Review

A review of unsteady aerodynamic modeling of aircrafts at high angles of attack

  • WANG Qing ,
  • QIAN Weiqi ,
  • DING Di
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  • 1. State Key Laboratory of Aerodynamics of China Aerodynamics Research and Development Center, Mianyang 621000, China;
    2. Computational Aerodynamics Institute of China Aerodynamics Research and Development Center, Mianyang 621000, China

Received date: 2016-01-11

  Revised date: 2016-03-07

  Online published: 2016-04-05

Abstract

Accurate unsteady aerodynamic models are the basis of control law design, flight dynamics analysis, and flight simulation of aircraft at high angles of attack. The advances in high angle-of-attack unsteady aerodynamic modeling are reviewed systematically. The developed modeling methods can be classed into two categories:mathematic methods and artificial intelligent methods. The mathematic models include those in the form of aerodynamic derivatives, nonlinear indicial response, internal state-space, differential equations, hybrid representation of nonlinear indicial response and internal state-space, flow incidence rate, etc. They are based on the understanding of unsteady flow phenomenon and mechanism. The intelligent methods, including fuzzy logic, neural networks, and support vector machines, avoid the complicated flow mechanism and are suitable to black-box system modeling especially. For individual aerodynamic models, their modeling ideas and methods and typical applications are described, and brief comments on their distinguishing features and limitations are put forward as well. Finally, the problems in current unsteady aerodynamic modeling researches and the future development directions are indicated.

Cite this article

WANG Qing , QIAN Weiqi , DING Di . A review of unsteady aerodynamic modeling of aircrafts at high angles of attack[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016 , 37(8) : 2331 -2347 . DOI: 10.7527/S1000-6893.2016.0072

