1202Accesses
1Altmetric
Abstract
This work presents machine learning techniques to estimate the aerodynamic coefficients of a 40° swept delta wing under the ground effect. For this purpose, three different approaches including feed-forward neural network (FNN), Elman neural network (ENN) and adaptive neuro-fuzzy interference system (ANFIS) have been used. The optimal configuration of these models was compared with each other, and the best accurate prediction model was determined. In the generated machine learning models, the liftCL and drag coefficientsCD of the delta wing under the ground proximity ofh/c = 0.4 were predicted by using the data of actualCL andCD of the delta wing under the ground proximities ofh/c = 1, 0.7, 0.55, 0.25 and 0.1. In FNN, ENN and ANFIS models, the angle of attackα and ground distanceh/c were utilized as input parameters,CL andCD as output parameters, separately. Although all three models estimate theCL andCD of the delta wing underh/c = 0.4 with very high accuracy, the ENN method predicts theCL andCD with much higher accuracy than the FNN and ANFIS models. For the estimation ofCL, while optimal configuration of ENN resulted in 1.0709% MAPE, 0.00595 RMSE and 0.00504 MAE, the best configurations of FNN and ANFIS end up with the results of 1.172% and 1.1028% MAPE, 0.00786 and 0.0071 RMSE, 0.00593 and 0.0054 MAE, respectively. Thus, results show that the developed FNN, ENN and ANFIS models can be accurately employed to forecast the aerodynamic coefficients of the delta wing under ground effect without the need of for many experimental measurements that causes extra time, labor and experimental costs.
This is a preview of subscription content,log in via an institution to check access.
Access this article
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
Price includes VAT (Japan)
Instant access to the full article PDF.

















Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Gursul I, Gordnier R, Visbal M (2005) Unsteady aerodynamics of nonslender delta wings. Prog Aerosp Sci 41:515–557.https://doi.org/10.1016/j.paerosci.2005.09.002
Ol MV, Gharib M (2003) Leading-edge vortex structure of nonslender delta wings at low reynolds number. AIAA J 41:16–26.https://doi.org/10.2514/2.1930
Gursul I, Allan MR, Badcock KJ (2005) Opportunities for the integrated use of measurements and computations for the understanding of delta wing aerodynamics. Aerosp Sci Technol 9:181–189.https://doi.org/10.1016/j.ast.2004.08.007
https://www.grc.nasa.gov/www/k12/airplane/liftco.html. Access date 08 June 2021, Adana
Kawazoe H, Morita S (2004) Ground effect on the dynamic characteristics of a wing-rock delta wing. In: 34th AIAA fluid dynamics conference and exhibit.https://doi.org/10.2514/6.2004-2352
Lee T, Huitema D, Leite P (2018) Ground effect on a cropped slender reverse delta wing with anhedral and Gurney flaplike side-edge strips. Proc Inst Mech Eng Part G J Aerosp Eng 233:2433–2444.https://doi.org/10.1177/0954410018779504
Tumse S, Tasci MO, Karasu I, Sahin B (2021) Effect of ground on flow characteristics and aerodynamic performance of a non-slender delta wing. Aerosp Sci Technol 110:106475.https://doi.org/10.1016/j.ast.2020.106475
Lee T, Ko LS (2018) Ground effect on the vortex flow and aerodynamics of a slender delta wing. J Fluids Eng 10(1115/1):4039232
Qu Q, Lu Z, Guo H et al (2015) Numerical investigation of the aerodynamics of a delta wing in ground effect. J Aircraft 52:329–340.https://doi.org/10.2514/1.c032735
Ahmed MR, Takasaki T, Kohama Y (2007) Aerodynamics of a NACA4412 airfoil in ground effect. AIAA J 45:37–47.https://doi.org/10.2514/1.23872
Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1:4–27.https://doi.org/10.1109/72.80202
