• 제목/요약/키워드: Sensitivity analysis

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퇴화최적해에서 일반감도분석 (Generalized Sensitivity Analysis at a Degenerate Optimal Solution)

  • 박찬규;김우제;박순달
    • 한국경영과학회지
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    • 제25권4호
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    • pp.1-14
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    • 2000
  • The methods of sensitivity analysis for linear programming can be classified in two types: sensitivity analysis using an optimal solution, and sensitivity analysis using an approximate optimal solution. As the methods of sensitivity analysis using an optimal solution, there are three sensitivity analysis methods: sensitivity analysis using an optimal basis, positive sensitivity analysis, and optimal partition sensitivity analysis. Since they may provide different characteristic regions under degeneracy, it is not easy to understand and apply the results of the three methods. In this paper, we propose a generalized sensitivity analysis that can integrate the three existing methods of sensitivity analysis. When a right-hand side or a cost coefficient is perturbed, the generalized sensitivity analysis gives different characteristic regions according to the controlling index set that denotes the set of variables allowed to have positive values in optimal solutions to the perturbed problem. We show that the three existing sensitivity analysis methods are special cases of the generalized sensitivity analysis, and present some properties of the generalized sensitivity analysis.

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On the Relationship between $\varepsilon$-sensitivity Analysis and Sensitivity Analysis using an Optimal Basis

  • Park, Chan-Kyoo;Kim, Woo-Je;Park, Soondal
    • Management Science and Financial Engineering
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    • 제10권2호
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    • pp.103-118
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    • 2004
  • $\epsilon$-sensitivity analysis is a kind of methods for performing sensitivity analysis for linear programming. Its main advantage is that it can be directly applied for interior-point methods with a little computation. Although $\epsilon$-sensitivity analysis was proposed several years ago, there have been no studies on its relationship with other sensitivity analysis methods. In this paper, we discuss the relationship between $\epsilon$-sensitivity analysis and sensitivity analysis using an optimal basis. First. we present a property of $\epsilon$-sensitivity analysis, from which we derive a simplified formula for finding the characteristic region of $\epsilon$-sensitivity analysis. Next, using the simplified formula, we examine the relationship between $\epsilon$-sensitivity analysis and sensitivity analysis using optimal basis when an $\epsilon$-optimal solution is sufficiently close to an optimal extreme solution. We show that under primal nondegeneracy or dual non degeneracy of an optimal extreme solution, the characteristic region of $\epsilon$-sensitivity analysis converges to that of sensitivity analysis using an optimal basis. However, for the case of both primal and dual degeneracy, we present an example in which the characteristic region of $\epsilon$-sensitivity analysis is different from that of sensitivity analysis using an optimal basis.

최소비용문제의 퇴화 정점 최적해에 대한 감도분석 (Sensitivity Analysis on the Degenerate Tree Solution of the Minimum Cost Flow Problem)

  • 정호연;박순달
    • 산업공학
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    • 제7권3호
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    • pp.193-199
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    • 1994
  • The purpose of this paper is to develop a method of the sensitivity analysis that can be applicable to a degenerate tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1 is the well known method applicable to a spanning tree solution. However, this method have some difficulties in case of being applied to a degenerate tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds remaining at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient, we present a method that the sensitivity analysis of Type 2 is solved by using the method of a sensitivity analysis of Type 1. Besides we also show that the results of sensitivity analysis of Type 2 are union set of those of Type 1 sensitivity analysis. For the right-hand side constant or the capacity, we present a simple method for the sensitivity analysis of Type 2 which uses arcs with intermediate values.

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ANSYS 비선형 정적설계민감도해석 외부모듈 개발 (Development of Nonlinear Static Design Sensitivity Analysis Based ANSYS)

  • 최병남;정재준;유정훈;이태희
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2001년도 춘계학술대회논문집C
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    • pp.543-547
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    • 2001
  • CAE has been settled down to an indispensable tool for the simulation of a mechanical system according to the development of computer-aided analysis rapidly. Particularly finite element programs have advanced to the one of most valuable things in the filed of CAE due to the remarkable progress in the implementation. But since this analysis tool mostly provides the result of the analysis, it cannot satisfy designers who are seeking for information to improve their designs. Therefore, design sensitivity analysis or optimization module has been incorporated into commercial FEA programs to satisfy the desire of designers since 1990s. Design sensitivity analysis is to compute the rate of change of response with respected to design variable. Design sensitivity analysis is classfied into static design sensitivity analysis, Eigenvalue design sensitivity analysis and dynamic design sensitivity analysis. In this research, it will be presented to nonlinear static design sensitivity analysis formulation and nonlinear static design sensitivity analysis external module based ANSYS have been developed and illustrated an example to verify the developed module.

