• Title, Summary, Keyword: adjoint variable method

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Adjoint Variable Method combined with Complex Variable for Structural Design Sensitivity (보조변수법과 복소변수를 연동한 설계 민감도 해석 연구)

  • Kim, Hyun-Gi;Cho, Maeng-Hyo
    • Proceedings of the KSME Conference
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    • pp.418-423
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    • 2008
  • Among various sensitivity evaluation techniques, semi-analytical method is quite popular since this method is more advantageous than analytical method and global finite difference method. However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, the adjoint variable method combined with complex variable is proposed to obtain the shape and size sensitivity for structural optimization. The complex variable can present accurate results regardless of the perturbation size as well as easy to be implemented. Through a few numerical examples of the static problem for the structural sensitivity, the efficiency and reliability of the adjoint variable method combined with complex variable is demonstrated.

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Adjoint Variable Method Combined with Complex Variable for Structural Design Sensitivity (보조변수법과 복소변수를 연동한 설계 민감도 해석 연구)

  • Kim, Hyun-Gi;Cho, Maeng-Hyo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.3
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    • pp.243-250
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    • 2009
  • The adjoint variable method can reduce computation time and save computer resources because it can selectively provide the sensitivity information for the positions that designers wish to measure. However, the adjoint variable method commonly employs exact analytical differentiation with respect to the design variables. It can be cumbersome to precisely differentiate every given type of finite element. This trouble can be overcome only if the numerical differentiation scheme can replace this exact manner of differentiation. But, the numerical differentiation scheme causes of severe inaccuracy due to the perturbation size dilemma. For assuring the accurate sensitivity without any dependency of perturbation size, this paper employs a complex variable that has been mainly used for computational fluid dynamics problems. The adjoint variable method combined with complex variables is applied to obtain the shape and size sensitivity for structural optimization. Numerical examples demonstrate that the proposed method can predict stable sensitivity results and that its accuracy is remarkably superior to traditional sensitivity evaluation methods.

An Adjoint Variable Method for Eigenproblem Design Sensitivity Analysis of Damped Systems (감쇠계 고유치문제의 설계민감도해석을 위한 보조변수법)

  • Lee, Tae Hee;Lee, Jin Min;Yoo, Jung Hoon;Lee, Min Uk
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.11
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    • pp.1527-1533
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    • 2005
  • Three methods for design sensitivity analysis such as finite difference method(FDM), direct differentiation method(DDM) and adjoint variable method(AVM) are well known. FDM and DDM for design sensitivity analysis cost too much when the number of design variables is too large. An AVM is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation. Because the adjoint equation is independent of the number of design variables, an AVM is efficient for when number of design variables is too large. In this study, AVM has been extended to the eigenproblem of damped systems whose eigenvlaues and eigenvectors are complex numbers. Moreover, this method is implemented into a commercial finite element analysis program by means of the semi-analytical method to show applicability of the developed method into practical structural problems. The proposed_method is compared with FDM and verified its accuracy for analytical and practical cases.

Topology Design Optimization of Heat Conduction Problems using Adjoint Sensitivity Analysis Method

  • Kim, Min-Geun;Kim, Jae-Hyun;Cho, Seon-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.6
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    • pp.683-691
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    • 2010
  • In this paper, using an adjoint variable method, we develop a design sensitivity analysis(DSA) method applicable to heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume respectively. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with finite difference ones, requiring less than 0.25% of CPU time for the finite differencing. Also, the topology optimization yields physical meaningful results.

