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Wang Zihao, Zhang Guiyong, Sun Tiezhi. Sparse modeling and prediction of the fluid dynamics system for pitching airfoils. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(9): 2533-2543

. DOI: 10.6052/0459-1879-24-094
Citation:

Wang Zihao, Zhang Guiyong, Sun Tiezhi. Sparse modeling and prediction of the fluid dynamics system for pitching airfoils. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(9): 2533-2543

. DOI: 10.6052/0459-1879-24-094

SPARSE MODELING AND PREDICTION OF THE FLUID DYNAMICS SYSTEM FOR PITCHING AIRFOILS

  • Received Date: February 28, 2024
  • Accepted Date: August 20, 2024
  • Available Online: August 20, 2024
  • Published Date: August 20, 2024
  • This study delves into the nonlinear dynamics of complex fluid flows over a pitching airfoil under conditions of low Reynolds numbers and high angles of attack. By integrating multiple interrelated variables, the research successfully achieves a low-dimensional representation of high-dimensional flow field data through the use of principal component analysis (PCA) and isometric mapping (ISOMAP) dimensionality reduction techniques. ISOMAP, in particular, stands out for its superior ability to describe the nonlinear characteristics of the flow field, offering greater flexibility in managing the intricate structures inherent in highly nonlinear systems. This flexibility makes ISOMAP an invaluable tool in capturing the subtle, yet critical, aspects of fluid flow that may be overlooked by more traditional methods.Building on this dimensionality reduction, the study introduces the least absolute shrinkage and selection operator (LASSO) model to construct ordinary differential equations that govern the flow field. The LASSO model is particularly effective in automatically detecting and selecting the most relevant nonlinear terms, thus simplifying the complex descriptions of the flow field. This simplification not only enhances our understanding of the intricate relationships among multiple variables but also improves the model’s predictive power, making it a more practical tool for real-world applications. To further refine the model's accuracy, the research employs the 5(4) Explicit Runge-Kutta method, a numerical technique that allows for high-precision and rapid predictions of multivariable nonlinear fluid dynamics. This method significantly enhances the model’s capability to predict dynamic behaviors over time, making it a robust tool for both scientific research and practical engineering applications. Overall, this research framework transcends the limitations of traditional univariate analyses by integrating multidimensional data, thereby providing a more comprehensive understanding of the complexities inherent in fluid flow. By incorporating advanced techniques such as manifold learning and sparse modeling, this study not only demonstrates the potential for comprehensive modeling and accurate prediction in high-dimensional nonlinear dynamical systems but also paves the way for future innovations in the field. The insights and methodologies developed here offer substantial advancements for applied science and engineering, opening up new avenues for understanding and predicting the nonlinear dynamic behaviors that characterize complex flow fields.
  • [1]
    Cenedese M, Axås J, Bäuerlein B, et al. Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds. Nature Communications, 2022, 13(1): 872 doi: 10.1038/s41467-022-28518-y
    [2]
    张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望. 航空学报, 2021, 42(4): 524689 (Zhang Weiwei, Kou Jiaqing, Liu Yilang. Prospect of artificial intelligence empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524689 (in Chinese)

    Zhang Weiwei, Kou Jiaqing, Liu Yilang. Prospect of artificial intelligence empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524689 (in Chinese)
    [3]
    王建春, 晋国栋. 机器学习在力学模拟与控制中的应用专题序. 力学学报, 2021, 53(10): 2613-2615 (Wang Jianchun, Jin Guodong. Preface of theme articles on applications of machine learning to simulations and controls in mechanics. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2613-2615 (in Chinese)

    Wang Jianchun, Jin Guodong. Preface of theme articles on applications of machine learning to simulations and controls in mechanics. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2613-2615 (in Chinese)
    [4]
    江昊, 王伯福, 卢志明. 基于数据驱动的流场控制方程的稀疏识别. 力学学报, 2021, 53(6): 1543-1551 (Jiang Hao, Wang Bofu, Lu Zhiming. Data-driven sparse identification of governing equations for fluid dynamics. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1543-1551 (in Chinese) doi: 10.6052/0459-1879-21-052

