Application of data-driven realizations to port-Hamiltonian flexible structures
Authors
Karim Cherifi, Andrea Brugnoli
Abstract
In this contribution, the validity of reduced order data-driven approaches for port-Hamiltonian systems is assessed by direct comparison with models obtained from finite element discretization. In particular, we consider examples arising from the structural dynamics of beams. Port-Hamiltonian beam models can be readily discretized by using mixed finite elements. The resulting numerical models are used to generate the input-output data. The data-driven realization is then compared to the original numerical model in terms of its bode plot and energy trend.
Keywords
Port-Hamiltonian systems; Structural dynamics; Mixed finite elements; Data-driven systems identification
Citation
- Journal: IFAC-PapersOnLine
- Year: 2021
- Volume: 54
- Issue: 19
- Pages: 180–185
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2021.11.075
- Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021
BibTeX
@article{Cherifi_2021,
title={{Application of data-driven realizations to port-Hamiltonian flexible structures}},
volume={54},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2021.11.075},
number={19},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Cherifi, Karim and Brugnoli, Andrea},
year={2021},
pages={180--185}
}
References
- Antoulas, A tutorial introduction to the Loewner framework for model reduction. (2017)
- Arnold, D. N. & Lee, J. J. Mixed Methods for Elastodynamics with Weak Symmetry. SIAM Journal on Numerical Analysis vol. 52 2743–2769 (2014) – 10.1137/13095032x
- Benner, P., Goyal, P. & Van Dooren, P. Identification of port-Hamiltonian systems from frequency response data. Systems & Control Letters vol. 143 104741 (2020) – 10.1016/j.sysconle.2020.104741
- Brugnoli, A., Alazard, D., Pommier-Budinger, V. & Matignon, D. Port-Hamiltonian flexible multibody dynamics. Multibody System Dynamics vol. 51 343–375 (2020) – 10.1007/s11044-020-09758-6
- Celledoni, Structure-preserving deep learning. European Journal of Applied Mathematics (2021)
- Cherifi, K. An overview on recent machine learning techniques for Port Hamiltonian systems. Physica D: Nonlinear Phenomena vol. 411 132620 (2020) – 10.1016/j.physd.2020.132620
- Cherifi, K., Goyal, P. & Benner, P. A greedy data collection scheme for linear dynamical systems. Data-Centric Engineering vol. 3 (2022) – 10.1017/dce.2022.16
- Hauschild, S.-A., Marheineke, N. & Mehrmann, V. Model reduction techniques for port‐Hamiltonian differential‐algebraic systems. PAMM vol. 19 (2019) – 10.1002/pamm.201900040
- Kirby, R. C. & Kieu, T. T. Symplectic-mixed finite element approximation of linear acoustic wave equations. Numerische Mathematik vol. 130 257–291 (2014) – 10.1007/s00211-014-0667-4
- Lepe, F., Mora, D. & Rodríguez, R. Locking-free finite element method for a bending moment formulation of Timoshenko beams. Computers & Mathematics with Applications vol. 68 118–131 (2014) – 10.1016/j.camwa.2014.05.011
- Rashad, R., Califano, F., van der Schaft, A. J. & Stramigioli, S. Twenty years of distributed port-Hamiltonian systems: a literature review. IMA Journal of Mathematical Control and Information vol. 37 1400–1422 (2020) – 10.1093/imamci/dnaa018