 분서하여 그 성능이 우수함을 입증하였다.

• Proceedings of the KIPE Conference
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• 2019.07a
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• pp.455-456
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• 2019

본 논문은 태양광 발전시스템에서 일사량이 급변했을 때 최대 전력점(MPP: Maximum Power Point)을 빠르게 추종할 수 있는 P&O(Perturb and Observe)기반 가변 스텝 알고리즘을 제안하였다. 제안한 기법은 일사량 또는 온도에 의해 환경 변화 시 최대 전력점에서의 전압 변화 특성을 이용하며, 가변 스텝 방식이 적용된 전압제어를 통해 MPP를 추종한다. 임계값 설정으로 일사량 급변을 판단하며, MPP를 빠르게 추종하기 위한 고속 모드로 동작한다. MPP에 도달하면 가변 모드로 전환하여 정상상태 오차를 최소화 한다. PV 시뮬레이터와 태양광 전력변환시스템을 통해 제안한 MPPT 알고리즘의 성능을 검증하였다.

• Proceedings of the KIPE Conference
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• 2018.11a
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• pp.24-26
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• 2018

본 논문은 일사량 변화 시, 최대 출력점을 추종하는 태양광 발전시스템의 동적 응답특성을 향상시키기 위해 가변 스텝 사이즈 기반의 P&O (perturb & observe) 알고리즘을 제안하였다. 제안된 기법은 일사량과 PV (photovoltaic) 전류 관계로부터 일사량 변화에 따른 최대 전력점 전류 $I_{MPP}$변화 특성을 이용하며, 새로운 I-V 곡선에서 PV 동작점을 최대 출력점으로 빠르게 이동시키는 고속모드와 정상상태 부근에서 정상상태 효율 향상을 위한 가변 스텝 모드로 구성된다. 시뮬레이션 및 실험을 통해 $500W/m^2$와 $1000W/m^2$ 일사량 증감 조건에서 제안된 MPPT(maximum power point tracking) 기법의 추종 성능을 검증하였으며, MPPT 주기가 2초이고 일사량 $500W/m^2$과 $1000W/m^2$ 증감을 할 때 추종시간은 약 30초 정도이며, 정상상태 PV 전압변동은 약 0.1V로써 일사량 변화 조건에서 제안된 MPPT 기법의 알고리즘 성능을 검증하였다.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.347-371
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• 2021

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.