Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk

• Autorzy: Li R. , Noack B. , Cordier L. , Borée J. , Kaiser E. , Harambat F.

Identyfikatory

DOI

10.24423/aom.3000

• Języki publikacji: EN

Abstrakty

EN

We advance Genetic Programming Control (GPC) for turbulence flow control application building on the pioneering work of [1]. GPC is a recently proposed model-free control framework which explores and exploits strongly nonlinear dynamics in an unsupervised manner. The assumed plant has multiple actuators and sensors and its performance is measured by a cost function. The control problem is to find a control logic which optimizes the given cost function. The corresponding regression problem for the control law is solved by employing linear genetic programming as an easy and simple regression solver in a high-dimensional control search space. This search space comprises open-loop actuation, sensor-based feedback and combinations thereof — thus generalizing former GPC studies [2, 3]. This new methodology is denoted as linear genetic programming control (LGPC). The focus of this study is the frequency crosstalk between unforced, unstable oscillation and the actuation at different frequencies. LGPC is first applied to the stabilization of a forced nonlinearly coupled three-oscillator model comprising open- and closed-loop frequency crosstalk mechanisms. LGPC performance is then demonstrated in a turbulence control experiment, achieving 22% drag reduction for a simplified car model. In both cases, LGPC identifies the best nonlinear control achieving the optimal performance by exploiting frequency crosstalk. Our control strategy is suited to complex control problems with multiple actuators and sensors featuring nonlinear actuation dynamics. Significant further performance enhancement is envisioned in the more general field of machine learning control [4].

Słowa kluczowe

EN

flow control; nonlinear dynamics; turbulent wake

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2018
• Tom: Vol. 70, nr 6
• Strony: 505--534
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Li R.

• Institut Pprime, CNRS - ISAE-ENSMA - Université de Poitiers Futuroscope Chasseneuil, France

autor

Noack B.

• LIMSI, UPR 3251, Orsay, France
• Technische Universität Braunschweig, Germany
• Technische Universität Berlin, Germany
• Harbin Institute of Technology Graduate School Shenzhen, China

autor

Cordier L.

• Institut Pprime, CNRS - ISAE-ENSMA - Université de Poitiers Futuroscope Chasseneuil, France

autor

Borée J.

• Institut Pprime, CNRS - ISAE-ENSMA - Université de Poitiers Futuroscope Chasseneuil, France

autor

Kaiser E.

• University of Washington Seattle, WA, U.S.A.

autor

Harambat F.

