• Structural Engineering and Mechanics
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• 제44권5호
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• pp.585-600
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• 2012

This paper presents a Modified Tikhonov Regularization (MTR) method in model updating for damage identification with model errors and measurement noise influences consideration. The identification equation based on sensitivity approach from the dynamic responses is ill-conditioned and is usually solved with regularization method. When the structural system contains model errors and measurement noise, the identified results from Tikhonov Regularization (TR) method often diverge after several iterations. In the MTR method, new side conditions with limits on the identification of physical parameters allow for the presence of model errors and ensure the physical meanings of the identified parameters. Chebyshev polynomial is applied to approximate the acceleration response for moderation of measurement noise. The identified physical parameter can converge to a relative correct direction. A three-dimensional unsymmetrical frame structure with different scenarios is studied to illustrate the proposed method. Results revealed show that the proposed method has superior performance than TR Method when there are both model errors and measurement noise in the structure system.

• Coupled systems mechanics
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• 제1권4호
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• 대한수학회지
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• 제52권5호
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• pp.1069-1096
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• 2015

In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

• Structural Engineering and Mechanics
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• 제64권2호
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• pp.271-278
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• 2017

In this paper, we propose a new conjugate gradient method which possesses the global convergence and apply it to solve inverse problems of the dynamic loads identification. Moreover, we strictly prove the stability and convergence of the proposed method. Two engineering numerical examples are presented to demonstrate the effectiveness and speediness of the present method which is superior to the Landweber iteration method. The results of numerical simulations indicate that the proposed method is stable and effective in solving the multi-source dynamic loads identification problems of practical engineering.

• 대한수학회지
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• 제57권4호
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• pp.915-933
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• 2020

A two-level finite element method based on the Newton iterative method is proposed for solving the Navier-Stokes/Darcy model. The algorithm solves a nonlinear system on a coarse mesh H and two linearized problems of different loads on a fine mesh h = O(H^4-𝜖). Compared with the common two-grid finite element methods for the considered problem, the presented two-level method allows for larger scaling between the coarse and fine meshes. Moreover, we prove the stability and convergence of the considered two-level method. Finally, we provide numerical experiment to exhibit the effectiveness of the presented method.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1998년도 춘계학술발표회논문집(1)
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• pp.87-92
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• 1998

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface noes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AEFEN method and the computing time is significantly reduced in comparison with the original AFEN method.

• Nuclear Engineering and Technology
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• 제51권4호
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• pp.954-962
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• 2019

It is well known that the variance of tally is biased in a Monte Carlo calculation based on the power iteration method. Several studies have been conducted to estimate the real variance. Among them, the batch method, which was proposed by Gelbard and Prael, has been utilized actively in many Monte Carlo codes because the method is straightforward, and it is easy to implement the method in the codes. However, there is a problem when utilizing the batch method because the estimated variance varies depending on batch size. Often, the appropriate batch size is not realized before the completion of several Monte Carlo calculations. This study recognizes this shortcoming and addresses it by permitting selection of an appropriate batch size.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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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.

• 한국지진공학회논문집
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• 제1권1호
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• pp.1-10
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• 1997

최근의 철근 콘크리트 구조물의 내진 설계 방식은 비탄성 거대 변형에 의한 에너지 방출에 의존하고 있다. 이러한 구조물의 거동에 대한 비선형 동적 해석은 특히 계산이 여러 번 반복되어 질 때 많은 시간과 비용이 요구된다. 그러므로 효율적이고 한편 정확한 계산 방법의 채택이 중요하게 되었다. 예측 접근 방법(PASM) 이라 불리는 새로운 방법을 제시하는 것이 현 연구의 주목적이다. 일반적인 동적 해석 방법에서는 매 시간 단계 혹은 반복 계산 때마다 수식계산을 위하여 메트릭스 삼각 분해가 요구되어지나, 예측 접근방법에서는 구조물이 정적 반복하중으로 비선형 범위로 변형되어졌을 때의 강성 상태에서 미리 얻어진 한정적 수의 분해된 메트릭스를 동적 해석에서 이용하게 된다. 이곳에서 제시될 접근 방법은 강성치를 매 시각 단계 혹은 반복 계산 단계마다 재산출해야 하는 다른 접근 방법들과 비교할 때 전체적 수치 해석 양을 줄이게 될 것이다.

• 대한원격탐사학회지
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• 제30권6호
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• pp.817-827
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• 2014

위성 원격 탐사에서는 센서 운영 환경으로 인하여 영상을 수집하는 동안 영상의 질 저하가 일어나며 이러한 영상의 질 저하는 관측된 자료로부터 유용한 정보를 확인하거나 추출하는 데 악 영향을 미치는 번짐 현상(blurring)과 잡음 (noise)을 야기시킨다. 본 연구는 원격 탐사 영상 자료의 질 저하 현상을 모형화하기 위해 Gaussian 가산 잡음과 Markov random field로 정의되는 공간적 연결성을 가정하였다. 그리고 질 저하된 관측 자료로부터 원래 강도의 영상을 복원하기 위한 Point-Jacobian 반복 maximum a posteriori (MAP) 추정 법을 제안한다. 제안 연구는 이웃 창의 형태로 8 개 방향의 창으로 구성된 방사형을 사용하며 각 방향에서의 중심 화소와의 이웃 화소들 간의 Mahalanobis 제곱 거리를 경계 근접성 측정치로 사용한다. 제안 방법의 성능을 평가하기 위해서 고해상도 영상 자료에 나타날 수 있는 다양한 형태의 패턴을 사용하는 simulation 자료를 생성하여 화소 단위 분류 법을 사용하여 정량적 평가를 수행하였고 한반도 안양 북부 지역에서 관측된 1 m 급 IKONOS 자료의 무감독 분할을 통해 정성적 평가를 수행하였다. 실험 결과는 고해상도 원격 탐사 자료 분석에서 제안 영상 복원 법을 적용하면 현저히 분석의 정확성을 높이는 것을 보여 준다.