Overview of Data-Driven Models for Wind Turbine Wake Flows

Abstract

With the rapid advancement of machine learning technology and its growing adoption in research and engineering applications, an increasing number of studies have embraced data-driven approaches for modeling wind turbine wakes. These models leverage the ability to capture complex, high-dimensional characteristics of wind turbine wakes while offering significantly greater efficiency in the prediction process than physics-driven models. As a result, data-driven wind turbine wake models are regarded as powerful and effective tools for predicting wake behavior and turbine power output. This paper aims to provide a concise yet comprehensive review of existing studies on wind turbine wake modeling that employ data-driven approaches. It begins by defining and classifying machine learning methods to facilitate a clearer understanding of the reviewed literature. Subsequently, the related studies are categorized into four key areas: wind turbine power prediction, data-driven analytic wake models, wake field reconstruction, and the incorporation of explicit physical constraints. The accuracy of data-driven models is influenced by two primary factors: the quality of the training data and the performance of the model itself. Accordingly, both data accuracy and model structure are discussed in detail within the review.

Keywords

Data-driven / Machine learning / Artificial neural networks / Wind turbine wake / Wake models

References

[1] Abdoos AA. A new intelligent method based on combination of VMD and ELM for short term wind power forecasting. Neurocomputing, 2016, 203: 111-120

[2] Ali N, Calaf M, Cal RB. Cluster-based probabilistic structure dynamical model of wind turbine wake. Journal of Turbulence, 2021, 22(8): 497-5164291392

[3] Amiri MM, Shadman M, Estefen SF. A review of physical and numerical modeling techniques for horizontal-axis wind turbine wakes. Renewable and Sustainable Energy Reviews, 2024, 193: 114279

[4] Anagnostopoulos S, Piggott M. Offshore wind farm wake modelling using deep feed forward neural networks for active yaw control and layout optimisation. Journal of Physics, 2022, 2151: 012011

[5] Anagnostopoulos SJ, Bauer J, Clare MCA, Piggott MD. Accelerated wind farm yaw and layout optimisation with multi-fidelity deep transfer learning wake models. Renewable Energy, 2023, 218: 119293

[6] Arbel J, Pitas K, Vladimirova M, Fortuin VA primer on Bayesian neural networks: Review and debates, 2023

[7] Ashwin Renganathan S, Maulik R, Letizia S, Iungo GV. Data-driven wind turbine wake modeling via probabilistic machine learning. Neural Comput & Applic, 2022, 34(8): 6171-6186

[8] Bastankhah M, Porté-Agel F. A new analytical model for wind-turbine wakes. Renewable Energy, 2014, 70: 116-123

[9] Bentsen L, Warakagoda ND, Stenbro R, Engelstad P. Wind park power prediction: Attention-based graph networks and deep learning to capture wake losses. Journal of Physics, 2022, 2265: 022035

[10] Breiman L. Random forests. Machine Learning, 2001, 45: 5-32

[11] Burmester S, Vaz G, el Moctar O. Towards credible CFD simulations for floating offshore wind turbines. Ocean Engineering, 2020, 209: 107237

[12] Cakiroglu C, Demir S, Ozdemir MH, Aylak BL, Sariisik G, Abualigah L. Data-driven interpretable ensemble learning methods for the prediction of wind turbine power incorporating SHAP analysis. Expert Systems With Applications, 2024, 237: 121464

[13] Calaf M, Meneveau C, Meyers J. Large eddy simulation study of fully developed wind-turbine array boundary layers. Physics of Fluids, 2010, 22(1): 015110

[14] Chen T, Chen H. Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans Neural Netw, 1995, 6(4): 911-917

[15] Chen T, Guestrin C. XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016San FranciscoACM785-794

[16] Chung J, Gulcehre C, Cho K, Bengio YEmpirical evaluation of gated recurrent neural networks on sequence modeling, 2014

[17] Draper M, Guggeri A, Mendina M, Usera G, Campagnolo F. A Large Eddy Simulation-Actuator Line Model framework to simulate a scaled wind energy facility and its application. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 182: 146-159

[18] Gajendran MK, Kabir IFSA, Vadivelu S, Ng EYK. Machine learning-based approach to wind turbine wake prediction under yawed Conditions. Journal of Marine Science and Engineering, 2023, 11: 2111

[19] Gao Z, Cecati C, Ding SX. A survey of fault diagnosis and fault-tolerant techniques—Part I: Fault diagnosis with model-based and signal-based approaches. IEEE Trans Ind Electron, 2015, 62(6): 3757-3767

