Automation of Krylov Subspace Model Order Reduction for Transient Response Analysis with Multiple Loading

Jeong Sam Han; Seung Hyun Kim

doi:10.7734/COSEIK.2021.34.2.101

All Issue

2021 Vol.34, Issue 2 Preview Page Next Page

Research Paper

Automation of Krylov Subspace Model Order Reduction for Transient Response Analysis with Multiple Loading 다중 하중 과도응답해석 과정에 대한 크리로프 부공간 모델차수축소법의 자동화

30 April 2021. pp. 101-111

PDF XML

Abstract

In general, several computational resources are required to perform multiple-loading transient response analyses. In this paper, we present the procedure for multiple-loading transient response analysis using the Krylov subspace model order reduction and Newmark’s time integration scheme. We utilized ANSYS MAPDL, Python, and ANSYS ACT to automate the transient response analysis procedure in the ANSYS Workbench environment and studied several engineering numerical examples to demonstrate the feasibility and efficiency of the proposed approach.

Keywords

krylov subspace

model order reduction

transient response analysis

ANSYS ACT

다중 하중 과도응답해석은 시간에 따른 작용 하중에 대한 과도응답을 확인하므로 정교한 시스템 모델링 및 조밀한 시간 간격을 가질수록 해당 시스템에 대한 동특성은 정확하게 나타내지만 이에 따른 계산 시간은 크게 증가하게 된다. 크리로프 부공간 기반 모델차수축소법은 기계 시스템이 가지는 동적 특성과 거의 동일한 결과를 나타내면서 계산 시간을 줄일 수 있기 때문에 효율적인 과도응답해석 방법이다. 본 연구에서는 다중 하중 및 이동 하중을 가지는 수치 예제를 통하여 크리로프 부공간 모델차수축소법 기반 과도응답해석을 수행하고, 이를 통해 초기 시스템 및 축소차수 모델의 정확성 및 효율성을 비교하였다. 또한, 시스템 행렬 추출, 크리로프 부공간의 기저 벡터로 구성되는 변환행렬 생성 및 축소차수모델 생성 그리고 이를 바탕으로 과도응답해석을 하는 절차를 수립하여 상용 유한요소 프로그램인 ANSYS Workbench ACT를 통해 과도응답해석 과정 자동화를 구현하여 그 효용성과 효율성을 보였다.

키워드

크리로프 부공간

모델차수축소법

과도응답해석

ANSYS ACT

References

ANSYS (2018) ANSYS ACT 19.2 Release API and XML Online Reference Guide for Mechanical, SAS IP, Inc.

Amin, N.M., Krisnamoorty, R.R. (2012) Krylov Subspace Model Order Reduction for FE Seismic Analysis, Business, Eng. & Ind. Appl., pp.239~243. 10.1109/ISBEIA.2012.6422877

Freund, R.W. (2000) Krylov-Subspace Methods for Reduced-Order Modeling in Circuit Simulation, J. Comput. & Appl. Math., 123, pp.395~421. 10.1016/S0377-0427(00)00396-4

Goo, S.Y., Kook, J.H., Hyun, J.H., Wang, S.M. (2012) A Comparison Study of Pad Approximation and Model Order Reduction Scheme for Efficient Acoustic Analysis, Trans. Korean Soc. Mech. Eng. Spring & Autumn Conf., pp.455~458.

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, 31(5), pp.541~549. 10.3795/KSME-A.2007.31.5.541

Han, J. S. (2010) Direct Design Sensitivity Analysis of Frequency Response Function using Krylov Subspace based Model order Reduction, J. Comput. Struct. Eng. Inst. Korea, 23(2), pp.153~163.

Han, J.S. (2013) Calculation of Design Sensitivity for Large-size Transient Dynamic Problems using Krylov Subspace-based Model Order Reduction, J. Mech. Sci. & Technol., 27(9), pp.2789~2800. 10.1007/s12206-013-0726-2

Han, J.S., Won, B.R., Park, W.S., Ko, J.H. (2016) Transient Response Analysis by Model Order Reduction of a Mokpo- Jeju Submerged Floating Tunnel under Seismic Excitations, Struct. Eng. & Mech., 57(5), pp.921~936. 10.12989/sem.2016.57.5.921

Han, J.S. (2020) Comparison of Model Order Reductions using Krylov and Modal Vectors for Transient Analysis under Seismic Loading, Struct. Eng. & Mech., 76(5), pp.643~651.