References

[1] ABZUG M J. Airplane stability and control[M]. Cambridge:Cambridge University Press, 1977:108-121.
[2] ETKIN B, REID L D. Dynamics of atmospheric flight:stability and control[M]. New York:John Wiley & Sons Inc, 1972:264-293.
[3] BRANDON J M, FOSTER J V. Recent dynamic measurements and considerations for aerodynamic modeling of fighter airplane configurations:AIAA-1998-4447[R]. Reston:AIAA, 1998.
[4] GREENWELL D I. Frequency effects on dynamic stability derivatives obtained from small-amplitude oscillatory testing[J]. Journal of Aircraft, 1998, 35(5):776-783.
[5] LIN G F, LAN C E. A generalized dynamic aerodynamic coefficient model for flight dynamics applications:AIAA-1997-3643[R]. Reston:AIAA, 1997.
[6] TOBAK M. On the use of the indicial function concept in the analysis of unsteady motion of wings and wing-tail combinations:NACA R-1188[R]. Washington, D.C.:NACA, 1954.
[7] TOBAK M, PEARSON W E. A study of nonlinear longitudinal dynamic stability:NASA TR R-209[R]. Washington, D.C.:NASA, 1964.
[8] TOBAK M. On nonlinear longitudinal dynamic stability[G]. AGARD CP-17, Part 1, Neuilly Sur Seine:AGARD, 1966.
[9] TOBAK M, SCHIFF L B. On the formulation of the aerodynamics in aircraft dynamics:NASA TR R-456[R]. Washington, D.C.:NASA, 1976.
[10] SCHIFF L B, TOBAK M, MALCOLM G N. Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers:AIAA-1980-1583[R]. Reston:AIAA, 1980.
[11] TOBAK M, SCHIFF L B. Aerodynamic mathematical modeling basic concepts[G]. AGARD LS-114, Lecture No.1, Neuilly Sur Seine:AGARD, 1981.
[12] TOBAK M, CHAPMAN G T, SCHIFF L B. Mathematical modeling of the aerodynamic characteristics in flight dynamics:NASA TM-85880[R]. Washington, D.C.:NASA, 1984.
[13] VOLTERRA V. Theory of functional and of integral and integro-differential equations[M]. New York:Dover Publications, Inc., 1959:23-28.
[14] TOBAK M, SCHIFF L B. The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics[G]. AGARG CP-235, Paper No.26, Neuilly Sur Seine:AGARD, 1978.
[15] TOBAK M, CHAPMAN G T, UNAL A. Modeling aerodynamic discontinuities and the onset of chaos in flight dynamical systems:NASA TM-89420[R]. Washington, D.C.:NASA, 1986.
[16] SINGH R, BAEDER J. Direct calculation of three-dimensional indicial lift response using computational fluid dynamics[J]. Journal of Aircraft, 1997, 34(4):465-471.
[17] GHOREYSHI M, CUMMINGS R M, DaRonch A, et al. Transonic aerodynamic load modeling of X-31 aircraft pitching motions[J]. AIAA Journal, 2013, 51(10):2447-2464.
[18] GHOREYSHI M, JIRASEK A, CUMMINGS R M. Reduced order unsteady aerodynamic modeling for stability and control analysis using computational fluid dynamics[J]. Progress of Aerospace Science, 2014, 71:167-217.
[19] GUPTA N K, ILIFF K W. Identification of aerodynamic indicial functions using flight data:AIAA-1982-1375[R]. Reston:AIAA, 1982.
[20] GUPTA N K, ILIFF K W. Identification of integro-differential system for application to unsteady aerodynamics and aeroelasticity:AIAA-1985-1763[R]. Reston:AIAA, 1985.
[21] KLEIN V, NODERER K D. Modeling of aircraft unsteady aerodynamic characteristics, Part 1-postulated models:NASA TM-109120[R]. Washington, D.C.:NASA, 1994.
[22] KLEIN V, NODERER K D. Modeling of aircraft unsteady aerodynamic characteristics, Part 2-parameter estimated from wind tunnel data:NASA TM-110161[R]. Washington, D.C.:NASA, 1995.
[23] KLEIN V, NODERER K D. Modeling of aircraft unsteady aerodynamic characteristics, Part 3-Parameter estimated from flight data:NASA TM-110259[R]. Washington, D.C.:NASA, 1996.
