• Title/Summary/Keyword: Direct Differentiation Method

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Ride Sensitivity Analysis of a Train Model with Non-linear Suspension Elements (비선형 현가요소를 가진 철도차량의 승차감 민감도 해석)

  • Tak, Tae-oh;Kim, Myung-hun
    • Journal of Industrial Technology
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    • v.18
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    • pp.233-240
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    • 1998
  • In this study, ride sensitivity analysis of train with non-linear suspension elements is performed. Non-linear characteristics of springs and dampers for primary and secondary suspensions of a train is parameterized. Equation of motion of the train model is derived, and using the direct differentiation method, sensitivity equations are obtained. For a nominal ride quality performance index, sensitivity analysis with respect to various design parameters regarding non-linear suspension parameters is carried out.

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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.

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Design Sensitivity Analysis for the Optimal Shape Design of Three-Dimensional Magnetostatic Problems (3차원 정자계 문제의 형상 최적설계를 위한 설계 민감도 해석)

  • 고창섭;정현교;한송엽
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.41 no.8
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    • pp.850-857
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    • 1992
  • Design sensitivity analysis is proposed for the optimal shape design of three-dimensional magnetostatic problems. The direct differentiation method is introduced for design sensitivity analysis and the boundary element method with reduced magnetic scalar potential as the state variable is used to analyze the magnetic characteristics. In the direct differentiation method, the design sensitivity, defined as the total derivative of the objective function with respect to the design variables, is calculated based on the variation of the state variable with respect to the design variable. And the variation of the state variable is calculated by differetiating the both sides of the system matrix equation obtained by applying boundary element method. Through the numerical example with simple electromagnet, the usefulness is proved.

Design Sensitivity Analysis of Welded Strut Joints on Vehicle Chassis Frame (샤시 프레임에 용접한 스트러트 접합부의 설계 민감도 해석)

  • 김동우;양성모;김형우;배대성
    • Journal of Welding and Joining
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    • v.16 no.3
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    • pp.141-147
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    • 1998
  • Design sensitivity analysis of a vehicle system is an essential tool for design optimization and trade-off studies. Most optimization algorithms require the derivatives of cost and constraint function with respect to design in order to calculate the next improved design. This paper presents an efficient algorithm application for the design sensitivity analysis, using the direct differentiation method. A mounting area of suspension that welded on chassis frame is analyzed to show the validity and the efficiency of the proposed method. A mounting area of suspension that welded on chassis frame is analyzed to show the validity and the efficiency of the proposed method.

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Design Sensitivity Analysis for the Optimal Shape Design of Magnetostatic Problems (정자계 문제의 형상 최적 설계를 위한 설계 민감도 해석)

  • Koh, Chang-Seop;Hahn, Song-Yop;Jung, Hyun-Kyo
    • Proceedings of the KIEE Conference
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    • pp.567-569
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    • 1992
  • Design sensitivity analysis is proposed for the optimal shape design of three dimensional magnetostatic problems. The direct differentiation method is introduced for design sensitivity analysis and the boundary element method with reduced magnetic scalar potential as the state variable is used to analyze the magnetic characteristics. In the direct differentiation method, the design sensitivity, defined as the total derivative of the objective function with respect to the design variables, is calculated based on the variation of the state variable with respect to the design variable. And the variation of He state variable is calculated by differentiating the both sides of the system matrix equation obtained by applying boundary element method. Through the numerical example with simple electromagnet, the usefullness is proved.

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Ride Sensitivity Analysis of a Train With Non-linear Suspension Elements (비선형 현가요소를 가진 철도차량의 승차감 민감도 해석)

  • 전형호;탁태오
    • Journal of the Korean Society for Railway
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    • v.5 no.1
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    • pp.40-47
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    • 2002
  • In this study, and analytical method for ride sensitivity analysis of a train with non-linear suspension elements are proposed. Non-linear characteristics of springs and dampers for primary and secondary suspensions of a train are parameterized using polynomial interpolation. Vertical dynamic model of a three-body train running on straight rail with the predetermined roughness expressed in terms of spectral density function is set up and its equations of motion for ride analysis are derived. Using the direct differentiation method, sensitivity equations of the vertical dynamic model with respect to design parameters associated with non-linearity of suspensions are obtained. Based on the sensitivity analysis, improvement of ride is achieved by varying appropriate suspension parameters.

Direct Differentiation Method for Shape Design Sensitivity Analysis of Axisymmetric Elastic Solids by the BEM and Shape Optimization of Turbin Disc (경계요소법에 의한 축대칭 탄성체의 형상설계 민감도해석을 위한 직접미분법과 터빈 디스크의 형상최적설계)

  • Lee, Bu-Yun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.5
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    • pp.1458-1467
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    • 1996
  • A direct differentiationmethod is presented for the shape design sensitivity analysis of axisymmeetric elastic solids. Based on the exisymmetric boundary integralequaiton formulation, a new boundary ntegral equatio for sensitivity analysis is derived by taking meterial derivative to the same integral identity that was used in the adjoint variable melthod. Numerical implementation is performed to show the applicaiton of the theoretical formulation. For a simple example with analytic solution, the sensitivities by present method are compared with analytic sensitivities. As an application to the shape optimization, an optimal shape of a gas turbine disc toinimize the weight under stress constraints is found by incorporating the sensitivity analysis algorithm in an optimizatio program.

Dynamic Analysis of Multi-body Systems Considering Probabilistic Properties

  • Choi, Dong-Hwan;Lee, Se-Jeong;Yoo, Hong-Hee
    • Journal of Mechanical Science and Technology
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    • v.19 no.spc1
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    • pp.350-356
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    • 2005
  • A method of dynamic analysis of mechanical systems considering probabilistic properties is proposed in this paper. Probabilistic properties that result from manufacturing tolerances can be represented by means and standard deviations (or variances). The probabilistic characteristics of dynamic responses of constrained multi-body systems are obtained by two ways : the proposed analytical approach and the Monte Carlo simulation. The formerpaper, necessitates sensitivity information to calculate the standard deviations. In this a direct differentiation method is employed to find the sensitivities of constrained multi-body systems. To verify the accuracy of the proposed method, numerical examples are solved and the results obtained by using the proposed method are compared to those obtained by Monte Carlo simulation.

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.

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Design Sensitivity Analysis of Coupled Thermo-elasticity Problems

  • Choi Jae-yeon;Cho Seonho
    • Journal of Ship and Ocean Technology
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    • v.8 no.3
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    • pp.50-60
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    • 2004
  • In this paper, a continuum-based design sensitivity analysis (DSA) method is developed for the weakly coupled thermo-elasticity problems. The temperature and displacement fields are described in a common domain. Boundary value problems such as an equilibrium equation and a heat conduction equation in steady state are considered. The direct differentiation method of continuum-based DSA is employed to enhance the efficiency and accuracy of sensitivity computation. We derive design sensitivity expressions with respect to thermal conductivity in heat conduction problem and Young's modulus in equilibrium equation. The sensitivities are evaluated using the finite element method. The obtained analytical sensitivities are compared with the finite differencing to yield very accurate results. Extensive developments of this method are useful and applicable for the optimal design problems incorporating welding and thermal deformation problems.