• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.418-423
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• 2008

Among various sensitivity evaluation techniques, semi-analytical method is quite popular since this method is more advantageous than analytical method and global finite difference method. However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, the adjoint variable method combined with complex variable is proposed to obtain the shape and size sensitivity for structural optimization. The complex variable can present accurate results regardless of the perturbation size as well as easy to be implemented. Through a few numerical examples of the static problem for the structural sensitivity, the efficiency and reliability of the adjoint variable method combined with complex variable is demonstrated.

• 한국항공우주학회지
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• 제33권1호
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• pp.1-10
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• 2005

비정렬 격자계에서 continuous adjoint 방정식을 사용하여 제자리 비행을 하는 헬리콥터 로터 블레이드에 대한 공력 형상 최적설계 기법을 개발하였다. 효율적인 민감도 계산을 위해 회전좌표계에서 continuous adjoint 민감도 해석 기법을 유도하였다. 설계과정의 반복적인 수치계산의 효율을 높이기 위해서 영역 분할 기법에 기반을 둔 병렬처리 기법을 도입하였다. 끝단 와류의 정확한 포착을 위해서 끝단와류를 따른 격자적응을 수행하였다. 이러한 방법은 Caradonna와 Tung의 실험형상 및 UH60 헬리콥터 로터 블레이드의 공력 최적설계에 적용되었으며, 본 연구에서 사용된 최적설계 기법을 이용하면 일정한 추력을 유지하면서 요구동력을 현저하게 줄일 수 있음을 보였다.

• 대한기계학회논문집A
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• 제33권3호
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• pp.243-250
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• 2009

The adjoint variable method can reduce computation time and save computer resources because it can selectively provide the sensitivity information for the positions that designers wish to measure. However, the adjoint variable method commonly employs exact analytical differentiation with respect to the design variables. It can be cumbersome to precisely differentiate every given type of finite element. This trouble can be overcome only if the numerical differentiation scheme can replace this exact manner of differentiation. But, the numerical differentiation scheme causes of severe inaccuracy due to the perturbation size dilemma. For assuring the accurate sensitivity without any dependency of perturbation size, this paper employs a complex variable that has been mainly used for computational fluid dynamics problems. The adjoint variable method combined with complex variables is applied to obtain the shape and size sensitivity for structural optimization. Numerical examples demonstrate that the proposed method can predict stable sensitivity results and that its accuracy is remarkably superior to traditional sensitivity evaluation methods.

• 대한수학회지
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• 제31권3호
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• pp.477-492
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• 1994

For the eigenvalue problem of $Au = \lambda u$ where A is considered as a semi-bounded self-adjoint operator on a Hilbert space, we are used to apply two complentary methods finding upper bounds and lower bounds to the eigenvalues. The most popular method for finding upper bounds may be the Rayleigh-Ritz method which was developed in the 19th century while a method for computing lower bounds may be the method of intermediate eigenvalue problems which has been developed since 1950's. In the method of intermediate eigenvalue problems (IEP), we consider the original operator eigenvalue problem as a perturbation of a simpler, resolvable, self-adjoint eigenvalue problem, called a base problem, that gives rough lower bounds.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1999년도 추계학술발표회요약집
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• pp.67.2-67
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• 1999

• 한국전산구조공학회논문집
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• 제23권6호
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• pp.683-691
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• 2010

In this paper, using an adjoint variable method, we develop a design sensitivity analysis(DSA) method applicable to heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume respectively. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with finite difference ones, requiring less than 0.25% of CPU time for the finite differencing. Also, the topology optimization yields physical meaningful results.

• 대한수학회지
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• 제53권6호
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• pp.1371-1389
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• 2016

In this paper, we propose a new rank two quasi-Newton method based on adjoint Broyden updates for solving symmetric nonlinear equations, which can be seen as a class of adjoint BFGS method. The new rank two quasi-Newton update not only can guarantee that $B_{k+1}$ approximates Jacobian $F^{\prime}(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive deniteness and least change property with BFGS method. Under suitable conditions, the proposed method converges globally and superlinearly. Some preliminary numerical results are reported to show that the proposed method is effective and competitive.

• International Journal of Aeronautical and Space Sciences
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• 제18권4호
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• pp.601-613
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• 2017

An adjoint-based error estimation and mesh adaptation study is conducted for two-dimensional viscous flows on unstructured hybrid meshes. The error in an integral output functional of interest is estimated by a dot product of the residual vector and adjoint variable vector. Regions for the mesh to be adapted are selected based on the amount of local error at each nodal point. Triangular cells in the adaptive regions are refined by regular refinement, and quadrangular cells near viscous walls are bisected accordingly. The present procedure is applied to single-element airfoils such as the RAE2822 at a transonic regime and a diamond-shaped airfoil at a supersonic regime. Then the 30P30N multi-element airfoil at a low subsonic regime with a high incidence angle (${\alpha}=21deg.$) is analyzed. The same level of prediction accuracy for lift and drag is achieved with much less mesh points than the uniform mesh refinement approach. The detailed procedure of the adjoint-based mesh refinement for the multi-element airfoil case show that the basic flow features around the airfoil should be resolved so that the adjoint method can accurately estimate an output error.

• 전기학회논문지P
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• 제65권3호
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• pp.171-177
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• 2016

Noise problem that occurs in living environment is a big trouble in the economic, social and environmental aspects. In this paper, the filtered-X LMS algorithms, the adjoint LMS algorithms, and the robust adjoint LMS algorithms will be introduced for applications in active noise control(ANC). The filtered-X LMS algorithms is currently the most popular method for adapting a filter when the filter exits a transfer function in the error path. The adjoint LMS algorithms, that prefilter the error signals instead of divided reference signals in frequency band, is also used for adaptive filter algorithms to reduce the computational burden of multi-channel ANC systems such as the 3D space. To improve performance of the adjoint LMS ANC system, an off-line measured transfer function is connected parallel to the LMS filter. This parallel-fixed filter acts as a noise controller only when the LMS filter is abnormal condition. The superior performance of the proposed system was compared through simulation with the adjoint LMS ANC system when the adaptive filter is in normal and abnormal condition.

• 지구물리와물리탐사
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• 제10권2호
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• pp.111-123
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• 2007

본 논문에서는 파동장 외삽(wavefield extrapolation)의 방향을 단순히 역시간(reverse time)으로 하여 적용하는 기존의 역시간 구조보정법(reverse time migration method)이 아닌, 묵시적으로 가정된 순방향 모델링(forward modeling) 연산자에 대한 정확한 어드조인트(adjoint) 연산자로서의 역시간 구조보정 연산자를 유도한다. 어드조인트 연산자를 얻는 방법으로는 우선 해당하는 순방향 연산자를 명시적인 행렬식의 형태로 정의하고 이에 대한 전치행렬식을 구한 후, 이러한 전치행렬식에 해당하는 연산자를 정의하는 접근법을 사용하였다. 정확한 어드조인트 관계에 있는 역시간 구조보정 연산자는 기존의 역시간 구조보정 연산자와 마찬가지로 구조보정의 목적으로 사용될 수 있을 뿐 아니라, 최소자승 구조보정(Least-squares migration)과 같은 역산을 통해서 지하구조 영상화를 할 때 필요로 하는 어드조인트 연산자를 정확하게 구현 할 수 있어 보다 정확한 역산 결과를 얻게 해준다.