Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Comparison of Projection-Based Model Order Reduction for Frequency Responses

주파수응답에 대한 투영기반 모델차수축소법의 비교

  • Won, Bo Reum (Coastal Development and Ocean Energy Research Division, KIOST) ;
  • Han, Jeong Sam (Dept. of Mechanical Design Engineering, Andong Nat'l Univ.)
  • 원보름 (한국해양과학기술원 연안개발.에너지연구부) ;
  • 한정삼 (안동대학교 기계설계공학과)
  • Received : 2014.02.24
  • Accepted : 2014.07.25
  • Published : 2014.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper provides a comparison between the Krylov subspace method (KSM) and modal truncation method (MTM), which are typical projection-based model order reduction methods. The frequency responses are compared to determine the numerical accuracies and efficiencies. In order to compare the numerical accuracies of the KSM and MTM, the frequency responses and relative errors according to the order of the reduced model and frequency of interest are studied. Subsequently, a numerical examination shows whether a reduced order can be determined automatically with the help of an error convergence indicator. As for the numerical efficiency, the computation time needed to generate the projection matrix and the solution time to perform a frequency response analysis are compared according to the reduced order. A finite element model for a car suspension is considered as an application example of the numerical comparison.

본 논문에서는 대표적 투영기반 모델차수축소법인 크리로프 부공간 모델차수축소법(KSM)과 모드중첩법(MTM)을 고려하여 주파수응답해석에 대한 수치적 정확도와 효율성을 비교하였다. 두 모델차수축소법의 수치 정확도 비교를 위하여 주파수응답해석 결과, 축소차수 및 관심주파수에 따른 상대오차를 고려하였으며 이후에 오차수렴지표를 통한 자동적인 축소차수의 결정이 가능 여부를 확인하였다. 효율성 비교를 위해서는 각 축소모델의 주파수응답 해석시간 및 축소차수에 따른 변환행렬 생성시간을 비교하였다. 자동차 현가장치에 대한 유한요소모델을 적용예제로 선정하여 수치 비교를 수행하였다.

Keywords

References

  1. Han, J. S., 2012, "Efficient Frequency Response and Its Direct Sensitivity Analysis for Large-size Finite Element Models using Krylov Subspace-based Model order reduction," Journal of Mechanical Science and Technology, Vol. 26, No. 4, pp. 1115-1126. https://doi.org/10.1007/s12206-012-0227-8
  2. Han, J. S. and Ko, J. H., 2009, "Frequency Response Analysis of Array-Type MEMS Resonators by Model Order Reduction Using Krylov Subspace Method," Trans. Korean Soc. Mech. Eng. A, Vol. 33, No. 9, pp. 878-885. https://doi.org/10.3795/KSME-A.2009.33.9.878
  3. Han, J. S., 2007, "Eigenvalue and Frequency Response Analyses of a Hard Disk Drive Actuator Using Reduced Finite Element Models," Trans. Korean Soc. Mech. Eng. A, Vol. 31, No. 5, pp. 541-549. https://doi.org/10.3795/KSME-A.2007.31.5.541
  4. Li, L., Hu, Y. J. and Wang, X. L., 2014, "Eliminating the Modal Truncation Problem Encountered in Frequency Responses of Viscoelastic Systems," Journal of Sound and Vibration, Vol. 333, pp. 1182-1192. https://doi.org/10.1016/j.jsv.2013.10.018
  5. Antoulas, A. C, 2006, "Approximation of Large-scale Dynamical Systems," Society for Industrial and Applied Mathematics, Vol. 6, pp. 376-377.
  6. Projection Based MOR, 2013, Wikipedia, http://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Projection_based_MOR.
  7. Freund, R. W., 2000, "Krylov-Subspace Methods for Reduced-Order Modeling in Circuit Simulation," Journal of Computational and Applied Mathematics, Vol. 123, pp. 395-421. https://doi.org/10.1016/S0377-0427(00)00396-4
  8. Han, J. S., 2013, "Calculation of Design Sensitivity for Large-size Transient Dynamic Problems using Krylov Subspace-based Model Order Reduction," Journal of Mechanical Science and Technology, Vol. 27, No. 9, pp. 2789-2800. https://doi.org/10.1007/s12206-013-0726-2
  9. Yang, J. Y. and Che, C. Y., 2004, "Extraction of Heat-transfer Macromodels for MEMS Devices," Journal of Micromechanics and Microengineering, Vol. 14, pp. 587-596. https://doi.org/10.1088/0960-1317/14/4/020
  10. Han, J. S., 2011, "Efficient Modal Analysis of Prestressed Structures via Model Order Reduction," Trans. Korean Soc. Mech. Eng. A, Vol. 35, No. 10, pp. 1211-1222. https://doi.org/10.3795/KSME-A.2011.35.10.1211
  11. Rudnyi, E. and Korvink, J., 2006, "Model Order Reduction for Large Scale Engineering Models Developed in ANSYS," Lecture Notes in Computer Science, Vol. 3732, pp. 349-356. https://doi.org/10.1007/11558958_41
  12. Zhang, X. P. and Kang, Z., 2013, "Topology Optimization of Damping Layers for Minimizing Sound Radiation of Shell Structures," Journal of Sound and Vibration, Vol. 333, pp. 2500-2519.
  13. Gugercin, S. and Antoulas, A. C, 2004, "A Survey of Model Reduction by Balanced Truncation and Some New Results," Int. J. Control, Vol. 77, No. 8, 748-766. https://doi.org/10.1080/00207170410001713448
  14. Azam, S. E. and Mariani, S., 2013, "Investigation of Computational and Accuracy Issues in POD-Based Reduced Order Modeling of Dynamic Structural Systems," Engineering Structures, Vol. 54, 150-167. https://doi.org/10.1016/j.engstruct.2013.04.004
  15. Qu, Z., 2004, "Model Order Reduction Techniques with Applications in Finite Element Analysis," Springer.
  16. ANSYS, 2012, ANSYS Mechanical APDL Theory Reference 14.5, SAS IP, Inc.