• 제목/요약/키워드: Adjoint sensitivity analysis

검색결과 99건 처리시간 0.024초

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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    • 제3권2호
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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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보조변수법을 이용한 감쇠계 고유치 설계민감도 해석 (Adjoint Design Sensitivity Analysis of Damped Systems)

  • 유정훈;이태희
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2001년도 춘계학술대회논문집C
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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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보조변수법을 이용한 Zwicker 라우드니스의 설계민감도 (Design Sensitivity Analysis of Zwicker's Loudness Using Adjoint Variable Method)

  • 왕세명;권대일;김좌일
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2006년도 춘계학술대회논문집
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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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Topology Design Optimization of Heat Conduction Problems using Adjoint Sensitivity Analysis Method

  • Kim, Min-Geun;Kim, Jae-Hyun;Cho, Seon-Ho
    • 한국전산구조공학회논문집
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    • 제23권6호
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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.

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

  • 이태희;이진민;유정훈;이민욱
    • 대한기계학회논문집A
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    • 제29권11호
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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.

A New Material Sensitivity Analysis for Electromagnetic Inverse Problems

  • Byun, Jin-Kyu;Lee, Hyang-Beom;Kim, Hyeong-Seok;Kim, Dong-Hun
    • Journal of Magnetics
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    • 제16권1호
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    • pp.77-82
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    • 2011
  • This paper presents a new self-adjoint material sensitivity formulation for optimal designs and inverse problems in the high frequency domain. The proposed method is based on the continuum approach using the augmented Lagrangian method. Using the self-adjoint formulation, there is no need to solve the adjoint system additionally when the goal function is a function of the S-parameter. In addition, the algorithm is more general than most previous approaches because it is independent of specific analysis methods or gridding techniques, thereby enabling the use of commercial EM simulators and various custom solvers. For verification, the method was applied to the several numerical examples of dielectric material reconstruction problems in the high frequency domain, and the results were compared with those calculated using the conventional method.

2007년 5월 6-8일 황사 현상의 예측 민감도 분석 (Forecast Sensitivity Analysis of An Asian Dust Event occurred on 6-8 May 2007 in Korea)

  • 김현미;계준경
    • 대기
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    • 제20권4호
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    • pp.399-414
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    • 2010
  • Sand and dust storm in East Asia, so called Asian dust, is a seasonal meteorological phenomenon. Mostly in spring, dust particles blown into atmosphere in the arid area over northern China desert and Manchuria are transported to East Asia by prevailing flows. An Asian dust event occurred on 6-8 May 2007 is chosen to investigate how sensitive the Asian dust transport forecast to the initial condition uncertainties and to interpret the characteristics of sensitivity structures from the viewpoint of dynamics and predictability. To investigate the forecast sensitivities to the initial condition, adjoint sensitivities that calculate gradient of the forecast aspect (i.e., response function) with respect to the initial condition are used. The forecast aspects relevant to Asian dust transports are dry energy forecast error and lower tropospheric pressure forecast error. The results show that the sensitive regions for the dry energy forecast error and the lower tropospheric pressure forecast error are initially located in the vicinity of the trough and then propagate eastward as the surface low system moves eastward. The vertical structures of the adjoint sensitivities for the dry energy forecast error are upshear tilted structures, which are typical adjoint sensitivity structures for extratropical cyclones. Energy distribution of singular vectors also show very similar structures with the adjoint sensitivities for the dry energy forecast error. The adjoint sensitivities of the lower tropospheric pressure forecast error with respect to the relative vorticity show that the accurate forecast of the trough (or relative vorticity) location and intensity is essential to have better forecasts of the Asian dust event. Forecast error for the atmospheric circulation during the dust event is reduced 62.8% by extracting properly weighted adjoint sensitivity perturbations from the initial state. Linearity assumption holds generally well for this case. Dynamics of the Asian dust transport is closely associated with predictability of it, and the improvement in the overall forecast by the adjoint sensitivity perturbations implies that adjoint sensitivities would be beneficial in improving the forecast of Asian dust events.

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

  • 문세준;하윤도;조선호
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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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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Sensitivity Analysis for the Navier-Stokes Equations with Two-Equation Turbulence Models

  • 김창성;김종암;노오현
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2000년도 춘계 학술대회논문집
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    • pp.66-72
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    • 2000
  • Aerodynamic sensitivity analysis is performed for the Navier-Stokes equations coupled with two-equation turbulence models using a discrete adjoint method and a direct differentiation method respectively. Like the mean flow equations, the turbulence model equations are also hand-differentiated to accurately calculate the sensitivity derivatives of flow quantities with respect to design variables in turbulent viscous flows. Both the direct differentiation code and the adjoint variable code adopt the same time integration scheme with the flow solver to efficiently solve the differentiated equations. The sensitivity codes are then compared with the flow solver in terms of solution accuracy, computing time and computer memory requirements. The sensitivity derivatives obtained from the sensitivity codes with different turbulence models are compared with each other. Using two-equation turbulence models, it is observed that a usual assumption of constant turbulent eddy viscosity in adjoint methods may lead to seriously inaccurate results in highly turbulent flows.

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Inverse Scattering of Two-Dimensional Objects Using Linear Sampling Method and Adjoint Sensitivity Analysis

  • Eskandari, Ahmadreza;Eskandari, Mohammad Reza
    • Journal of Electrical Engineering and Technology
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    • 제10권1호
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    • pp.308-313
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    • 2015
  • This paper describes a technique for complete identification of a two-dimensional scattering object and multiple objects immersed in air using microwaves where the scatterers are assumed to be a homogenous dielectric medium. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. Incident waves are assumed to be TM (Transverse Magnetic) plane waves. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects.