• Title, Summary, Keyword: Sensitivity Method

### 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.

### 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.

### 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.

### A Second-Order Design Sensitivity-Assisted Monte Carlo Simulation Method for Reliability Evaluation of the Electromagnetic Devices

• Ren, Ziyan;Koh, Chang-Seop
• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.780-786
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• 2013
• In the reliability-based design optimization of electromagnetic devices, the accurate and efficient reliability assessment method is very essential. The first-order sensitivity-assisted Monte Carlo Simulation is proposed in the former research. In order to improve its accuracy for wide application, in this paper, the second-order sensitivity analysis is presented by using the hybrid direct differentiation-adjoint variable method incorporated with the finite element method. By combining the second-order sensitivity with the Monte Carlo Simulation method, the second-order sensitivity-assisted Monte Carlo Simulation algorithm is proposed to implement reliability calculation. Through application to one superconductor magnetic energy storage system, its accuracy is validated by comparing calculation results with other methods.

### DESIGN SENSITIVITY ANALYSIS AND OPTIMIZATION OF ZWICKER'S LOUDNESS (Zwicker 라우드니스에 대한 설계 민감도 해석 및 최적화)

• Kang, Jung-Hwan;Wang, Se-Myung
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.149-154
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• 2004
• The design sensitivity analysis of Zwicker's loudness with respect to structural sizing design variables is developed. The loudness sensitivity in the critical band is composed of two equations, the derivative of main specific loudness with respect to 1/3-oct band level and global acoustic design sensitivities. The main specific loudness is calculated by using FEM, BEM tools. i.e. MSC/NASTRAN and SYSNOISE. And global acoustic sensitivity is calculated by combining acoustic and structural sensitivity using the chain rule. Structural sensitivity is obtained by using semi-analytical method and acoustic sensitivity is implemented numerically using the boundary element method. For sensitivity calculation, sensitivity analyzer of loudness (SOLO), in-house program is developed. A 1/4 scale car cavity model is optimized to show the effectiveness of the proposed method.

### Design Sensitivity Analysis for the Vibration Characteristic of Vehicle Structure (수송체 구조물의 진동특성에 관한 설계민감도 해석)

• 이재환
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.19-24
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• 1992
• Design sensitivity analysis method for the vibration of vehicle structure is developed using adjoint variable method. A variational approach with complex response method is used to derive sensitivity expression. To evaluate sensitivity, FEM analysis of ship deck and vehicle structure are performed using MSC/NASTRAN on the super computer CRAY2S, and sensitivity computation is carried on PC. The accuracy of sensitivity is verified by the results of finite difference method. When compared to structural analysis time on CRAY2S, sensitivity computation is remarkably economical. The sensitivity of vehicle frame can be used to reduce the vibration responses such as displacement and acceleration of vehicle.

### Sensitivity Analysis of Processing Parameters for the Laser Surface Hardening Treatment by Using the Finite Element Method (유한요소법을 이용한 레이저 표면경화처리 공정변수의 민감도 해석)

• 이세환;양영수
• Journal of Welding and Joining
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• v.19 no.2
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• pp.228-234
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• 2001
• A methodology is developed and used to evaluate the response sensitivity of the thermal systems to variations in their design parameters. Technique for computing the sensitivity of temperature distributions to changes in processing parameters needed to decide the more effective laser input parameters for laser surface hardening treatment is considered. In this study, a state equation governing the heat flow in laser surface treatment is analyzed using a three-dimensional finite element method and sensitivity data of the processing parameter obtained using a direct differentiation method is applied to the sensitivity analysis. The interesting processing parameters are taken as the laser scan velocity and laser beam radius ( $r_{ b}$), and the sensitivities of the temperature T versus v and $r_{b}$ are analyzed. These sensitivity results are obtained with another parameters fixed. To verify the numerical analysis results, hardened layer dimensions (width and depth) of the numerical analysis are compared with the experimental ones.nes.

### DEVELOPMENT OF CALCULATION METHOD OF SENSITIVITIES FOR LIGHT WATER REACTORS

• Takeda, Toshikazu;Foad, Basma
• Nuclear Engineering and Technology
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• v.45 no.6
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• pp.753-758
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• 2013
• A new method of calculating sensitivity coefficients of core characteristics relative to infinite-dilution cross sections has been developed. Conventional sensitivity coefficients are evaluated for the changes of effective cross sections which are dependent on individual models of core and cell. Therefore a correction has been derived to the conventional sensitivity coefficients based on the perturbation theory. The accuracy of the present method has been verified by comparing numerical results of sensitivity coefficients with a reference Monte-Carlo method.

### Sensitivity Analysis using FRF-based Substructuring Method (전달함수합성법을 이용한 민감도 해석)

• Lee, Doo-Ho;Hwang, Woo-Seok;Kim, Chan-Mook
• Proceedings of the KSME Conference
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• pp.602-606
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• 2000
• A general procedure for the design sensitivity analysis of structural dynamic problems has been presented in frame of the FRF-based substructuring formulation. In the procedure, the direct differentiation method is used for the sensitivity formula. For a system response function, the proposed method gives a parametric design sensitivity formula in terms of the partial derivatives of the connection element properties and the transfer matrix of the subsystems. The derived design sensitivity formula is applied to a numerical example. The comparison of sensitivities derived by the proposed method and the finite difference method shows that the proposed method is efficient and accurate.

### Adjoint Design Sensitivity Analysis of Damped Systems (보조변수법을 이용한 감쇠계 고유치 설계민감도 해석)

• Yoo, Jung-Hoon;Lee, Tae-Hee
• Proceedings of the KSME Conference
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• pp.398-401
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• 2001
• There are two methods to calculate design sensitivity such as direct differentiation method and adjoint method. A sort of direct differentiation method for design sensitivity analysis costs too much when number of design variables is much larger than the number of response functions whose design sensitivity analyses are required. Therefore, an adjoint method is suggested for the case that the dimension of design variables is lager than the number of response function. An adjoint method is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation, requiring only the eigenvalue and its associated eigenvectors for mode being differentiated. This method has been extended to the repeated eigenvalue problem. In this paper, we propose an adjoint method for deign sensitivity analysis of damped vibratory systems with distinct eigenvalues.