[20] Ge M, Wu Y, Liu Y, Li Q. A two-dimensional model based on the expansion of physical wake boundary for wind-turbine wakes. Applied Energy, 2019, 233: 975-984

[21] Geibel M, Bangga G. Data reduction and reconstruction of wind turbine wake employing data driven approaches. Energies, 2022, 15: 3773

[22] Gu B, Zhang T, Meng H, Zhang J. Short-term forecasting and uncertainty analysis of wind power based on long short-term memory, cloud model and non-parametric kernel density estimation. Renewable Energy, 2021, 164: 687-708

[23] Guo NZ, Shi KZ, Bo L, Qi LW, Wu HH, Zhang ZL, Xu JZ. A physics-inspired neural network model for short-term wind power prediction considering wake effects. Energy, 2022, 261: 125208

[24] Guo NZ, Zhang MM, Li B. A data-driven analytical model for wind turbine wakes using machine learning method. Energy Conversion and Management, 2022, 252: 115130

[25] Guo Z, Xu L, Zhou G, Zhang K. A non-intrusive reduced-order model for wind farm wake analysis based on SPOD-DNN. Wind Engineering, 2023, 47(4): 852-866

[26] He R, Yang H, Shilin S, Lu L, Sun H, Xiaoxia G. A machine learning-based fatigue loads and power prediction method for wind turbines under yaw control. Applied Energy, 2022, 326: 120013

[27] Hearst MA. Support vector machines. IEEE Intell Syst Their Appl, 1998, 13(4): 18-28

[28] Helvig S d J, Vinnes MK, Segalini A, Worth NA, Hearst RJ. A comparison of lab-scale free rotating wind turbines and actuator disks. Journal of Wind Engineering and Industrial Aerodynamics, 2021, 209: 104485

[29] Hochreiter S, Schimidhuber J. Long short-term memory. Neural Computation, 1997, 9: 1835-1780

[30] Hong YY, Rioflorido CLPP. A hybrid deep learning-based neural network for 24-h ahead wind power forecasting. Applied Energy, 2019, 250: 530-539

[31] Isele D, Rahimi R, Cosgun A, Subramanian K, Fujimura KNavigating occluded intersections with autonomous vehicles using deep reinforcement learning, 2018

[32] Kabir IFSA, Safiyullah F, Ng EYK, Tam VWY. New analytical wake models based on artificial intelligence and rivalling the benchmark full-rotor CFD predictions under both uniform and ABL inflows. Energy, 2020, 193: 116761

[33] Kim H, Kim J, Won S, Lee C. Unsupervised deep learning for super-resolution reconstruction of turbulence. J Fluid Mech, 2021, 910: A294202470

[34] Kisvari A, Lin Z, Liu X0. Wind power forecasting-A data-driven method along with gated recurrent neural network. Renewable Energy, 2021, 163: 1895-1909

[35] Kober J, Peters J. Reinforcement learning in robotics: A Survey. Learning Motor Skills, 2014ChamSpringer International Publishing9-67

[36] Kou P, Wang C, Liang D, Cheng S, Gao L. Deep learning approach for wind speed forecasts at turbine locations in a wind farm. IET Renew Power Gener, 2020, 14(13): 2416-2428

[37] LeCun Y, Bengio Y. Convolutional networks for images, speech, and time-series. The handbook of brain theory and neural networks, 1998CambridgeMIT Press255-258

[38] Lecun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444

[39] Lejeune M, Moens M, Chatelain P. A meandering-capturing wake model coupled to rotor-based flow-sensing for operational wind farm flow prediction. Front Energy Res, 2022, 10: 884068

[40] Li B, Ge M, Li X, Liu Y. A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines. Physics of Fluids, 2024, 36(3): 035143

[41] Li H. Short-term wind power prediction via spatial temporal analysis and deep residual networks. Frontiers in Energy Research, 2022, 10: 920407

[42] Li H, Yang Q, Li T. Wind turbine wake prediction modelling based on transformer-mixed conditional generative adversarial network. Energy, 2024, 291: 130403

[43] Li R, Zhang J, Zhao X. Dynamic wind farm wake modeling based on a Bilateral Convolutional Neural Network and high-fidelity LES data. Energy, 2022, 258: 124845

[44] Li R, Zhang J, Zhao X. Multi-fidelity modeling of wind farm wakes based on a novel super-fidelity network. Energy Conversion and Management, 2022, 270: 116185

[45] Li S, Zhang M, Piggott MD. End-to-end wind turbine wake modelling with deep graph representation learning. Applied Energy, 2023, 339: 120928