    Jiang Hao, Wang Bofu, Lu Zhiming. Data-driven sparse identification of governing equations for fluid dynamics. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1543-1551 (in Chinese) doi: 10.6052/0459-1879-21-052
    [5]
    Brunton SL, Hemati MS, Taira K. Special issue on machine learning and data-driven methods in fluid dynamics. Theoretical and Computational Fluid Dynamics, 2020, 34(4): 333-337 doi: 10.1007/s00162-020-00542-y
    [6]
    Wang Z, Zhang G, Sun T, et al. Data-driven methods for low-dimensional representation and state identification for the spatiotemporal structure of cavitation flow fields. Physics of Fluids, 2023, 35(3): 033318
    [7]
    Zhang G, Wang Z, Huang H, et al. Comparison and evaluation of dimensionality reduction techniques for the numerical simulations of unsteady cavitation. Physics of Fluids, 2023, 35(7): 073322
    [8]
    Wang Z, Zhang G, Xing X, et al. Comparison of dimensionality reduction techniques for multi-variable spatiotemporal flow fields. Ocean Engineering, 2024, 291: 116421 doi: 10.1016/j.oceaneng.2023.116421
    [9]
    Lumley JL. The structure of inhomogeneous turbulent flows//Atmospheric Turbulence and Radio Wave Propagation, 1967: 166-178
    [10]
    Taira K, Brunton SL, Dawson STM, et al. Modal analysis of fluid flows: An overview. Aiaa Journal, 2017, 55(12): 4013-4041 doi: 10.2514/1.J056060
    [11]
    Schmid PJ. Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 2010, 656: 5-28 doi: 10.1017/S0022112010001217
    [12]
    Mendez MA. Linear and nonlinear dimensionality reduction from fluid mechanics to machine learning. Measurement Science and Technology, 2023, 34(4): 042001 doi: 10.1088/1361-6501/acaffe
    [13]
    Franz T, Zimmermann R, Görtz S, et al. Interpolation-based reduced-order modelling for steady transonic flows via manifold learning. International Journal of Computational Fluid Dynamics, 2014, 28(3-4): 106-121 doi: 10.1080/10618562.2014.918695
    [14]
    Halder R, Fidkowski K, Maki K. Local non-intrusive reduced order modeling using isomap//AIAA SCITECH 2022 Forum. 2022: 0081
    [15]
    Farzamnik E, Ianiro A, Discetti S, et al. From snapshots to manifolds–a tale of shear flows. Journal of Fluid Mechanics, 2023, 955: A34 doi: 10.1017/jfm.2022.1039
    [16]
    Rudy SH, Brunton SL, Proctor JL, et al. Data-driven discovery of partial differential equations. Science Advances, 2017, 3(4): e1602614 doi: 10.1126/sciadv.1602614
    [17]
    Raissi M, Yazdani A, Karniadakis GE. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 2020, 367(6481): 1026-1030 doi: 10.1126/science.aaw4741
    [18]
    Thompson R, Dezfouli A. The contextual lasso: Sparse linear models via deep neural networks. arXiv:2302.00878
    [19]
    Brunton SL, Proctor JL, Kutz JN. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 2016, 113(15): 3932-3937 doi: 10.1073/pnas.1517384113
    [20]
    Fukami K, Murata T, Zhang K, et al. Sparse identification of nonlinear dynamics with low-dimensionalized flow representations. Journal of Fluid Mechanics, 2021, 926: A10 doi: 10.1017/jfm.2021.697
    [21]
    Callaham JL, Brunton SL, Loiseau JC. On the role of nonlinear correlations in reduced-order modelling. Journal of Fluid Mechanics, 2022, 938: A1 doi: 10.1017/jfm.2021.994
    [22]
    Conti P, Gobat G, Fresca S, et al. Reduced order modeling of parametrized systems through autoencoders and SINDy approach: Continuation of periodic solutions. Computer Methods in Applied Mechanics and Engineering, 2023, 411: 116072 doi: 10.1016/j.cma.2023.116072
    [23]
    Wang Z, Zhang G, Zhou B, et al. Identification of control equations using low-dimensional flow representations of pitching airfoil. Physics of Fluids, 2024, 36(4): 045128
    [24]
    Wang Z, Zhang G, Huang H, et al. Joint proper orthogonal decomposition: A novel perspective for feature extraction from multivariate cavitation flow fields. Ocean Engineering, 2023, 288: 116003 doi: 10.1016/j.oceaneng.2023.116003
    [25]
    Wang Z, Zhang G, Sun T, et al. Information sharing-based multivariate proper orthogonal decomposition. Physics of Fluids, 2023, 35(10): 104108
    [26]
    Wang Z, Zhao W, Pan Z, et al. Temporal information sharing-based multivariate dynamic mode decomposition. Physics of Fluids, 2024, 36(2): 025174
    [27]
    Tenenbaum JB, Silva V, Langford JC. A global geometric framework for nonlinear dimensionality reduction. Science, 2000, 290(5500): 2319-2323 doi: 10.1126/science.290.5500.2319
    [28]
    Carroll JD, Arabie P. Multidimensional scaling. Measurement, judgment and decision making, 1998: 179-250
    [29]
    Towne A, Dawson ST M, Brès G A, et al. A database for reduced-complexity modeling of fluid flows. AIAA Journal, 2023, 61(7): 062203
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