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최소비용문제의 비정점 최적해에 대한 감도분석 (Sensitivity Analysis on the Non-tree Solution of the Minimum Cost Flow Problem)

  • 정호연;박순달
    • 한국경영과학회지
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    • 제20권1호
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    • pp.1-10
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    • 1995
  • The purpose of this paper is to develop a method of the sensitivity analysis that can be applied to a non-tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1a is the well known method applicable to a tree solution. However this method can not be applied to a non-tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient we present a method that the sensitivity analysis of Type 2 is solved by finding the shortest path. Besides we also show that the results of Type 2 and Type 1 are the same in a spanning tree solution. For the right-hand side constant or the capacity, the sensitivity analysis of Type 2 is solved by a simple calculation using arcs with intermediate values.

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철도차량의 설계 민감도 해석을 위한 효율적인 알고리즘 개발 (An Efficient Algorithm for Design Sensitivity Analysis of railway Vehicle Systems)

  • 배대성;조희제;백성호;이관섭;조연옥
    • 한국철도학회:학술대회논문집
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    • 한국철도학회 1998년도 창립기념 춘계학술대회 논문집
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    • pp.299-306
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    • 1998
  • Design sensitivity analysis of a mechanical system is an essential tool for design optimization and trade-off studies. This paper presents an efficient algorithm for the design sensitivity analysis of railway vehicle systems, using the direct differentiation method. The cartesian coordinate is employed as the generalized coordinate. The governing equations of the design sensitivity analysis are formulated as the differential equations. Design sensitivity analysis of railway vehicle systems is performed to show the validity and efficiency of the proposed method.

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민감도 해석 및 구조 변경법을 이용한 차실 소음 저감 (Interior Noise Reduction Using Sensitivity Analysis and Structural Dynamic Modification)

  • 황우석
    • 소음진동
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    • 제9권6호
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    • pp.1145-1151
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    • 1999
  • Sensitivity analysis and structural modification technique are used to reduce the interior noise of a passenger car. The sensitivity analysis for the noise level at the rear seat shows that the stiffness change at the front lower member and the rear roof rail are sensitive. Using the structural modification method, we verified that the reinforcements at those members decrease the noise transfer function from the body to the rear seat. The combined application of the sensitivity analysis and structural modification method can decrease the noise level effectively.

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민감도 해석을 이용한 현가장치의 동역학적 최적설계 (Optimal Design of Vehicle Suspenion Systems Using Sensitivity Analysis)

  • 탁태오
    • 한국자동차공학회논문집
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    • 제2권3호
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    • pp.50-61
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    • 1994
  • A method for performing dynamic design sensitivity analysis of vehicle suspension systems which have three dimensional closed-loop kinematic structure is presented. A recursive form of equations of motion for a MacPherson suspension system is derived as basis for sensitivity analysis. By directly differentiating the equations of motion with respect to design variables, sensitivity equations are obtained. The direct generalize for the application of multibody dynamic sensitivity analysis. Based on the proposed sensitivity analysis, optimal design of a MacPherson suspension system is carried out taking unsprung mass, spring and damping coefficients as design variables.

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NASTRAN을 이용한 고유치 문제의 설계 민감도 해석 (Design Sensitivity Analysis of Eigen Problem Using NASTRAN)

  • 윤광수;이태희
    • 한국정밀공학회:학술대회논문집
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    • 한국정밀공학회 1997년도 춘계학술대회 논문집
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    • pp.508-512
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    • 1997
  • Design sensitivity analysis of Eigen Problem give systematic design improvement information for noise and vibration of a system. Based on reliable results form commercial FE code(UAI/NASTRAN), three computational procedures for design sensitivity analysis of eigen problem are suggested. Those methods are finite difference,design sensitivity analysis using external module and design sensitivity analysis running with NASTRAN. To verify the suggested methods, a numerical example is given and these results are compared with the results from UAI/NASTRAN eigen sensitivity option. We can conclude that design sensitivity coefficient of eigen proplems can be computed outside of the FE code as easy as inside of the FE code.

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누수성 프락탈 대수층내의 일정 또는 다단계 양수시험의 민감성 분석에 의한 수리상수 결정 (Hydraulic Parameter Evaluation by Sensitivity Analysis of Constant and Variable Rate Pump Test in Leaky Fractal Aquifer)

  • 함세영
    • 지질공학
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    • 제4권3호
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    • pp.311-319
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    • 1994
  • 본 논문은 누수를 포함하는 프락탈 대수층의 수리상수의 최적값을 구하기 위한 민감성 분석에 대한 것이다. 민감성 분석은 최소자승법을 이용한다. 민감성 분석에 의하여 수리상수(일반화 투수량계수와 일반화 저유계수)는 여러가지 흐름의 차원과 여러 값의 누수계수에 대해서 쉽게 결정될 수 있다. 아울러, 민감성, 분석은 다수의 양수정의 다단계 양수에도 적용되었다. 민감성 분석을 이용한 프락탈 대수층의 수리상수 산출을 위하여 컴퓨터 프로그램이 개발되었다.

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