[46] Liu B, Tang J, Huang H, Lu XY. Deep learning methods for super-resolution reconstruction of turbulent flows. Physics of Fluids, 2020, 32(2): 025105

[47] Lu L, Jin P, Pang G, Zhang Z, Karniadakis GE. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intell, 2021, 3(3): 218-229

[48] Luo Z, Luo W, Xie J, Xu J, Wang L. A new three-dimensional wake model for the real wind farm layout optimization. Energy Exploration & Exploitation, 2022, 40(2): 701-723

[49] Luo Z, Wang L, Xu J, Wang Z, Yuan J, Tan ACC. A reduced order modeling-based machine learning approach for wind turbine wake flow estimation from sparse sensor measurements. Energy, 2024, 294: 130772

[50] Martínez-Tossas LA, Churchfield MJ, Leonardi S. Large eddy simulations of the flow past wind turbines: actuator line and disk modeling. Wind Energy, 2015, 18: 1047-1060

[51] Moussaoui H, El Akkad N, Benslimane M. Reinforcement Learning: A review. IJCDS, 2023, 13(1): 1465-1483

[52] Myles AJ, Feudale RN, Liu Y, Woody NA, Brown SD. An introduction to decision tree modeling. Journal of Chemometrics, 2004, 18: 275-285

[53] Nakhchi ME, Naung SW, Rahmati. Wake and power prediction of horizontal-axis wind farm under yaw-controlled conditions with machine learning. Energy Conversion and Management, 2023, 296: 117708

[54] Naranjo-Torres J, Mora M, Hernández-García R, Barrientos RJ, Fredes C, Valenzuela A. A review of convolutional neural network applied to fruit image processing. Applied Sciences, 2020, 10: 3343

[55] Nascimento EGS, de Melo TAC, Moreira DM. A transformer-based deep neural network with wavelet transform for forecasting wind speed and wind energy. Energy, 2023, 278: 127678

[56] Nilsson K, Shen WZ, Sørensen JN, Breton S-P, Ivanell S. Validation of the actuator line method using near wake measurements of the MEXICO rotor. Wind Energy, 2015, 18: 499-514

[57] Optis M, Perr-Sauer J. The importance of atmospheric turbulence and stability in machine-learning models of wind farm power production. Renewable and Sustainable Energy Reviews, 2019, 112: 27-41

[58] Pawar S, Sharma A, Vijayakumar G, Bay CJ, Yellapantula S, San O. Towards multi-fidelity deep learning of wind turbine wakes. Renewable Energy, 2022, 200: 867-879

[59] Popescu MC, Balas VE, Perescu-Popescu L, Mastorakis N. Multilayer Perceptron and Neural Networks. Wseas Transactions on Circuits and Systems, 2009, 8(7): 579-588

[60] Pujari KN, Miriyala SS, Mitra K. Jensen-ANN: A machine learning adaptation of jensen wake model. IFAC-PapersOnLine, 2023, 56(2): 4651-4656

[61] Purohit S, Ng EYK, Syed Ahmed Kabir IF. Evaluation of three potential machine learning algorithms for predicting the velocity and turbulence intensity of a wind turbine wake. Renewable Energy, 2022, 184: 405-420

[62] Qu Z, Hou X, Li J, Hu W. Short-term wind farm cluster power prediction based on dual feature extraction and quadratic decomposition aggregation. Energy, 2024, 290: 130155

[63] Raissi M, Karniadakis GE. Hidden physics models: Machine learning of nonlinear partial differential equations. Journal of Computational Physics, 2018, 357: 125-1413759415

[64] Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 2019, 378: 686-7073881695

[65] Romero DA, Hasanpoor S, Antonini EGA, Amon CH. Predicting wind farm wake losses with deep convolutional hierarchical encoder-decoder neural networks. APL Machine Learning, 2024, 2(1): 016111

[66] Ronneberger O, Fischer P, Brox TU-Net: Convolutional networks for biomedical image segmentation, 2015

[67] Rumelhart DE, Hintont GE, Williams RJ. Learning representations by back-propagating errors. Nature, 1986, 323(9): 533-536

[68] Santoni C, Zhang D, Zhang Z, Samaras D, Sotiropoulos F, Khosronejad A. Toward ultra-efficient high-fidelity predictions of wind turbine wakes: Augmenting the accuracy of engineering models with machine learning. Physics of Fluids, 2024, 36(6): 065159

[69] Santos FDN, Duthé G, Abdallah I, Réthoré P-É, Weijtjens W, Chatzi E, Devriendt C. Multivariate prediction on wake-affected wind turbines using graph neural networks. J Phys: Conf Ser, 2024, 2647(11): 112006

