• 한국산학기술학회논문지
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• 제13권10호
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• pp.4411-4417
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• 2012

본 연구에서는 축소모델을 기반으로 비행체 날개를 최적화하는 기법을 제안한다. 잘 구축된 축소모델은 고유치 문제나 동적 해석 시 정확한 해석결과를 제공하며, 최적화 과정에서 필요한 민감도 계산에서도 정확한 결과를 제공할 수 있다. 이러한 축소모델은 모드기반으로 구축되는 축소차수모델(Reduce Order Model)과 자유도기반으로 구축되는 축소시스템(Reduced System)으로 구분되는데, 본 연구에서 사용하는 자유도 기반 축소시스템은 구조물의 거동에 지배적인 자유도를 적절히 선정하는 것이 중요하므로, 이를 위하여 기존 연구에서 신뢰성이 검증된 2단계 축소방법을 사용하였고, IRS(Improved Reduced System)에 의해 최종시스템을 구축하였다. 수치예제에서 최적화 과정에서 계산되는 등가응력, 고유치 및 설계민감도는 모두 축소시스템 기반으로 구해지며, 축소시스템을 통해 구속조건을 잘 만족하면서 목적함수에 대한 최적 결과를 얻을 수 있음을 보인다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.453-458
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• 2004

This study proposes a new two-level condensation scheme for the construction of a reduced system. In the first step, the candidate area is selected for the construction of the reduced system by energy estimation in element-level. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements. Numerical examples demonstrate that the proposed method saves the computational cost effectively and provides a reduced system which predicts the eigenvalues accurately. Moreover, the well-constructed reduced system can present the reliable behavior of the structure under arbitrary dynamic loads comparing to that of global system. Time integration in a reduced system can save the computing time remarkably. Through a few numerical examples, the efficiency and reliability of the proposed scheme are verified.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• 한국전산구조공학회논문집
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• 제21권5호
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• pp.439-450
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• 2008

잘 구축된 축소시스템은 동하중을 받는 구조물의 거동을 정확하게 계산할 수 있으며, 유한요소 기반 동적해석에서 문제가 될 수 있는 계산시간과 전산자원의 문제를 해결할 수 있다. 본 연구에서는 축소모델 기반 동적해석 알고리즘을 개발하였고, 동적 축소모델의 구축을 위한 주자유도 선정방법을 제안하였다. 이 과정에서 기존 연구에서 신뢰성이 검증된 2단계 축소기법을 사용하여 중요 자유도를 선정하고, IRS 방법에 의해 최종 축소모델을 구축하였다. 이를 임의의 동하중을 받는 수치예제에 적용하고 전체시스템의 동적해석 결과와 비교하여 제안 방법의 신뢰성을 검증하였다.

• 대한기계학회논문집A
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• 제30권9호
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• pp.1070-1077
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• 2006

In the present study, sizing and shape optimizations are performed based on the reduced system of large-scaled problem. In the analysis part to achieve efficiency and reliability of computation, two-level condensation scheme is applied. In the construction of reduced system of large scaled problems, it is much more efficient to use sub-domain method. Thus, in the present paper, two-level reduction method combined with sub-domain method is employed. Once the reduced system is constructed, it is straightforward to obtain design sensitivities from the analysis results of the reduced system We use semi-analytic method to obtain design sensitivities. Performance of the efficiency and reliability of the present reduction method in the structural optimization problem is demonstrated through the numerical examples. The present framework of reduction method should serve as a fast and reliable design tool in analysis and design of large-scaled dynamic problems.

• 전자공학회논문지S
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• 제34S권9호
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• pp.50-59
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• 1997

This paper is on the generalized singular perturbation approximation (GSPA) preserving the discrete positive real property. We transform the discrete positive real(PR) system into a stochastically banlanced system and get the reduced order discrete system from the GSPA of the full order stochastically balanced system. eSPECIALLY, WHEN THE FREE PARAMETER OF THE gspa IS .+-.1, we show that the reduced order discrete system retains stability, minimality, and positive real and stochstically balancing properties. And we derived the .inf.-norm error bound with the reduced order discrete strictly positive real(SPR) system by the proposed method. Finally, we give an example to ascertain the properties of the proposed reduced order discrete system and to compare with the conventional methods.

• 대한전기학회논문지:시스템및제어부문D
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• 제53권9호
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• pp.630-637
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• 2004

In this paper, we present a local reduced-order observer for a class of nonlinear systems that have full robust relative degree. The proposed observer utilizes the coordinate change which transforms a nonlinear system into an approximate normal form. The proposed reduce order observer is applied to a ball and beam system, and simulation results show that substantial improvement in the performance was achieved compared with the jacobian linearization observers.

• 대한기계학회논문집A
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• 제30권9호
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• pp.1062-1069
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• 2006

Reduction schemes approximate the lower eigenvalues that represent the global behavior of the structures. But, they are not efficient to be applied to large-scaled problems because these schemes require considerable amount of computing time in constructing reduced one from the original large-scaled systems. In addition, the selection of the primary degrees of freedom might be localized to cause the excessive emphasis of the lower mode or lost of the important modes. In the present study, a new reduction method combined with the subdomain method is proposed. For the construction of the final reduced system the system of each domain subdivided into primary, slave and interface degrees of freedom. It is remarkably efficient and accurate comparable to full-scale system. Numerical examples demonstrate that the proposed method saves computational cost effectively and provides a reduced system which predicts accurate eigen-pairs of global system.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.631-636
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• 2007

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the, we proposed a two-level condensation scheme(TLCS) for the construction of a reduced system. In first step, the of candidate elements by energy estimation, Rayleigh quotient, through Ritz vector calculation, and next, the primary degrees of freedom is selected by sequential elimination from the degrees of freedom connected the candidate elements in the first step. In the present study, we propose TLCS combined with iterative improved reduced system(IIRS) to increase accuracy of higher modes intermediate range. Also, it possible to control the accuracy of the eigenvalues and eigenmodes of the reduced system. Numerical examples demonstrate performance of proposed method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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• pp.19-26
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• 2004

This study constructs the reduced system by two-level condensation scheme. This scheme consists of two steps. First step selects the candidate area for the primary degrees of freedom by energy estimation in element level. In the second step, the primary degrees of freedom are selected by the sequential elimination scheme. The efficiency and reliability of this scheme is shown through the prediction of eigenvalues of a few numerical examples. Time integration in the reduced system can save the computing time effectively. The well-constructed reduced system can present the accurate behavior of the structure under arbitrary dynamic loads so much as the global system. Through the numerical example, the efficiency and reliability of the proposed scheme will be demonstrated.