Hunt KJ, Sbarbaro D, Żbikowski R, Gawthrop PJ (1992) Neural networks for control systems—a survey. Automatica 28:1083–1112.https://doi.org/10.1016/0005-1098(92)90053-i
Calise AJ, Rysdyk RT (1998) Nonlinear adaptive flight control using neural networks. IEEE Control Syst 18:14–25.https://doi.org/10.1109/37.736008
Gim Y, Jang DK, Sohn DK et al (2020) Three-dimensional particle tracking velocimetry using shallow neural network for real-time analysis. Exp Fluids.https://doi.org/10.1007/s00348-019-2861-8
Rabault J, Kolaas J, Jensen A (2017) Performing particle image velocimetry using artificial neural networks: a proof-of-concept. Meas Sci Technol 28:125301.https://doi.org/10.1088/1361-6501/aa8b87
Cai S, Liang J, Gao Q, Xu C, Wei R (2020) Particle image velocimetry based on a deep learning motion estimator. IEEE Trans Instrum Meas 69:3538–3554.https://doi.org/10.1109/tim.2019.2932649
Rabault J, Kuhnle A (2019) Accelerating deep reinforcement learning strategies of flow control through a multi-environment approach. Phys Fluids 31:094105.https://doi.org/10.1063/1.5116415
Tang H, Rabault J, Kuhnle A et al (2020) Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning. Phys Fluids 32:053605.https://doi.org/10.1063/5.0006492
Belus V, Rabault J, Viquerat J et al (2019) Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Adv 9:125014.https://doi.org/10.1063/1.5132378
Akbiyik H, Yavuz H (2021) Artificial neural network application for aerodynamics of an airfoil equipped with plasma actuators. J Appl Fluid Mech.https://doi.org/10.47176/jafm.14.04.32133
Adique M, Amiralaei M, Alighanbari H (2010) Application of artificial neural networks in aerodynamics prediction of low-reynolds-number figure-eight motion of an airfoil. AIAA Atmos Flight Mech Conf.https://doi.org/10.2514/6.2010-8120
Akansu YE, Sarıoğlu M, Seyhan M (2016) Aerodynamic drag force estimation of a truck trailer model using artificial neural network. Int J Autom Eng Technol 5:168–175.https://doi.org/10.18245/ijaet.287182
Rokhsaz K, Steck JE (1993) Use of neural networks in control of high-alpha maneuvers. J Guid Control Dyn 16:934–939.https://doi.org/10.2514/3.21104
Rokhsaz K, Steck JE (1993) Application of artificial neural networks in nonlinear aerodynamics and aircraft design. SAE Tech Paper Ser.https://doi.org/10.4271/932533
Alkhedher M, Al-Aribe khaled (2019) Estimation and prediction of nonlinear aerodynamics using artificial intelligence. In: 2019 7th International conference on future internet of things and cloud workshops (FiCloudW).https://doi.org/10.1109/ficloudw.2019.00033
Kurtulus DF (2008) Ability to forecast unsteady aerodynamic forces of flapping airfoils by artificial neural network. Neural Comput Appl 18:359–368.https://doi.org/10.1007/s00521-008-0186-2
Gomec FS, Canibek M (2017) Aerodynamic database improvement of aircraft based on neural networks and genetic algorithms. In: 7th European Conference for aeronautics and space sciences (Eucass)
Soltani M, Sadati N, Davari A (2003) Neural network: a new prediction tool for estimating the aerodynamic behavior of a pitching delta wing. In: 21st AIAA applied aerodynamics conference.https://doi.org/10.2514/6.2003-3793
Ignatyev D, Khrabrov A (2018) Experimental study and neural network modeling of aerodynamic characteristics of canard aircraft at high angles of attack. Aerospace 5:26.https://doi.org/10.3390/aerospace5010026
Rodriguez-Eguia I, Errasti I, Fernandez-Gamiz U et al (2020) A parametric study of trailing edge flap implementation on three different airfoils through an artificial neuronal network. Symmetry 12:828.https://doi.org/10.3390/sym12050828
Secco NR, Mattos BS (2017) Artificial neural networks to predict aerodynamic coefficients of transport airplanes. Aircr Eng Aerosp Technol 89:211–230.https://doi.org/10.1108/aeat-05-2014-0069