[70] Scarselli F, Gori M, Ah Chung T, Hagenbuchner M, Monfardini G. The graph neural network model. IEEE Trans Neural Netw, 2009, 20(1): 61-80

[71] Shakoor R, Hassan MY, Raheem A, Wu YK. Wake effect modeling: A review of wind farm layout optimization using Jensen’s model. Renewable and Sustainable Energy Reviews, 2016, 58: 1048-1059

[72] Sun H, Qiu C, Lu L, Gao X, Chen J, Yang H. Wind turbine power modelling and optimization using artificial neural network with wind field experimental data. Applied Energy, 2020, 280: 115880

[73] Sun S, Cui S, He T, Yao Q. An integrated deep neural network framework for predicting the wake flow in the wind field. Energy, 2024, 291: 130400

[74] Ti Z, Deng XW, Yang H. Wake modeling of wind turbines using machine learning. Applied Energy, 2020, 257: 114025

[75] Ti Z, Deng XW, Zhang M. Artificial neural networks based wake model for power prediction of wind farm. Renewable Energy, 2021, 172: 618-631

[76] Troldborg NActuator line modeling of wind turbine wakes, 2009CopenhagenTechnical University of Denmark

[77] Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser L, Polosukhin I. Attention is all you need. 31st Conference on Neural Information Processing Systems, NIPS 2017, Long Beach, USA, 2017

[78] Veers P, Dykes K, Lantz E, Barth S, Bottasso CL, Carlson O, Clifton A, Green J, Green P, Holttinen H, Laird D, Lehtomäki V, Lundquist JK, Manwell J, Marquis M, Meneveau C, Moriarty P, Munduate X, Muskulus M, Naughton J, Pao L, Paquette J, Peinke J, Robertson A, Rodrigo JS, Sempreviva AM, Smith JC, Tuohy A, Wiser R. Grand challenges in the science of wind energy. Science, 2019, 366(6464): eaau2027

[79] Vogel CR, Willden RHJ. Investigation of wind turbine wake superposition models using Reynolds-averaged Navier-Stokes simulations. Wind Energy, 2020, 23(3): 593-607

[80] Wang D, Yang M, Zhang W. Wind power group prediction model based on multi-task learning. Electronics, 2023, 12(17): 3683

[81] Wang H, Li G, Wang G, Peng J, Jiang H, Liu Y. Deep learning based ensemble approach for probabilistic wind power forecasting. Applied Energy, 2017, 188: 56-70

[82] Wang L, Chen M, Luo Z, Zhang B, Xu J, Wang Z, Tan ACC. Dynamic wake field reconstruction of wind turbine through physics-informed neural network and sparse LiDAR data. Energy, 2024, 291: 130401

[83] Wang Q, Wang Y, Zhang K, Liu Y, Qiang W, Han Wen Q. Artificial intelligent power forecasting for wind farm based on multi-source data fusion. Processes, 2023, 11(5): 1429

[84] Wu Z, Pan S, Chen F, Long G, Zhang C, Yu PS. A comprehensive survey on graph neural networks. IEEE Trans Neural Netw Learning Syst, 2021, 32(1): 4-244205495

[85] Xiong J, Peng T, Tao Z, Zhang C, Song S, Nazir MS. A dual-scale deep learning model based on ELM-BiLSTM and improved reptile search algorithm for wind power prediction. Energy, 2023, 266: 126419

[86] Xu K, Hu W, Leskovec J, Jegelka SHow Powerful are Graph Neural Networks?, 2019

[87] Yan CWind turbine wakes: from numerical modeling to machine learning, 2018NewarkUniversity of Delaware

[88] Yan C, Pan Y, Archer CL. A general method to estimate wind farm power using artificial neural networks. Wind Energy, 2019, 22(11): 1421-1432

[89] Yang K, Deng X, Ti Z, Yang S, Huang S, Wang Y. A data-driven layout optimization framework of large-scale wind farms based on machine learning. Renewable Energy, 2023, 218: 119240

[90] Yang S, Deng X, Ti Z, Yan B, Yang Q. Cooperative yaw control of wind farm using a double-layer machine learning framework. Renewable Energy, 2022, 193: 519-537

[91] Yang S, Yang K, Deng X, Yang J. Smart cooperative control scheme for large-scale wind farms based on a double-layer machine learning framework. Energy Conversion and Management, 2023, 285: 116949