[24] KLEIN V, MURPHY P C, CURRY T J, et al. Analysis of wind tunnel longitudinal static and oscillatory data of the F-16XL aircraft:NASA TM-97-206276[R]. Washington, D.C.:NASA, 1997.
[25] KLEIN V, MURPHY P C. Estimation of aircraft nonlinear unsteady parameters from wind tunnel data:NASA TM-1998-208969[R]. Washington, D.C.:NASA, 1998.
[26] SMITH M S. Analysis of wind tunnel oscillatory data of the X-31A aircraft:NASA CR-1999-208725[R]. Washington, D.C.:NASA, 1999.
[27] MURPHY P C, KLEIN V. Estimation of aircraft nonlinear unsteady parameters from dynamic wind tunnel testing:AIAA-2001-4016[R]. Reston:AIAA, 2001.
[28] REISENTHEL P H. Development of a nonlinear indicial model for maneuvering fighter aircraft:AIAA-1996-0896[R]. Reston:AIAA, 1996.
[29] REISENTHEL P H. Application of nonlinear indicial model to the prediction of a dynamically stalling wing:AIAA-1996-2493[R]. Reston:AIAA, 1996
[30] REISENTHEL P H, BETTENCOURT M T, MYATT J H, et al. A nonlinear indicial prediction tool for unsteady aerodynamic modeling:AIAA-1998-4350[R]. Reston:AIAA, 1998.
[31] REISENTHEL P H, BETTENCOURT M T. Data-based aerodynamic modeling using nonlinear indicial theory:AIAA-1999-0763[R]. Reston:AIAA, 1999.
[32] REISENTHEL P H, BETTENCOURT M T. Extraction of nonlinear indicial and critical state responses from experimental data:AIAA-1999-0764[R]. Reston:AIAA, 1999.
[33] Гоман, М Г, Столяров Г И, Тартышников С Л, et al. Описание продольных аэродинамичес характеристик самолета гольших углах атак с учтом динамических зффектов отривного обтекания[C]//Издательский Отдел ЦАГИ, Препринт No.9. Москва:ЦАГИ, 1990. GOMAN M G, KHRABROV A N, STOLYAROV G I, et al. Mathematical description of longitudinal aerodynamic characteristics of an aircraft at high angles of attack with accounting for dynamic effects of separated flow[C]//Preprint of TsAGI, No.9. Moscow:TsAGI, 1990(in Russian).
[34] GOMAN M, KHRABROV A. State-space representation of aerodynamic characteristics of an aircraft at high angles of attack:AIAA-1992-4651[R]. Reston:AIAA, 1992.
[35] GOMAN M G, KHRABROV A N, USOLTSEV S P. Unsteady aerodynamic model for large amplitude maneuvers and its parameter identification[C]//The International Federation of Automatic Control, 11th IFAC Symposium on System Identification. Kitakyushu:IFAC, 1997:399-404.
[36] Гоман, М Г. Математическое Описамие Азродинамических и Моментов на Неустановившихся Режимах Обтекания Неединственной Структурой[C]//Труды ЦАГИ, Выпуск 2195. Москва:ЦАГИ, 1983. GOMAN M G. Mathematical description of aerodynamic forces and moments at nonstationary flow regimes with a nonunique structure[C]//Proceedings of TsAGI, Issue 2195. Moscow:TsAGI, 1983(in Russian).
[37] LAN C E, HSU C H. Effects of vortex breakdown on longitudinal and lateral-directional aerodynamics of slender wings by the suction analogy:AIAA-1982-1385[R]. Reston:AIAA, 1982.
[38] Головкин М А, Горбань В П, Ефремов А А, Симусева Е В. Гистереэисные Явления в Положении Областей Взрыва Вихрей при Нестционарных Движениях Треугольного Крыла[C]//Труды ЦАГИ, Выпуск 2319. Москва:ЦАГИ, 1986. GOLOVKIN M A, GORBAN V P, YEFREMOV A A, et al. Hysteretic phenomena in vortex burst region position at nonstationary delta wing motions[C]//Proceedings of TsAGI, Issue 2319. Moscow:TsAGI, 1986(in Russian).
[39] ABRAMOV N B, GOMAN M G, KHRABROV A N, et al. Simple wings unsteady aerodynamics at high angles of attack-experimental and modeling results:AIAA-1999-4013[R]. Reston:AIAA, 1999.