Rai MM, Madavan NK (2001) Application of artificial neural networks to the design of turbomachinery airfoils. J Propul Power 17:176–183.https://doi.org/10.2514/2.5725
Faller W, Schreck S, Luttges M (1994) Real-time prediction and control of three-dimensional unsteady separated flow fields using neural networks. In: 32nd Aerospace sciences meeting and exhibit.https://doi.org/10.2514/6.1994-532
Post ML, Corke TC (2006) Separation control using plasma actuators: dynamic stall vortex control on oscillating airfoil. AIAA J 44:3125–3135.https://doi.org/10.2514/1.22716
Winslow J, Otsuka H, Govindarajan B, Chopra I (2018) Basic understanding of airfoil characteristics at low Reynolds numbers (104–105). J Aircr 55:1050–1061.https://doi.org/10.2514/1.c034415
Hand B, Kelly G, Cashman A (2017) Numerical simulation of a vertical axis wind turbine airfoil experiencing dynamic stall at high Reynolds numbers. Comput Fluids 149:12–30.https://doi.org/10.1016/j.compfluid.2017.02.021
Hezaveh SH, Bou-Zeid E, Lohry MW, Martinelli L (2016) Simulation and wake analysis of a single vertical axis wind turbine. Wind Energy 20:713–730.https://doi.org/10.1002/we.2056
Linse DJ, Stengel RF (1993) Identification of aerodynamic coefficients using computational neural networks. J Guid Control Dyn 16:1018–1025.https://doi.org/10.2514/3.21122
Schreck SJ, Faller WE, Luttges MW (1995) Neural network prediction of three-dimensional unsteady separated flowfields. J Aircr 32:178–185.https://doi.org/10.2514/3.46698
Naderpour H, Mirrashid M (2021) Innovative models for capacity estimation of reinforced concrete elements in terms of soft computing techniques. Pract Period Struct Des Constr 26:04021038.https://doi.org/10.1061/(asce)sc.1943-5576.0000614
Sada SO, Ikpeseni SC (2021) Evaluation of ann and ANFIS modeling ability in the prediction of AISI 1050 steel machining performance. Heliyon.https://doi.org/10.1016/j.heliyon.2021.e06136
Armaghani DJ, Asteris PG (2020) A comparative study of Ann and ANFIS models for the prediction of cement-based mortar materials compressive strength. Neural Comput Appl 33:4501–4532.https://doi.org/10.1007/s00521-020-05244-4
Naderpour H, Mirrashid M (2020) Proposed soft computing models for moment capacity prediction of reinforced concrete columns. Soft Comput 24:11715–11729.https://doi.org/10.1007/s00500-019-04634-8
Akbiyik H, Yavuz H (2020) Dbd Plazma Aktüatör Sürüm Frekansının Uçak Kanadı Etrafındaki Akışın Kontrolüne Etkisinin İncelenmesi. Konya J Eng Sci 8:522–528
Akbiyik H, Yavuz H, Akansu YE (2017) Comparison of the linear and spanwise-segmented dbd plasma actuators on flow control around a NACA0015 airfoil. IEEE Trans Plasma Sci 45:2913–2921.https://doi.org/10.1109/tps.2017.2754949
Arora I, Gambhir J, Kaur T (2020) Data normalisation-based solar irradiance forecasting using artificial neural networks. Arab J Sci Eng 46:1333–1343.https://doi.org/10.1007/s13369-020-05140-y
Rana MJ, Shahriar MS, Shafiullah M (2017) Levenberg–Marquardt neural network to estimate UPFC-coordinated PSS parameters to enhance power system stability. Neural Comput Appl 31:1237–1248.https://doi.org/10.1007/s00521-017-3156-8
Karri V, Ho TN (2008) Predictive models for emission of hydrogen powered car using various artificial intelligent tools. Neural Comput Appl 18:469–476.https://doi.org/10.1007/s00521-008-0218-y
Yu H, Wilamowski BM (2018) Levenberg–marquardt training. Intell Syst.https://doi.org/10.1201/9781315218427-12
Liemberger W, Miltner M, Harasek M (2018) Reduced model describing efficient extraction of hydrogen transported as co-stream in the natural gas grid. Comput Aided Chem Eng.https://doi.org/10.1016/b978-0-444-64235-6.50242-4