Kerschen, G., Golinval, Jc., Vakakis, A.F., Bergman, L.A. (2005) The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview, Nonlinear Dyn., 41, pp.147~169. 10.1007/s11071-005-2803-2

Kim, J.G., Park, Y.J., Lee, G.H., Kim, D.N. (2017) A General Model Reduction with Primal Assembly in Structural Dynamics, Comput. Methods Appl. Mech. & Eng., 324, pp.1~28. 10.1016/j.cma.2017.06.007

Kim, J.H., Yoon, G.H. (2016) Multi-Component Quasi-Static Ritz Vector (MCQSRV) Method by using Krylov Subspaces and Eigenvectors for Multibody Simulation, Trans. Korean Soc. Mech. Eng. Spring & Autumn Conf., pp.60~61.

Kim, M.C. (2018) Development of Automated Optimization Process for Journal Bearing Analysis in the Driving System of Engine, Trans. Korean Soc. Automot. Eng., pp.83~89.

Moon, S.I., Kang, T., Han, S.W. (2018) Automated Loose-Part Impact Analysis System for Big Data Construction of Nuclear Component, Trans. Korean Soc. Mech. Eng. Spring & Autumn Conf., pp.3145~3150.

Nam, Y.W., Lee, S.H., Lee, D.G., Im, S.J., Noh, S.D. (2020) Digital Twin-based Application for Design of Human-Machine Collaborative Assembly Production Lines, J.Korean Inst. Ind. Eng., 46(1), pp.42~54. 10.7232/JKIIE.2020.46.1.042

Oh, S.I., Park, D.U., Baek, H.W., Kim, S.H., Lee, J.K., Kim, J.G. (2020) Virtual Sensing System of Structural Vibration using Digital Twin, Trans. Korean Soc. Noise & Vib. Eng., 30(2), pp.149~160. 10.5050/KSNVE.2020.30.2.149

Park, B.G., Jeong, J.W., Ko, J.S. (2018) Micro Shock Switch with Additional Mass, Korean J. Air-Cond. & Refrig. Eng., 30(2), pp.586~592. 10.6110/KJACR.2018.30.12.586

Python Software Foundation (2018) Python 3.7 Documentation.

Qu, Z.Q. (2004) Model Order Reduction Techniques: With Application In Finite Element Analysis, Springer Science & Business Media. 10.1007/978-1-4471-3827-3_2

Saad, Y. (1983) Projection Methods for Solving Large Sparse Eigenvalue Problems, Matrix Pencils, 973, pp.121~144. 10.1007/BFb0062098

Seo, H.W., Kim, M.G., Lee, H.M., Han, J.S. (2020) Automation Tool for VDI 2230 Based Structural Analysis and Evaluation of Bolted Joints Using ANSYS and MS Excel, Trans. Korean Soc. Mech. Eng. A, 44(2), pp.149~158. 10.3795/KSME-A.2020.44.2.149

Shin, S.H., Park, M.C. (2020) Implementation of Digital Twin based Building Control System using Wireless Sensor Box, J. Korea Soc. Comput. & Inf., 25(5), pp.57~64.

Su, T.J., Craig, Jr.R.R. (1991) Krylov Model Reduction Algorithm for Undamped Structural Dynamics Systems, J. Guidance, 14(6), pp.1311~1313. 10.2514/3.20789

Won, B.R., Han, J.S. (2014) Comparison of Projection-Based Model Order Reduction for Frequency Responses, Trans. Korean Soc. Mech. Eng. A, 38(9), pp.933~941. 10.3795/KSME-A.2014.38.9.933

Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 34
No :2
Pages :101-111
Received Date : 2021-01-05
Revised Date : 2021-02-03
Accepted Date : 2021-02-04
DOI :https://doi.org/10.7734/COSEIK.2021.34.2.101

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

All Issue