年間 6 号発行
ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352
Indexed in
Order Reduction for Large-Scale Finite Element Models: A Systems Perspective
要約
Large-scale finite element models are routinely used in design and optimization for complex engineering systems. However, the high model order prevents efficient exploration of the design space. Many model reduction methods have been proposed in the literature on approximating the high-dimensional model with a lower-order model. These methods typically replace a fine-scale model with a coarser-scale model in schemes, such as coarse graining, macromodeling, domain decomposition, and homogenization. This paper takes a systems perspective by stating the model reduction objective in terms of the approximation of the mapping between specified input and output variables. Methods from linear systems theory, including balance truncation and optimal Hankel norm approximation, are reviewed and compared to the standard modal truncation. For high-order systems, computational load, numerical stability, and memory storage become key considerations. We discuss several computationally more attractive iterative schemes that generate the approximate Gramian matrices needed in the model reduction procedure. A numerical example is also included to illustrate the model reduction algorithms discussed in the paper. We envision that these systems-oriented model reduction methods complementing the existing methods to produce low-order models suitable for design, optimization, and control.
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Fish Jacob, Bridging the scales in nano engineering and science, Journal of Nanoparticle Research, 8, 5, 2006. Crossref
-
Fehr J., Fischer M., Haasdonk B., Eberhard P., Greedy-based approximation of frequency-weighted Gramian matrices for model reduction in multibody dynamics, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 93, 8, 2013. Crossref
-
Grossard Mathieu, Hubert Arnaud, Régnier Stéphane, Chaillet Nicolas, Flexible Structures' Representation and Notable Properties in Control, in Flexible Robotics, 2013. Crossref
-
Feng Tianheng, Vadali Madhu, Ma Zheren, Chen Dongmei, Dykstra Jason, A Finite Element Method With Full Bit-Force Modeling to Analyze Drillstring Vibration, Journal of Dynamic Systems, Measurement, and Control, 139, 9, 2017. Crossref
-
Liu Ying, Li Hongguang, Li Yun, Du Huanyu, A Component-Based Parametric Reduced-Order Modeling Method Combined with Substructural Matrix Interpolation and Automatic Sampling, Shock and Vibration, 2019, 2019. Crossref
-
Wu Jiulin, Zeng Lizhan, Han Bin, Luo Xin, Chen Xuedong, Jiang Wei, Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems, Mathematical Problems in Engineering, 2020, 2020. Crossref
-
Fassah Abdul Rozak Rivai, Mkhoyan Tigran, de Visser Coen C., Developing the Model Reduction Framework in High Frame Rate Visual Tracking Environment, AIAA Scitech 2021 Forum, 2021. Crossref
-
Dogančić Bruno, Jokić Marko, Discretization and Model Reduction Error Estimation of Interconnected Dynamical Systems, IFAC-PapersOnLine, 55, 4, 2022. Crossref