• 대한수학회지
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• 제57권5호
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• pp.1079-1101
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• 2020

This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a levelset curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.391-396
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady state heat conduction problems. The only inside of complicated domain is identified by the level set functions and taken into account in computation. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. The nucleation of holes is possible whenever and wherever necessary during the optimization using a topological derivative concept.

• 한국구조물진단유지관리공학회 논문집
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• 제12권6호
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• pp.241-248
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• 2008

민감도 해석은 구조 모델링 변수의 변화에 따른 역학적인 거동의 특성을 찾는 것을 목적으로 한다. 따라서 건물의 구조 진단과 보수 보강 분야에서 특히 중요한 설계 자료로서 활용되고 있다. 본 연구는 구조물의 위상학적 최적 모델링에서 중요하게 다루어지는 민감도 해석을 다양한 방법을 사용하여 공식화하였다. 감차법과 변분법을 적용하여 직접법과 수반법으로서 최종적인 해석적인 민감도 식들을 유도하였다. 구조 해석에 관한 간단한 수치예제를 통하여 유도된 민감도 식들의 해가 적절함을 수치적인 민감도 해석치와 비교하여 검증하였고, 최종적으로 이산화 민감도 해석에 의한 밀도분배법의 위상학적 최적 모델링을 수행하여 민감도 공식들을 위상 최적화 문제에서 정식화하였다.

• 농촌계획
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• 제7권1호
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• pp.37-48
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• 2001

The purpose of this study is to suggest the landscape potential index for visualizing landscape information in the conservation of hilly landscape in urban fringe. For the visual and quantitative approach to topological landscape assessment, numerical entity data of DEM(digital elevation model) were processed with CAD-based utilities that we developed and were mainly focused on analysis of visibility and visual sensitivity. Some results, with reference in assessing greenbelt area of Eodeung Mt. in Gwangju, proved to be considerable in the landscape assessment of suburban hilly landscapes. 1) Since the viewpoints and viewpoint fields were critical to landscape structure, randomized 194 points(spatially 500m interval) were applied to assessing the generalized visual sensitivity, we called. Because there were similar patterns of distribution comparing to those by 56 points and 18 Points given appropriately, it could be more efficient by a few viewpoints which located widely. 2) Regressional function was derived to represent the relationships between probabilities of visibility frequency and the topological factors(topological dominance, landform complexity and relational aspect) of target field. 3) Visibility scores of each viewpoint were be calculated by summing the visual sensitivity indices within a scene. The scores to the upper part including ridge line have been more representative to overall distributions of visual sensitivities. Also, with sum of deviations of sensitivity indices from each single point's specific index to the weighting values of view points could be estimated rotationally. 4) The deviational distributions of visual sensitivity classes in the topological unit of target field were proved to represent the visual vulnerability of the landform. 5) Landscape potential indices combined with the visual sensitivity and the DGN(degree of green naturality) were proposed as visualized landscape information distributed by topological unit.

• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1102-1108
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• 2002

In this study, a topological design sensitivity of the ai. bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.

• 한국전산구조공학회논문집
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• 제21권3호
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• pp.239-245
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• 2008

확장 B-스플라인 기저함수(extended B-spline basis functions)을 이용한 레벨셋 기반의 위상 형상 최적설계 기법을 정상 상태의 열전도 문제에 대하여 개발하였다. 본 해석법은 레벨셋으로 결정된 영역 안쪽만 고려하여 해석을 수행하게 되므로 열전달 문제에서 생길 수 있는 영역 바깥부분 영향을 제거할 수 있다. 설계민감도 해석으로부터 결정되는 법선속도를 활용하여 헤밀턴-자코비 방정식의 해를 구하게 되며, 주어진 체적조건 하에서 열 컴플라이언스(thermal compliance)가 최소가 되는 방향으로 최적의 형상을 결정할 수 있다. 형상 설계민감도를 정확하게 얻기 위해서는 레벨셋 함수와 B-스플라인 함수를 이용하여 수직 단위 벡터와 형상의 곡률을 정확히 결정하며, 위상 설계민감도를 통해 최적화과정 동안 필요한 위치와 시점에서 위상의 변화를 주는 홀을 쉽게 생성할 수 있다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.299-306
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• 2006

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The 'Hamilton-Jacobi (H-J)' equation and computationally robust numerical technique of 'up-wind scheme' lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H -J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes is not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• 전기학회논문지
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• 제58권10호
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• pp.1936-1941
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• 2009

This paper deals with a new methodology for topology optimization in which the topology of the design domain may change during the shape optimization process. To achieve this, the concept of the topological gradient is introduced to compute the sensitivity of an objective function when a small hole is drilled in the domain. Based on shape and topological sensitivity values, the shape and topology of the design domain may be simultaneously changed during design iterations if necessary. To verify the advantages and also to facilitate understanding of the method itself, two electrostatic design problems have been tested by using 2D finite element analysis: the first is the inverse problem of a simple dielectric model and the second is the rotor design of a MEMS actuator.

• 한국데이타베이스학회:학술대회논문집
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• 한국데이타베이스학회 1999년도 춘계공동학술대회: 지식경영과 지식공학
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• pp.281-287
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• 1999

Decision class analysis (DCA) is viewed as a classification problem where a set of input data (situation-specific knowledge) and output data (a topological leveled influence diagram (ID)) is given. Situation-specific knowledge is usually given from a decision maker (DM) with the help of domain expert(s). But it is not easy for the DM to know the situation-specific knowledge of decision problem exactly. This paper presents a methodology fur sensitivity analysis of DCA under incomplete information. The purpose of sensitivity analysis in DCA is to identify the effects of incomplete situation-specific frames whose uncertainty affects the importance of each variable in the resulting model. For such a purpose, our suggested methodology consists of two procedures: generative procedure and adaptive procedure. An interactive procedure is also suggested based the sensitivity analysis to build a well-formed ID. These procedures are formally explained and illustrated with a raw material purchasing problem.

• 한국지능정보시스템학회:학술대회논문집
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• 한국지능정보시스템학회 1999년도 춘계공동학술대회-지식경영과 지식공학
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• pp.281-287
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• 1999

Decision class analysis (DCA) is viewed as a classification problem where a set of input data (situation-specific knowledge) and output data(a topological leveled influence diagram (ID)) is given. Situation-specific knowledge is usually given from a decision maker (DM) with the help of domain expert(s). But it is not easy for the DM to know the situation-specific knowledge of decision problem exactly. This paper presents a methodology for sensitivity analysis of DCA under incomplete information. The purpose of sensitivity analysis in DCA is to identify the effects of incomplete situation-specific frames whose uncertainty affects the importance of each variable in the resulting model. For such a purpose, our suggested methodology consists of two procedures: generative procedure and adaptive procedure. An interactive procedure is also suggested based the sensitivity analysis to build a well-formed ID. These procedures are formally explained and illustrated with a raw material purchasing problem.