[40] ABRAMOV N B, GOMAN M G, GREENWELL D I, et al. Two-step linear regression method for identification of high incidence unsteady model:AIAA-2001-4080[R]. Reston:AIAA, 2001.
[41] FAN Y G, LUTZE F H. Identification of an unsteady aerodynamic model at high angles of attack:AIAA-1996-3407[R]. Reston:AIAA, 1996.
[42] FAN Y G. Identification of an unsteady aerodynamic model up to high angle of attack regime[D]. Blacksburg, VA:Virginia Polytechnic Institute and State University, 1997.
[43] LUTZE F H, FAN Y G, STAGG G. Multiaxis Unsteady Aerodynamic Characteristics of an Aircraft:AIAA-1999-4011[R]. Reston:AIAA, 1999.
[44] 高正红, 焦天峰. 飞行器快速俯仰产生大迎角非定常气动力数学模型研究[J]. 西北工业大学学报, 2001, 19(4):506-510. GAO Z H, JIAO T F. On an unsteady aerodynamics model for pitching-oscillating body at high angle of attack[J]. Journal of Northwestern Polytechnical University, 2001, 19(4):506-510(in Chinese).
[45] JIAO T F, GAO Z H. Unsteady aerodynamic modeling at high angles of attack:AIAA-2000-3908[R]. Reston:AIAA, 2000.
[46] GREENWELL D I. A review of unsteady aerodynamic modeling for flight dynamics of maneuverable aircraft. AIAA-2004-5276[R]. Reston:AIAA, 2004.
[47] FISCHENBERG D. Identification of an unsteady aerodynamic stall model from flight test data:AIAA-1995-3438[R]. Reston:AIAA, 1995.
[48] SINGH J, JATEGAONKAR R V. Flight determination of configurational effects on aircraft stall behavior:AIAA-1996-3441[R]. Reston:AIAA, 1996.
[49] JATEGAONKAR R V, MONNICH W. Identification of DO-328 aerodynamic database for a Level D flight simulator:AIAA-1997-3729[R]. Reston:AIAA, 1997.
[50] SINGH J, JATEGAONKAR R V. Identification of lateral-direction behavior in stall from flight data[J]. Journal of Aircraft, 1996, 33(3):627-630.
[51] PASHILKAR A A, PRADEEP S. Unsteady aerodynamic modeling using multivariate orthogonal polynomials:AIAA-1999-4014[R]. Reston:AIAA, 1999.
[52] 汪清, 蔡金狮. 飞机大迎角非定常气动力建模与辨识[J]. 航空学报, 1996, 17(4):391-398. WANG Q, CAI J S. Unsteady aerodynamic modeling and identification of airplane at high angles of attack[J]. Acta Aeronautica et Astronautica Sinica, 1996, 17(4):391-398(in Chinese).
[53] CAI J S, WANG Q. Nonlinear unsteady aerodynamic mathematical models for aircraft[C]//Proceedings of the First Asian Computational Fluid Dynamics Conference. Hong Kong:The Hong Kong University, 1995:273-280.
[54] HE K F, WANG Q, CAI J S. Unsteady aerodynamic models at high angles-of-attack and their application to numerical simulation of post stall maneuvers[C]//Proceedings of the 6th Sino-Russian Symposium on Aerodynamics. Moscow:TsAGI, 1997:146-157.
[55] 汪清. 飞机大迎角非定常气动力建模及其应用研究[D]. 西安:西北工业大学, 1994. WANG Q. Unsteady aerodynamic modeling of aircraft at high angles of attack and its applications[D]. Xi'an:Northwestern Polytechnical University, 1994(in Chinese).
[56] 汪清, 何开锋, 钱炜祺, 等. 飞机大迎角空间机动气动力建模研究[J]. 航空学报, 2004, 25(5):447-451. WANG Q, HE K F, QIAN W Q, et al. Aerodynamic modeling of spatial maneuvering aircraft at high angle of attack[J]. Acta Aeronautica et Astronautica Sinica, 2004, 25(5):447-451(in Chinese).
[57] ABRAMOV N B, GOMAN M G, KHRABROV A N. Aircraft dynamics at high incidence flight with account of unsteady aerodynamic effects:AIAA-2004-5274[R]. Reston:AIAA, 2004.
[58] CHIN S, LAN C E. Fourier functional analysis for unsteady aerodynamic modeling[J]. AIAA Journal, 1992, 30(9):2259-2266.
[59] HU C C, LAN C E, BRANDON J. Unsteady aerodynamic modeling for maneuvering aircraft:AIAA-1993-3626[R]. Reston:AIAA, 1993.
