Comptes Rendus
Nonintrusive data-based learning of a switched control heating system using POD, DMD and ANN
Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 793-805.

The aim of this work is to derive an accurate model of two-dimensional switched control heating system from data generated by a Finite Element solver. The nonintrusive approach should be able to capture both temperature fields, dynamics and the underlying switching control rule. To achieve this goal, the algorithm proposed in this paper will make use of three main ingredients: proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and artificial neural networks (ANN). Some numerical results will be presented and compared to the high-fidelity numerical solutions to demonstrate the capability of the method to reproduce the dynamics.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2019.11.005
Keywords: Data-driven model, Heating system, Switched control, Heat equation, Model order reduction, POD, DMD, ANN, Machine learning

Tarik Fahlaoui 1; Florian De Vuyst 1

1 Laboratoire de mathématiques appliquées de Compiègne EA 2222, Université de technologie de Compiègne, Alliance Sorbonne Université, 60200 Compiègne, France
@article{CRMECA_2019__347_11_793_0,
     author = {Tarik Fahlaoui and Florian De Vuyst},
     title = {Nonintrusive data-based learning of a switched control heating system using {POD,} {DMD} and {ANN}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {793--805},
     publisher = {Elsevier},
     volume = {347},
     number = {11},
     year = {2019},
     doi = {10.1016/j.crme.2019.11.005},
     language = {en},
}
TY  - JOUR
AU  - Tarik Fahlaoui
AU  - Florian De Vuyst
TI  - Nonintrusive data-based learning of a switched control heating system using POD, DMD and ANN
JO  - Comptes Rendus. Mécanique
PY  - 2019
SP  - 793
EP  - 805
VL  - 347
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2019.11.005
LA  - en
ID  - CRMECA_2019__347_11_793_0
ER  - 
%0 Journal Article
%A Tarik Fahlaoui
%A Florian De Vuyst
%T Nonintrusive data-based learning of a switched control heating system using POD, DMD and ANN
%J Comptes Rendus. Mécanique
%D 2019
%P 793-805
%V 347
%N 11
%I Elsevier
%R 10.1016/j.crme.2019.11.005
%G en
%F CRMECA_2019__347_11_793_0
Tarik Fahlaoui; Florian De Vuyst. Nonintrusive data-based learning of a switched control heating system using POD, DMD and ANN. Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 793-805. doi : 10.1016/j.crme.2019.11.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.005/

[1] M.A. Ahmad; S.-I. Azuma; I. Baba; T. Sugie Switching controller design for hybrid electric vehicles, SICE J. Control, Meas., Syst. Integr., Volume 7 (2014) no. 5, pp. 273-282

[2] A. Ferrara; J. Paderno Application of switching control for automatic pre-crash collision avoidance in cars, Nonlinear Dyn., Volume 46 (2006) no. 3, pp. 307-321 | DOI

[3] D. Liberzon Switching in Systems and Control, Springer Science & Business Media, 2003

[4] H. Lin; P.J. Antsaklis Stability and stabilizability of switched linear systems: a survey of recent results, IEEE Trans. Autom. Control, Volume 54 (2009) no. 2, pp. 308-322

[5] M.O. Williams; I.G. Kevrekidis; C.W. Rowley A data–driven approximation of the Koopman operator: extending dynamic mode decomposition, J. Nonlinear Sci., Volume 25 (2015) no. 6, pp. 1307-1346

[6] Q. Li; F. Dietrich; E.M. Bollt; I.G. Kevrekidis Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator, Chaos, Interdiscip. J. Nonlinear Sci., Volume 27 (2017) no. 10

[7] B.A. Pearlmutter Learning state space trajectories in recurrent neural networks, Neural Comput., Volume 1 (1989) no. 2, pp. 263-269

[8] R. Pascanu; T. Mikolov; Y. Bengio On the difficulty of training recurrent neural networks, International Conference on Machine Learning, 2013, pp. 1310-1318

[9] G. Lee; Z. Marinho; A.M. Johnson; G.J. Gordon; S.S. Srinivasa; M.T. Mason Unsupervised learning for nonlinear piecewise smooth hybrid systems, 2017 (arXiv preprint) | arXiv

[10] S. Peitz; S. Klus Koopman operator-based model reduction for switched-system control of pdes, 2017 (arXiv preprint) | arXiv

[11] J.L. Proctor; S.L. Brunton; J.N. Kutz Dynamic mode decomposition with control, SIAM J. Appl. Dyn. Syst., Volume 15 (2016) no. 1, pp. 142-161

[12] D. Tharayil; A.G. Alleyne A survey of iterative learning control: a learning-based method for highperformance tracking control, IEEE Control Syst. Mag., Volume 26 (2006) no. 3, pp. 96-114

[13] D.H. Owens; K. Feng Parameter optimization in iterative learning control, Int. J. Control, Volume 76 (2003) no. 11, pp. 1059-1069

[14] S. Arimoto; S. Kawamura; F. Miyazaki Bettering operation of robots by learning, J. Robot. Syst., Volume 1 (1984) no. 2, pp. 123-140

[15] S. Volkwein Proper Orthogonal Decomposition: Theory and Reduced-Order Modelling, Lecture Notes, vol. 4, University of Konstanz, 2013

[16] I. Jolliffe Principal Component Analysis, Springer Verlag, 1986

[17] A. Alexanderian A brief note on the Karhunen-Loève expansion, 2015 (arXiv preprint) | arXiv

[18] P.J. Schmid Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech., Volume 656 (2010), pp. 5-28

[19] J.H. Tu; C.W. Rowley; D.M. Luchtenburg; S.L. Brunton; J.N. Kutz On dynamic mode decomposition: theory and applications, 2013 (arXiv preprint) | arXiv

[20] S.B. Kotsiantis; I. Zaharakis; P. Pintelas Supervised machine learning: a review of classification techniques, Emerg. Artif. Intell. Appl. Comput. Eng., Volume 160 (2007), pp. 3-24

[21] S.K. Murthy Automatic construction of decision trees from data: a multi-disciplinary survey, Data Min. Knowl. Discov., Volume 2 (1998) no. 4, pp. 345-389 | DOI

[22] C.J. Burges A tutorial on support vector machines for pattern recognition, Data Min. Knowl. Discov., Volume 2 (1998) no. 2, pp. 121-167

[23] P. Cunningham; S.J. Delany k-nearest neighbour classifiers, Mult. Classif. Syst., Volume 34 (2007) no. 8, pp. 1-17

[24] D.E. Rumelhart; G.E. Hinton; R.J. Williams Learning representations by back-propagating errors, Nature, Volume 323 (1986) no. 6088, p. 533

[25] T. Fahlaoui Réduction de modèles et apprentissage de solutions spatio-temporelles paramétrées, Université de Technologie de Compiègne, France, 2020 PhD thesis Submitted (defense in Jan 2020)

[26] F. Hecht New development in freefem++, J. Numer. Math., Volume 20 (2012) no. 3–4, pp. 251-265

[27] F. Pedregosa; G. Varoquaux; A. Gramfort; V. Michel; B. Thirion; O. Grisel; M. Blondel; P. Prettenhofer; R. Weiss; V. Dubourg et al. Scikit-learn: machine learning in python, J. Mach. Learn. Res., Volume 12 (2011), pp. 2825-2830

Cited by Sources:

Comments - Policy