Reduced-order model of unsteady wind turbine wake based on a multifunctional recurrent fuzzy neural network

Abstract

To enhance the prediction accuracy of unsteady wakes behind wind turbines, a novel reduced-order model is proposed by integrating a multifunctional recurrent fuzzy neural network (MFRFNN) and proper orthogonal decomposition (POD). First, POD is employed to reduce the dimensionality of the wind field data, extracting spatiotemporally correlated modal coefficients and modes. These reduced-order variables can effectively capture the essential features of unsteady wake behaviors. Next, MFRFNN is utilized to predict the time series of modal coefficients. Finally, by combining the predicted modal coefficients with their corresponding modes, a flow field is reconstructed, allowing accurate prediction of unsteady wake dynamics. The predicted wake data exhibit high consistency with large eddy simulation results in both the near- and far-wake regions and outperform existing data-driven methods. This approach offers significant potential for optimizing wind farm design and provides a new solution for the precise prediction of wind turbine wake behavior.

Keywords

computational fluid dynamics (CFD) / reduced-order model / deep learning / wind turbine / wake model

References

[1] DING H Y, HAN T Q, ZHANG P Y, et al. Influence of helical blades on horizontal bearing capacity of spiral piles for offshore wind power[J]. Journal of Southeast University (English Edition), 2025, 41(3): 314-324.

[2] XU B F, SHI T, LI Z, et al. Power regulation strategy of downwind wind turbines based on cone angle control[J]. Journal of Southeast University (Natural Science Edition), 2024, 54(3): 747-753. (in Chinese)

[3] ZHANG P Y, XIONG L C, LE C H, et al. Comparison analysis of the bearing capacity of rock-socketed piles and sand piles for offshore wind turbines[J]. Journal of Southeast University (English Edition), 2023, 39(4): 384-392.

[4] BARTHELMIE R J, HANSEN K, FRANDSEN S T, et al. Modelling and measuring flow and wind turbine wakes in large wind farms offshore[J]. Wind Energy, 2009, 12(5): 431-444.

[5] THOMSEN K, SØRENSEN P. Fatigue loads for wind turbines operating in wakes[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 80(1/2): 121-136.

[6] PIGGOTT M D, KRAMER S C, FUNKE S W, et al. Optimization of marine renewable energy systems[M]// Comprehensive Renewable Energy. Amsterdam, the Netherlands: Elsevier, 2022: 176-220.

[7] JENSEN N O. A note on wind generator interaction, Technical Report Riso-M-2411[R]. Roskilde, Denmark: Riso National Laboratory, 1983.

[8] FRANDSEN S, BARTHELMIE R, PRYOR S, et al. Analytical modelling of wind speed deficit in large offshore wind farms[J]. Wind Energy, 2006, 9(1/2): 39-53.

[9] BASTANKHAH M, PORTÉ-AGEL F. A new analytical model for wind-turbine wakes[J]. Renewable Energy, 2014, 70: 116-123.

[10] ZHANG J C, ZHAO X W. A novel dynamic wind farm wake model based on deep learning[J]. Applied Energy, 2020, 277: 115552.

[11] LI S Y, ZHANG M R, PIGGOTT M D. End-to-end wind turbine wake modelling with deep graph representation learning[J]. Applied Energy, 2023, 339: 120928.

[12] HAN W, KIM H, SON E, et al. Assessment of yaw-control effects on wind turbine-wake interaction: A coupled unsteady vortex lattice method and curled wake model analysis[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2023, 242: 105559.

[13] TI Z L, DENG X W, YANG H X. Wake modeling of wind turbines using machine learning[J]. Applied Energy, 2020, 257: 114025.

[14] ZHANG J C, ZHAO X W. Wind farm wake modeling based on deep convolutional conditional generative adversarial network[J]. Energy, 2022, 238: 121747.

[15] LI R, ZHANG J C, ZHAO X W. Dynamic wind farm wake modeling based on a bilateral convolutional neural network and high-fidelity LES data[J]. Energy, 2022, 258: 124845.

[16] ZHOU L, WEN J H, WANG Z K, et al. High-fidelity wind turbine wake velocity prediction by surrogate model based on d-POD and LSTM[J]. Energy, 2023, 275: 127525.

[17] WANG L, DONG M, YANG J, et al. Wind turbine wakes modeling and applications: Past, present, and future[J]. Ocean Engineering, 2024, 309: 118508.

[18] LUO Z H, WANG L Y, FU Y X, et al. Wind turbine dynamic wake flow estimation (DWFE) from sparse data via reduced-order modeling-based machine learning approach[J]. Renewable Energy, 2024, 237: 121552.

[19] LUO Z H, WANG L Y, XU J, et al. A reduced order modeling-based machine learning approach for wind turbine wake flow estimation from sparse sensor measurements[J]. Energy, 2024, 294: 130772.

[20] HAN H G, CHEN Z Y, LIU H X, et al. A self-organizing interval Type-2 fuzzy-neural-network for modeling nonlinear systems[J]. Neurocomputing, 2018, 290: 196-207.

[21] JUANG C F, LIN Y Y, TU C C. A recurrent self-evolving fuzzy neural network with local feedbacks and its application to dynamic system processing[J]. Fuzzy Sets and Systems, 2010, 161(19): 2552-2568.

[22] SAMANTA S, PRATAMA M, SUNDARAM S. A novel spatio-temporal fuzzy inference system (SPATFIS) and its stability analysis[J]. Information Sciences, 2019, 505: 84-99.

[23] SAMANTA S, SURESH S, SENTHILNATH J, et al. A new neuro-fuzzy inference system with dynamic neurons (NFIS-DN) for system identification and time series forecasting[J]. Applied Soft Computing, 2019, 82: 105567.

[24] NASIRI H, EBADZADEH M M. MFRFNN: Multi-functional recurrent fuzzy neural network for chaotic time series prediction[J]. Neurocomputing, 2022, 507: 292-310.

[25] CAO Y, PING H, TAMURA T, et al. Wind peak pressures on a square-section cylinder: Flow mechanism and standard/conditional POD analyses[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2022, 222: 104918.

[26] WEN J H, ZHOU L, ZHANG H F. Mode interpretation of blade number effects on wake dynamics of small-scale horizontal axis wind turbine[J]. Energy, 2023, 263: 125692.

[27] ZHANG H F, WEN J H, ZHAN J, et al. Effects of blade number on the aerodynamic performance and wake characteristics of a small horizontal-axis wind turbine[J]. Energy Conversion and Management, 2022, 273: 116410.

Funding

The National Natural Science Foundation of China(51908107)