• Groupe PSA, Vélizy-Villacoublay, France

Bibliografia

• 1. D.C. Dracopoulos, Evolutionary Learning Algorithms for Neural Adaptive Control, Springer, London, 2013.
• 2. N. Gautier, J.-L. Aider, T. Duriez, B.R. Noack, M. Segond, W.M. Abel, Closed-loop separation control using machine learning, Journal of Fluid Mechanics, 770, 424–441, 2015.
• 3. V. Parezanovic, L. Cordier, A. Spohn, T. Duriez, B.R. Noack, J.-P. Bonnet, M. Segond, M. Abel, S. Brunton, Frequency selection by feedback control in a turbulent shear flow, Journal of Fluid Mechanics, 797, 247–283, 2016.
• 4. T. Duriez, S. Brunton, B.R. Noack, Machine Learning Control—Taming Nonlinear Dynamics and Turbulence, Fluid Mechanics and Its Applications, 116, Springer, 2016.
• 5. S.L. Brunton, B.R. Noack, Closed-loop turbulence control: Progress and challenges, Applied Mechanics Review, 67, 5, 050801:01–48, 2015.
• 6. C.W. Rowley, D.R. Williams, T. Colonius, R.M. Murray, D.G. MacMynowski, Linear models for control of cavity flow oscillations, Journal of Fluid Mechanics, 547, 317–330, 2006.
• 7. P.J. Schmid, D. Sipp, Linear control of oscillator and amplifier flows, Physical Review Fluids, 1, 4, 040501, 2016.
• 8. K. Roussopoulos, Feedback control of vortex shedding at low Reynolds numbers, Journal of Fluid Mechanics, 248, 267–296, 1993.
• 9. J.H. Holland, Outline for a logical theory of adaptive systems, Journal of the Association of Computing Machinery, 9, 3, 297–314, 1962.
• 10. I. Rechenberg, Cybernetic Solution Path of an Experimental Problem, Roy. Airc. Establ., Libr. Transl., 1122, Hants, Farnborough, 1965.
• 11. H.P. Schwefel, Projekt MHD-Staustrahlrohr: Experimentelle Optimierung einer Zweiphasendüse. Teil I, 11, Technical Report, AEG Forschungsinstitut, Berlin, 1968.
• 12. D.C. Dracopoulos, S. Kent, Genetic programming for prediction and control, Neural Computing and Applications, 6, 214–228, 1997.
• 13. P.J. Fleming, R.C. Purshouse, Evolutionary algorithms in control systems engineering: a survey, Control Engineering Practice, 10, 11, 1223–1241, 2002.
• 14. J. Koza, Genetic Programming: on the Programming of Computers by Means of Natural Selection, vol. 1, MIT Press, U.S.A., 1992. LGPC for strongly nonlinear dynamics 533
• 15. N. Benard, P.J. Pons, J.F. Periaux, C. Bugeda, J.-P. Bonnet, E. Moreau, Multi-input genetic algorithm for experimental optimization of the reattachment downstream of a backward-facing step with surface plasma actuator, 46th AIAA Plasmadynamics and Lasers Conference, 1–23, AIAA, 2015.
• 16. A.Debien, K.A.F.F. von Krbek, N. Mazellier, T. Duriez, L. Cordier, B.R. Noack, M.W. Abel, A. Kourta, Closed-loop separation control over a sharp-edge ramp using genetic programming, Experiments in Fluids, 57, 40, 1–19, 2016.
• 17. M. Brameier, W. Banzhaf, Linear Genetic Programming, Springer Science & Business Media, Berlin, 2007.
• 18. R. Li, B.R. Noack, L. Cordier, J. Borée, F. Harambat, Drag reduction of a car model by linear genetic programming control, Experiments in Fluids, 58, 103, 1–20, 2017.
• 19. K. Thulasiraman, M.N.S. Swamy, 5.7 Acyclic directed graphs, Graphs: Theory and Algorithms, 118, 1992.
• 20. D.M. Luchtenburg, B. Günter, B.R. Noack, R. King, G. Tadmor, A generalized mean-field model of the natural and actuated flows around a high-lift configuration, Journal of Fluid Mechanics, 623, 283–316, 2009.
• 21. J. Östh, S. Krajnović, B.R. Noack, D. Barros, J. Borée, On the need for a non-linear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body, Journal of Fluid Mechanics, 747, 518–544, 2014.
• 22. S.R. Ahmed, G. Ramm, G. Faltin, Some salient features of the time averaged ground vehicle wake, Society of Automotive Engineers, SAE Inc., 840300, 1984.
• 23. D. Barros, J. Borée, B.R. Noack, A. Spohn, T. Ruiz, Bluff body drag manipulation using pulsed jets and Coanda effect, Journal of Fluid Mechanics, 805, 422–459, 2016.
• 24. A.R. Oxlade, J.F. Morrison, A. Qubain, G. Rigas, High-frequency forcing of a turbulent axisymmetric wake, Journal of Fluid Mechanics, 770, 305–318, 2015.
• 25. SH.J. Schmidt, R. Woszidlo, C.N. Nayeri, C.O. Paschereit, The effect of flow control on the wake dynamics of a rectangular bluff body in ground proximity, Experiments in Fluids, 59, 6, 107, 2018.
• 26. E. Berger, D. Scholz, M. Schumm, Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations, Journal of Fluids and Structures, 4, 3, 231–257, 1990.
• 27. B. Khalighi, S. Zhang, C. Koromilas, S.R. Balkanyi, L.P. Bernal, G. Laccarino, P. Moin, Experimental and computational study of unsteady wake flow behind a bluff body with a drag reduction device, Technical Report, SAE Technical Paper, 2001.
• 28. E. Kaiser, B.R. Noack, A. Spohn, L.N. Cattafesta, M. Morzyński, Cluster-based control of nonlinear dynamics, Theoretical and Computational Fluid Dynamics, (online), 1–15, 2017,
• 29. K.V. Mardia, J.T. Kent, J.M. Bibby, Multivariate Analysis, Academic Press, U.S.A., 1979.
• 30. I.J. Schoenberg, Remarks to Maurice Fréchet’s article ‘Sur la définition axiomatique d’une classe d’espaces distanciés vectoriellement applicable sur l’espace de Hilbert’, Annals of Mathematics, 38, 724–732, 1935.
• 31. G. Young, A.S. Householder, Discussion of a set of points in terms of their mutual distances, Psychometrika, 3, 19–22, 1938.
• 32. E. Kaiser, R. Li, B.R. Noack, On the control landscape topology, [in:] The 20th World Congress of the International Federation of Automatic Control pp. 1–5, (IFAC), Toulouse, France, 2017.
• 33. Z. Michalewicz, M. Schoenauer, Evolutionary algorithms for constrained parameter optimization problems, Evolutionary Computation, 4, 1, 1–32, 1996.
• 34. Z. Michalewicz, D. Dasgupta, R.G. Le Riche, M. Schoenauer, Evolutionary algorithms for constrained engineering problems, Computers & Industrial Engineering, 30, 4, 851–870, 1996.
• 35. J.-C. Loiseau, B.R. Noack, S.L. Brunton, Sparse reduced-order modelling: sensor-based dynamics to full-state estimation, Journal of Fluid Mechanics, 844, 459–490, 2018.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).