IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2708-d876956.html
   My bibliography  Save this article

Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning

Author

Listed:
  • Konstantin Barkalov

    (Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, Russia)

  • Ilya Lebedev

    (Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, Russia)

  • Marina Usova

    (Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, Russia)

  • Daria Romanova

    (Ivannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia
    Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia)

  • Daniil Ryazanov

    (Ivannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia)

  • Sergei Strijhak

    (Ivannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia
    Moscow Aviation Institute, Volokolamskoe Shosse 4, 125993 Moscow, Russia)

Abstract

The paper considers the slope flow simulation and the problem of finding the optimal parameter values of this mathematical model. The slope flow is modeled using the finite volume method applied to the Reynolds-averaged Navier–Stokes equations with closure in the form of the k − ω S S T turbulence model. The optimal values of the turbulence model coefficients for free surface gravity multiphase flows were found using the global search algorithm. Calibration was performed to increase the similarity of the experimental and calculated velocity profiles. The Root Mean Square Error (RMSE) of derivation between the calculated flow velocity profile and the experimental one is considered as the objective function in the optimization problem. The calibration of the turbulence model coefficients for calculating the free surface flows on test slopes using the multiphase model for interphase tracking has not been performed previously. To solve the multi-extremal optimization problem arising from the search for the minimum of the loss function for the flow velocity profile, we apply a new optimization approach using a Peano curve to reduce the dimensionality of the problem. To speed up the optimization procedure, the objective function was approximated using an artificial neural network. Thus, an interdisciplinary approach was applied which allowed the optimal values of six turbulence model parameters to be found using OpenFOAM and Globalizer software.

Suggested Citation

  • Konstantin Barkalov & Ilya Lebedev & Marina Usova & Daria Romanova & Daniil Ryazanov & Sergei Strijhak, 2022. "Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2708-:d:876956
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2708/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2708/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rommel Regis & Christine Shoemaker, 2005. "Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions," Journal of Global Optimization, Springer, vol. 31(1), pages 153-171, January.
    2. Cheung, Sai Hung & Oliver, Todd A. & Prudencio, Ernesto E. & Prudhomme, Serge & Moser, Robert D., 2011. "Bayesian uncertainty analysis with applications to turbulence modeling," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1137-1149.
    3. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zheng, Liang & Xue, Xinfeng & Xu, Chengcheng & Ran, Bin, 2019. "A stochastic simulation-based optimization method for equitable and efficient network-wide signal timing under uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 287-308.
    2. Hoseinzade, Davood & Lakzian, Esmail & Hashemian, Ali, 2021. "A blackbox optimization of volumetric heating rate for reducing the wetness of the steam flow through turbine blades," Energy, Elsevier, vol. 220(C).
    3. Juliane Müller & Christine Shoemaker & Robert Piché, 2014. "SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications," Journal of Global Optimization, Springer, vol. 59(4), pages 865-889, August.
    4. Jae-Hyeon Bae & Kyoungsik Chang & Gong-Hee Lee & Byeong-Cheon Kim, 2022. "Bayesian Inference of Cavitation Model Coefficients and Uncertainty Quantification of a Venturi Flow Simulation," Energies, MDPI, vol. 15(12), pages 1-18, June.
    5. Hou, Tianfeng & Nuyens, Dirk & Roels, Staf & Janssen, Hans, 2019. "Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    6. H. Le Thi & A. Vaz & L. Vicente, 2012. "Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 190-214, April.
    7. Saleem Ramadan, 2016. "A Hybrid Global Optimization Method Based on Genetic Algorithm and Shrinking Box," Modern Applied Science, Canadian Center of Science and Education, vol. 10(2), pages 1-67, February.
    8. Zhe Zhou & Fusheng Bai, 2018. "An adaptive framework for costly black-box global optimization based on radial basis function interpolation," Journal of Global Optimization, Springer, vol. 70(4), pages 757-781, April.
    9. Taimoor Akhtar & Christine Shoemaker, 2016. "Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection," Journal of Global Optimization, Springer, vol. 64(1), pages 17-32, January.
    10. Sergey S. Ketkov & Oleg A. Prokopyev & Lisa M. Maillart, 2023. "Planning of life-depleting preventive maintenance activities with replacements," Annals of Operations Research, Springer, vol. 324(1), pages 1461-1483, May.
    11. Rommel G. Regis & Christine A. Shoemaker, 2009. "Parallel Stochastic Global Optimization Using Radial Basis Functions," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 411-426, August.
    12. Lehmann, Sebastian & Huth, Andreas, 2015. "Fast calibration of a dynamic vegetation model with minimum observation data," Ecological Modelling, Elsevier, vol. 301(C), pages 98-105.
    13. Linas Stripinis & Remigijus Paulavičius, 2023. "Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions," Mathematics, MDPI, vol. 11(13), pages 1-19, June.
    14. Krityakierne, Tipaluck & Baowan, Duangkamon, 2020. "Aggregated GP-based Optimization for Contaminant Source Localization," Operations Research Perspectives, Elsevier, vol. 7(C).
    15. Merle, X. & Cinnella, P., 2019. "Robust prediction of dense gas flows under uncertain thermodynamic models," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 400-421.
    16. Jesús Martínez-Frutos & David Herrero-Pérez, 2016. "Kriging-based infill sampling criterion for constraint handling in multi-objective optimization," Journal of Global Optimization, Springer, vol. 64(1), pages 97-115, January.
    17. Driessen, L. & Brekelmans, R.C.M. & Gerichhausen, M. & Hamers, H.J.M. & den Hertog, D., 2006. "Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models," Other publications TiSEM 45a73d28-9fed-4b4c-a909-1, Tilburg University, School of Economics and Management.
    18. Alberto Bemporad, 2020. "Global optimization via inverse distance weighting and radial basis functions," Computational Optimization and Applications, Springer, vol. 77(2), pages 571-595, November.
    19. Zhang, Jincheng & Zhao, Xiaowei, 2020. "Quantification of parameter uncertainty in wind farm wake modeling," Energy, Elsevier, vol. 196(C).
    20. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2708-:d:876956. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.