Hagan MT, Demuth HB, Beale MH (1996) Neural network design. PWS Publishing, Boston
Graves A, Liwicki M, Fernandez S et al (2009) A novel connectionist system for unconstrained handwriting recognition. IEEE Trans Pattern Anal Mach Intell 31:855–868.https://doi.org/10.1109/tpami.2008.137
Chandra R, Zhang M (2012) Cooperative coevolution of Elman recurrent neural networks for chaotic time series prediction. Neurocomputing 86:116–123.https://doi.org/10.1016/j.neucom.2012.01.014
Cacciola M, Megali G, Pellicanó D, Morabito FC (2011) Elman neural networks for characterizing voids in welded strips: a study. Neural Comput Appl 21:869–875.https://doi.org/10.1007/s00521-011-0609-3
Elman JL (1990) Finding structure in time. Cogn Sci 14:179–211.https://doi.org/10.1207/s15516709cog1402_1
Wang J, Zhang W, Li Y et al (2014) Forecasting wind speed using empirical mode decomposition and Elman neural network. Appl Soft Comput 23:452–459.https://doi.org/10.1016/j.asoc.2014.06.027
Jang J-SR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685.https://doi.org/10.1109/21.256541
Sugeno M (1985) Industrial applications of fuzzy control. Elsevier, Amsterdam
Asghar AB, Liu X (2018) Adaptive neuro-fuzzy algorithm to estimate effective wind speed and optimal rotor speed for variable-speed wind turbine. Neurocomputing 272:495–504.https://doi.org/10.1016/j.neucom.2017.07.022
Talpur N, Salleh MN, Hussain K (2017) An investigation of membership functions on performance of ANFIS for solving classification problems. IOP Conf Ser Mater Sci Eng 226:012103.https://doi.org/10.1088/1757-899x/226/1/012103
https://www.mathworks.com/help/fuzzy/ Access 08 June 2021, Adana
Baughman DR, Liu YA (1995) Fundamental and practical aspects of neural computing. Neural Netw Bioprocess Chem Eng.https://doi.org/10.1016/b978-0-12-083030-5.50008-4
Omlin CW, Giles CL (1996) Extraction of rules from discrete-time recurrent neural networks. Neural Netw 9:41–52.https://doi.org/10.1016/0893-6080(95)00086-0
Stage P, Sendhoff B (1999) Organisation of past states in recurrent neural networks: implicit embedding. In: Mohammadian M (ed) Computational intelligence for modelling, control and automation. IOS Press, Amsterda, pp 21–27
Başakın EE, Ekmekcioğlu Ö, Çıtakoğlu H, Özger M (2021) A new insight to the wind speed forecasting: robust multi-stage ensemble soft computing approach based on pre-processing uncertainty assessment. Neural Comput Appl.https://doi.org/10.1007/s00521-021-06424-6
Citakoglu H (2021) Comparison of multiple learning artificial intelligence models for estimation of long-term monthly temperatures in Turkey. Arab J Geosci.https://doi.org/10.1007/s12517-021-08484-3
Funding
This research work does not receive any external funding.
Author information
Authors and Affiliations
Department of Mechanical Engineering, Faculty of Engineering, Cukurova University, Adana, Turkey
Sergen Tumse & Besir Sahin
Department of Mechanical Engineering, Ceyhan Engineering Faculty, Cukurova University, Adana, Turkey
Mehmet Bilgili
- Sergen Tumse
You can also search for this author inPubMed Google Scholar
- Mehmet Bilgili
You can also search for this author inPubMed Google Scholar
- Besir Sahin
You can also search for this author inPubMed Google Scholar
Corresponding author
Correspondence toBesir Sahin.
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tumse, S., Bilgili, M. & Sahin, B. Estimation of aerodynamic coefficients of a non-slender delta wing under ground effect using artificial intelligence techniques.Neural Comput & Applic34, 10823–10844 (2022). https://doi.org/10.1007/s00521-022-07013-x
Received:
Accepted:
Published:
Issue Date:
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative