Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
권호 표지

Structural System Identification by Iterative IRS

반복적 IRS를 이용한 구조 시스템 식별

  • 백승민 (서울대학교 기계항공공학부 대학원) ;
  • 김현기 (현대중공업 기술개발본부 구조연구실) ;
  • 김기욱 (인하대학교 기계공학부) ;
  • 조맹효 (서울대학교 기계항공공학부)
  • Published : 2007.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

In the inverse perturbation method, enormous computational resource was required to obtain reliable results, because all unspecified DOFs were considered as unknown variables. Thus, in the present study, a reduced system method is used to condense the unspecified DOFs by using the specified DOFs, and to improve the computational efficiency as well as the solution accuracy. In most of the conventional reduction methods, transformation errors occur in the transformation matrix between the unspecified DOFs and the specified DOFs. Thus it is hard to obtain reliable and accurate solution of inverse perturbation problems by reduction methods due to the error in the transformation matrix. This numerical trouble is resolved in the present study by adopting iterative improved reduced system(IIRS) as well as by updating the transformation matrix at every step. In this reduction method, system accuracy is related to the selection of the primary DOFs and Iteration time. And both are dependent to each other So, the two level condensation method (TLCS) is selected as Selection method of primary DOFs for increasing accuracy and reducing iteration time. Finally, numerical verification results of the present iterative inverse perturbation method (IIPM) are presented.

구조 역섭동 문제에서, 신뢰할 만한 결과를 얻기 위해서는 정의되지 않은 모든 자유도가 미지변수로 간주되기 때문에 많은 전산자원이 필요하다. 본 연구에서는 축소시스템 기법과의 연동을 통해 정의되지 않은 자유도를 축소시스템에서 정의된 자유도 정보로 대체함으로써 해의 정확성과 계산의 효율성을 확보하는 기법을 제안한다. 일반적으로 구조 시스템을 축소할 경우, 시스템 축소변환 행렬에 오차가 포함되게 된다. 이 오차로 인해 축소기법을 적용하여 역섭동 문제의 정확한 해를 구하는 것은 쉽지 않은 문제이다. 이러한 문제를 해결하기 위해서 자유도 변환행렬을 매 단계마다 개선하는 반복적 축소 시스템 기법을 적용한다. 자유도 기반 축소시스템의 신뢰성은 주자유도 선정 위치와 변환행렬의 반복 계산 횟수에 의해 결정되며, 변환행렬의 반복 계산을 줄이기 위해서는 시스템 구축 초기에 주자유도가 잘 선정되어야 한다. 따라서, 본 연구에서는 축소모델의 정확도를 향상시키고 변환 행렬의 반복 계산을 최소화하기 위해 2단계 축소기법을 적용하여 주자유도 위치를 선정한다. 최종적으로 수치예제를 통해서 반복적 역섭동법의 효용성을 확인한다.

Keywords

References

  1. Aminpour, M.A. (1992), Direct Formulation of a Hybrid 4-Node Shell Element with Drilling Degrees of Freedom, International Journal for Numerical Methods in Engineering, 35, pp.997-1013 https://doi.org/10.1002/nme.1620350504
  2. Baek, S.M., Cho, M.H., Kim, K.O.(2006), System Identification by Sub-domain reduction method, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA. 2006-2121
  3. Cho, M.H., Kim, H.G.(2004), Element-Based Node Selection Method for Reduction of Eigenvalue problem, AIAA Journal, 42(8), pp.1677-1684 https://doi.org/10.2514/1.5407
  4. Cho, M.H., Kim, H.G.(2004), Two-Level Scheme for Selection of Degrees of Freedom by Energy Estimation Combined with Sequential Elimination, International Council of the Aeronautical Sciences 2004 Congress
  5. Choi, Y.J., Lee, U.S,(2003), An Accelerated Inverse Perturbation Method for Structural Damage Identification, KSME International Journal, 17(5), pp. 637-646
  6. Choi, Y.J. (2001), System Reduction and Selection of Degrees of Freedom in Structural Dynamic Inverse Problem, Ph.D. Dissertation, In-ha Univ., In-chon, Korea
  7. Friswell, M.I., Garvey, S.D., Penny, J.E.T.(1998), the convergence of the iterated IRS method, Journal of Sound and Vibration, 211(1), pp.123-132 https://doi.org/10.1006/jsvi.1997.1368
  8. Friswell, M.I., Mottershead, J.E. (1995), Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publisher, Netherlands
  9. Guvan, R.J. (1965), Reduction of stiffness and mass matrices, AIAA Journal, 3(2), p.380 https://doi.org/10.2514/3.2874
  10. Henshell, R.D., Ong, J.H.(1975), Automatic masters from eigenvalues economization, Journal of Earthquake Equation and Structural Dynamic, 3, pp.375-383
  11. Kim, H.G., Cho, M.H. (2004), Construction of Reduced System by Two-Level Scheme and Refined Semi-Analytic Sensitivity Analysis Based on the Reduced System, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA.2004-17317
  12. Kim, H.G., Cho, M.H.(2005), Dynamic Analysis of Reduced System Partitioned by Domain Decomposition, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA. 2005-2297
  13. Kim, H.G., Cho, M.H.(2006), Improvement of Reduction Method Combined with Sub-domain Scheme in Large scale Problem, International Journal for numerical methods in engineering, accepted
  14. Kim, K.O., Kang, M.K.(2001), Convergence Acceleration of iterative Modal Reduction methods, AIAA Journal, 39(1), pp.134-140 https://doi.org/10.2514/2.1281
  15. Kim, K.O., Choi, D.H.(2006), System Identification for Inverse Problems of Linear Dynamic Structures, Inverse Problem in Science in Engineering, 14(3), pp.267-285 https://doi.org/10.1080/17415970500473134
  16. Kim, K.O., Cho, J.Y., Choi, Y.J.(2004), Direct approach in inverse problems for dynamic system, AIAA Journal, 42(8), pp.1698-1704 https://doi.org/10.2514/1.941
  17. Kim, K.O., Choi, Y.J. (2000), Energy method for selection of degrees of freedom in condensation, AIAA Journal. 38(7), pp.1253-1259 https://doi.org/10.2514/2.1095
  18. O'callahan, J.(1989), A Procedure for an improved reduced system (IRS) model, Proceedings of of 7th International Modal Analysis Conference, pp.17-21
  19. Prathap, G., Somashekar, B.R.(1988) , Field- and edge-comsistency synthesis of a 4-noded quadrilateral plate bending element, International Journal for Numerical Method In Engineering, 26, pp.1693-1708 https://doi.org/10.1002/nme.1620260803
  20. Sampaio, R.P.C., Maia,N.M.M, Silva, J.M.M.(1999), Damage Detection using the Frequency-Response-Function Curvature Method, Journal of Sound and Vibration, 226(5), pp.1029-1042 https://doi.org/10.1006/jsvi.1999.2340
  21. Shah,V.N., Raymund, M. (1982), Analytical selection of masters for the reduced eigenvalue problem, International Journal for Numerical Method In Engineering, 18(1), pp.89-98 https://doi.org/10.1002/nme.1620180108
  22. Xia, Y., Lin, R. (2004), Improvement on the iterated IRS method for structural eigensolution, Journal of sound and vibration, 270, pp.713-727 https://doi.org/10.1016/S0022-460X(03)00188-3
  23. Zhang, D. W., Li, S. (1995), Succession-level approximate reduction (SAR) technique for structural dynamic model, Analysis conference(Nashville, TN), Union college press, Schenectady, NY, pp.435-441