Multi-Level Optimization of Framed Structures Using Automatic Differentiation

자동미분을 이용한 뼈대구조의 다단계 최적설계

  • 조효남 (한양대학교 토목.환경공학과) ;
  • 정지승 ((주) 삼보기술단) ;
  • 민대홍 (한양대학교 토목.환경공학과) ;
  • 이광민 (한양대학교 토목.환경공학과)
  • Received : 2000.06.21
  • Published : 2000.10.27

Abstract

An improved multi-level (IML) optimization algorithm using automatic differentiation (AD) of framed structures is proposed in this paper. For the efficiency of the proposed algorithm, multi-level optimization techniques using a decomposition method that separates both system-level and element-level optimizations, that utilizes and an artificial constraint deletion technique, are incorporated in the algorithm. And also to save the numerical efforts, an efficient reanalysis technique through approximated structural responses such as moments and frequencies with respect to intermediate variables is proposed in the paper. Sensitivity analysis of dynamic structural response is executed by AD that is a powerful technique for computing complex or implicit derivatives accurately and efficiently with minimal human effort. The efficiency and robustness of the IML algorithm, compared with a plain multi-level (PML) algorithm, is successfully demonstrated in the numerical examples.

본 논문에서는 지진하중이 작용하는 뼈대구조에 대해 자동미분(Automatic Differentiation)을 이용한 개선된 다단계 최적설계 알고리즘을 제안하고자 한다. 제안된 알고리즘의 효율성을 위해 전체구조계와 구조요소계 최적설계를 각각 분리하는 분해기법을 적용한 다단계 최적설계기법과 제약조건소거기법을 본 알고리즘에서 조합하여 사용하였다. 또한 수치계산을 효율적으로 수행하기 위해 중간매개변수를 사용하여 휨모멘트나 진동수와 같은 근사구조응답을 이용한 효율적인 재해석기법을 제시하였다. 복잡한 음함수 형태인 동적구조응답에 대한 민감도분석을 정확하고 효율적으로 계산하기 위해 자동미분기법을 사용하였다. 수치예제를 근거로 다단계알고리즘의 효율성과 신뢰성을 기존의 단순다단계알고리즘과 비교하여 제시하였다.

Keywords

Acknowledgement

Supported by : BK21

References

  1. Computational differentiation-techniques, tools, and applications Berz. M.;Bischof, C.;Corliss. G.;Griewank, A.(eds.)
  2. Scientific Programming v.1 no.1 ADIFOR-generating derivative codes from FORTRAN 77 programs Bichof, C.;Carle, A.;Corliss, G.;Griewank, A.;Hovland, P.
  3. IEEE Computational Sci. & Engrg. v.3 no.3 The ADIFOR2.0 system for the automatic defferentiation of FORTRAN 77 programs Bischof, C.;Carle, A.;Khademi, P.;Mauer, A.
  4. ADIC-an extensible automatic differentiation tool for ANSI-C, Preprint ANL/MCS-P626-1196 Bischof, C.;Roh. L.;Mauer, A.
  5. Engineering Structures v.21 Multiobjective and Multilevel Optimization for Steel Frames Li, Gang (et al.)
  6. AIAA Journal v.31 no.7 Multiobjective Optimization of Large-Scale Structures Grandhi, R.V.;Bharatram, Geetha
  7. On automatic differentiation, Mathematical programming: recent developments and applications Griewank, A.;Norwell, A.L.(ed.)
  8. Automatic differentiation of algorithms thoery. implementation, and application Griewank. A.;Corliss, G.F.(eds.)
  9. ACM Trans. on Mathematical Software v.22 no.2 ADOL-C: a package for the automatic differentiation of algorithms written in C/C++ Griewank. A.;Juedes, D.;Utke, J.
  10. Journal of structural Mechanics v.12 An Improved Computational Approach for Multilevel Optimization Design Hafkta, R.T.
  11. ASCE Journal of the Structural Division v.101 no.ST4 Multilevel Approach to Optimum structural Design Kirsch, U.
  12. Tellus v.45a no.4 Automatic differentiation in ODYSSEE Roasting, N.;Dalmas, S.;Galligo, A.
  13. AIAA Journal v.8 no.5 Derivatives of Eigenvalues and Eigenvectors Rogers, L.C.
  14. AIAA Journal v.30 no.3 Multiobjective Shape and Material Optimization of Composite Structure Including Damping Saravanos, D.A.;Chamis, C.C.
  15. ADOL-F: Automatic differentiation of FORTRAN codes, Computational differentiation-techniques, tools, and applications Shiriaev, D.;Griewank, A.
  16. AIAA Journal v.23 Structural Optimization by Multilevel Decomposition Sobieszczanski-Sobieski, J.;James, B.B.;Dovi, A.R.
  17. AIAA/ AS ME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conference Alternative Approximation Concepts for Space Frame Synthesis Lust, R.V.;Schmit, L.A.