[92] Ye M, Chen H, Wan D, Ye M, Chen H, Wan D. Quantification of numerical uncertainties of CFD-predicted wind turbine performance with overset grids. Ocean Engineering, 2024, 298: 117231

[93] Ye M, Chen HC, Koop A. Verification and validation of CFD simulations of the NTNU BT1 wind turbine. Journal of Wind Engineering and Industrial Aerodynamics, 2023, 234: 105336

[94] Ye M, Chen HC, Koop A. High-fidelity CFD simulations for the wake characteristics of the NTNU BT1 wind turbine. Energy, 2023, 265: 126285

[95] Ye M, Ma C, Wan D, Chen HC. A comparative study of different artificial neural-network architectures in the prediction of riser VIV. Proceedings of the Thirty-fourth International Ocean and Polar Engineering Conference, 20242770-2777

[96] Yin X, Zhao X. Big data driven multi-objective predictions for offshore wind farm based on machine learning algorithms. Energy, 2019, 186: 115704

[97] Yousif MZ, Lim HC. Reduced-order modeling for turbulent wake of a finite wall-mounted square cylinder based on artificial neural network. Physics of Fluids, 2024, 34: 015116

[98] Yu R, Gao J, Yu M, Lu W, Xu T, Zhao M, Zhang J, Zhang R, Zhang Z. LSTM-EFG for wind power forecasting based on sequential correlation features. Future Generation Computer Systems, 2019, 93: 33-42

[99] Yu R, Liu Z, Li X, Lu W, Ma D, Yu M, Wang J, Li B. Scene learning: Deep convolutional networks for wind power prediction by embedding turbines into grid space. Applied Energy, 2019, 238: 249-257

[100] Yu Y, Han X, Yang M, Yang J. Probabilistic prediction of regional wind power based on spatiotemporal quantile regression. IEEE Trans on Ind Applicat, 2020, 56(6): 6117-6127

[101] Zehtabiyan-Rezaie N, Iosifidis A, Abkar M. Physics-guided machine learning for wind-farm power prediction: Toward interpretability and generalizability. PRX Energy, 2023, 2(1): 013009

[102] Zhang J, Yan J, Infield D, Liu Y, Lien F. Short-term forecasting and uncertainty analysis of wind turbine power based on long short-term memory network and Gaussian mixture model. Applied Energy, 2019, 241: 229-244

[103] Zhang J, Zhao X. A novel dynamic wind farm wake model based on deep learning. Applied Energy, 2020, 277: 115552

[104] Zhang J, Zhao X. Wind farm wake modeling based on deep convolutional conditional generative adversarial network. Energy, 2022, 238: 121747

[105] Zhang J, Zhao X. Spatiotemporal wind field prediction based on physics-informed deep learning and LIDAR measurements. Applied Energy, 2021, 288: 116641

[106] Zhang J, Zhao X. Digital twin of wind farms via physics-informed deep learning. Energy Conversion and Management, 2023, 293: 117507

[107] Zhang W, Lin Z, Liu X. Short-term offshore wind power forecasting-A hybrid model based on Discrete Wavelet Transform (DWT), Seasonal Autoregressive Integrated Moving Average (SARIMA), and deep-learning-based Long Short-Term Memory (LSTM). Renewable Energy, 2022, 185: 611-628

[108] Zhang Z, Santoni C, Herges T, Sotiropoulos F, Khosronejad A. Time-averaged wind turbine wake flow field prediction using autoencoder convolutional neural networks. Energies, 2021, 15(1): 41

[109] Zhao Z, Yun S, Jia L, Guo J, Meng Y, He N, Li X, Shi J, Yang L. Hybrid VMD-CNN-GRU-based model for short-term forecasting of wind power considering spatio-temporal features. Engineering Applications of Artificial Intelligence, 2023, 121: 105982

[110] Zhou H, Qiu Y, Feng Y, Liu J. Power prediction of wind turbine in the wake using hybrid physical process and machine learning models. Renewable Energy, 2022, 198: 568-586

[111] Zhou J, Cui G, Hu S, Zhang Z, Yang C, Liu Z, Wang L, Li C, Sun M. Graph neural networks: A review of methods and applications. AI Open, 2020, 1: 57-81

[112] Zhou L, Wen J, Wang Z, Deng P, Zhang H. High-fidelity wind turbine wake velocity prediction by surrogate model based on d-POD and LSTM. Energy, 2023, 275: 127525

[113] Zhu A, Li X, Mo Z, Wu R. Wind power prediction based on a convolutional neural network. 2017 International Conference on Circuits, Devices and Systems, 2017ChengduICCDS, IEEE131-135

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