Simultaneous identification of damage in bridge under moving mass by Adjoint variable method

  • Mirzaee, Akbar;Abbasnia, Reza;Shayanfar, Mohsenali
    • Smart Structures and Systems
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    • v.21 no.4
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    • pp.449-467
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    • 2018
  • In this paper, a theoretical and numerical study on bridge simultaneous damage detection procedure for identifying both the system parameters and input excitation mass, are presented. This method is called 'Adjoint Variable Method' which is an iterative gradient-based model updating method based on the dynamic response sensitivity. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. Moving mass is a model which takes into account the inertia effects of the vehicle. This interaction model is a time varying system and proposed method is capable of detecting damage in this variable system. Robustness of proposed method is illustrated by correctly detection of the location and extension of predetermined single, multiple and random damages in all ranges of speed and mass ratio of moving vehicle. A comparison study of common sensitivity and proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. Various sources of errors including the effects of measurement noise and initial assumption error in stability of method are also discussed.

AERODYNAMIC SENSITIVITY ANALYSIS FOR NAVIER-STOKES EQUATIONS

  • Kim, Hyoung-Jin;Kim, Chongam;Rho, Oh-Hyun;Lee, Ki Dong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.3 no.2
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    • pp.161-171
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    • 1999
  • Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

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Design Sensitivity Analysis of Zwicker's Loudness Using Adjoint Variable Method (보조변수법을 이용한 Zwicker 라우드니스의 설계민감도)

  • Wang, Se-Myung;Kwon, Dae-Il;Kim, Chaw-Il
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.1432-1436
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    • 2006
  • Feasibility of optimizing Zwicker's loudness has been shown by using MSC/NASTRAN, SYSNOISE, and a semi-analytical design sensitivity by Wang and Kang. Design sensitivity analysis of Zwicker's loudness is developed by using ANSYS, COMET, and an adjoint variable method in order to reduce computation. A numerical example shows significant reduction of computation time for design sensitivity analysis.

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Analysis of Microwave Inverse Scattering Using the Broadband Electromagnetic waves (광대역 전자파를 이용한 역산란 해석 연구)

  • Lee, Jung-Hoon;Chung, Young-Seek
    • Proceedings of the Korea Electromagnetic Engineering Society Conference
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    • pp.169-174
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    • 2005
  • In this paper, we proposed a new algorithm of the inverse scattering for the reconstruction of unknown dielectric scatterers using the finite-difference time-domain method and the design sensitivity analysis. We introduced the design sensitivity analysis based on the gradient for the fast convergence of the reconstruction. By introducing the adjoint variable method for the efficient calculation, we derived the adjoint variable equation. As an optimal algorithm we used the steepest descent method and reconstructed the dielectric targets using the iterative estimation. To verify our algorithm we will show the numerical examples for the two-dimensional $TM^2$ cases.

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Development of An Optimal Design Program for Open-Chain Dynamic Systems (불구속연쇄 동적시스템을 위한 최적설계 프로그램 개발)

  • 최동훈;한창수;이동수;서문석
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.1
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    • pp.12-23
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    • 1994
  • This paper proposes an optimal design software for the open-chain dynamic systems whose governing equations are expressed as differential equation. In this software, an input module and an automatic creation module of the equation of motion are developed to contrive the user's convenience. To analyze the equation of motion of the dynamic systems, variable-order and variable-stepsize Adams-Bashforth-Moulton predictor-corrector method is used to improve the efficiency. For the optimization and the design sensitivity analysis, ALM(augmented lagrange multiplier)method and adjoint variable method are adopted respectively. An output module with which the user can compare and investigate the analysis and the optimization results through tables and graphs is also provided. The developed software is applied to three typical dynamic response optimization problems, and the results compare very well with those available in the literature, demonstrating its effectiveness.

Topology Design Optimization of Nonlinear Thermoelasticity Problems (비선형 열탄성 연성 구조물에 대한 위상 최적설계)

  • 문세준;하윤도;조선호
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.347-354
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    • 2004
  • Using an efficient adjoint variable method, we develop a unified design sensitivity analysis (DSA) method considering both steady state nonlinear heat conduction and geometrical nonlinear elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Beside the temperature and displacement adjoint equations, another coupled one is defined regarding the obtained adjoint displacement field as the adjoint load in temperature field. The developed DSA method is shown to be very efficient and further extended to a topology design optimization method for the nonlinear weakly coupled thermo-elasticity problems using a density approach.

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