• Title, Summary, Keyword: sensitivity analysis

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

  • 박찬규;김우제;박순달
    • Journal of the Korean Operations Research and Management Science Society
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    • v.25 no.4
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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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    • v.10 no.2
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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.

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

  • Chung, Ho-Yeon;Park, Soon-Dal
    • IE interfaces
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    • v.7 no.3
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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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Development of Nonlinear Static Design Sensitivity Analysis Based ANSYS (ANSYS 비선형 정적설계민감도해석 외부모듈 개발)

  • Choi, Byung-Nam;Jung, Jae-Jun;Yoo, Jung-Hoon;Lee, Tae-Hee
    • Proceedings of the KSME Conference
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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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Augmented Displacement Load Method for Nonlinear Semi-analytical Design Sensitivity Analysis (준해석적 비선형 설계민감도를 위한 개선된 변위하중법)

  • Lee, Min-Uk;Yoo, Jung-Hun;Lee, Tae-Hee
    • Proceedings of the KSME Conference
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    • pp.492-497
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    • 2004
  • Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

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

  • 윤광수;이태희
    • Proceedings of the Korean Society of Precision Engineering Conference
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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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Exploring the Role of Sensitivity on Fashion Innovativeness (민감성이 패션 혁신성에 미치는 영향)

  • Park, Hye-Jung
    • The Research Journal of the Costume Culture
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    • v.15 no.6
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    • pp.1078-1083
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    • 2007
  • The purpose of this study is to identify the relationships among price sensitivity, brand sensitivity, and fashion innovativeness. The data used in this study were gathered through surveying university students residing in Seoul metropolitan area using convenience sampling method. One hundred thirty eight questionnaires were used in statistical analysis, confirmatory factor analysis and path analysis using structural equation modeling. The results showed that the higher the price sensitivity, the lower the fashion innovativeness and the brand sensitivity.

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

  • 정호연;박순달
    • Journal of the Korean Operations Research and Management Science Society
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    • v.20 no.1
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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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Displacement-Load Method for Semi-Analytical Design Sensitivity Analysis (준해석 설계민감도를 위한 변위하중법)

  • Yoo Jung Hun;Kim Heung Seok;Lee Tae Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.28 no.10
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    • pp.1590-1597
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    • 2004
  • Three methods of design sensitivity analysis for structures such as numerical method, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis can provide very exact result, it is difficult to implement into practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable fur most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate in nonlinear design sensitivity analysis because its computational cost depends on the number of design variables and large numerical errors can be included. Thus the semi-analytical method is more suitable for complicated design problems. Moreover, semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure fur the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and the computational technique is proposed for evaluating the partial differentiation of internal nodal force, so called pseudo-load. Numerical examples coupled with commercial finite element package are shown to verify usefulness of proposed semi-analytical sensitivity analysis procedure and computational technique for pseudo-load.

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

  • 배대성;조희제;백성호;이관섭;조연옥
    • Proceedings of the KSR Conference
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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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