[60] PESKETT J P. The development of unsteady aerodynamic mathematical models[D]. Bristol:University of Bristol, 1998.
[61] 黄达, 李志强, 吴根兴. 大振幅非定常实验数学模型与动导数仿真实验. 空气动力学学报, 1999, 17(2):219-223. HUANG D, LI Z Q, WU G X. Dynamic derivative simulation and mathematical model of the wind tunnel test about a model pitching in very large amplitude[J]. Acta Aerodynamica Sinica, 1999, 17(2):219-223(in Chinese).
[62] 姜裕标, 沈礼敏. 非定常气动力试验与建模研究[J]. 流体力学实验与测量, 2000, 14(4):26-31. JIANG Y B, SHEN L M. An experimental investigation on unsteady aerodynamics and modeling for a fighter configuration[J]. Experiments and Measurements In Fluid Mechanics, 2000, 14(4):26-31(in Chinese).
[63] 赵磊. 大迎角气动力预示方法研究[D]. 北京:北京空气动力研究所, 1997. ZHAO L. Prediction methods of aerodynamics at high angles of attack[D]. Beijing:Beijing Aerodynamics Institute, 1997(in Chinese).
[64] 杨小平, 孙秀佳. 飞机大迎角机动非线性气动力模型的辨识[J]. 飞行力学, 1998, 16(1):37-42. YANG X P, SUN X J. Identification of nonlinear aerodynamic model for maneuvering aircraft at high angle of attack[J]. Flight Dynamics, 1998, 16(1):37-42(in Chinese).
[65] HUANG X Z, LOU H Y, HANFF E S. Nonlinear indicial response and internal state-space representation for free-to-roll trajectory prediction of 65° delta wing at high incidence:AIAA-2002-4713[R]. Reston:AIAA, 2002.
[66] HUANG X Z, HANFF E S. Hysteresis and bifurcation analysis of a fighter and a delta wing at high incidence:AIAA-2002-4714[R]. Reston:AIAA, 2002.
[67] HUANG X Z. Nonlinear indicial response/internal state-space representation and its application on delta wing aerodynamics:AIAA-2003-3944[R]. Reston:AIAA, 2003.
[68] PASHILKAR A A. Unsteady aerodynamic modeling at high incidence for flight dynamic analysis:AIAA-2001-4079[R]. Reston:AIAA, 2001.
[69] PASHILKAR A A. Flow incidence rate model for unsteady aerodynamics at high angles of attack:AIAA-2001-2469[R]. Reston:AIAA, 2001.
[70] PASHILKAR A A. Flight dynamic analysis of the flow incidence rate model:AIAA-2002-0098[R]. Reston:AIAA, 2002.
[71] ROKHSAZ K, STECK J E. Use of neural network in control of high-alpha maneuvers[J]. Journal of Guidance, Control, and Dynamics, 1993, 16(5):934-939.
[72] ROKHSAZ K, STECK J E. Application of artificial neural networks in nonlinear aerodynamics and aircraft design[J]. Journal of Aerospace, 1993, 102:1790-1798.
[73] WANG Q, WU K Y, ZHANG T J, et al. Aerodynamic modeling and parameter estimation from the QAR data of an airplane approaching high-altitude airport[J]. Chinese Journal of Aeronautics, 2012, 25(3):361-371.
[74] WANG Q, HE K F, QIAN W Q, et al. Unsteady aerodynamics modeling for flight dynamics application[J]. Acta Mechanica Sinica, 2012, 28(1):14-23.
[75] 龚正, 沈宏良. 非定常气动力的结构自适应神经网络建模方法[C]//中国航空学会第22届飞行力学与飞行试验学术交流会论文集. 北京:中国航空学会, 2006:67-71. GONG Z, SHEN H L. Unsteady aerodynamic modeling method using structural adaptive neural network[C]//Proceedings of the 22th Chinese Symposium on Flight Dynamics and Flight Tests. Beijing:Chinese Society of Aeronautics and Astronautics, 2006:67-71(in Chinese).
[76] WANG Z, LAN C E, BRANDON J M. Fuzzy logic modeling of nonlinear unsteady aerodynamics:AIAA-1998-4351[R]. Reston:AIAA, 1998.
[77] WANG Z, LAN C E, BRANDON J M. Fuzzy logic modeling of lateral-directional unsteady aerodynamics:AIAA-1999-4012[R]. Reston:AIAA, 1998.
[78] WANG Z, LI J, LAN C E, et al. Estimation of unsteady aerodynamic models from flight test data:AIAA-2001-4017[R]. Reston:AIAA, 2001.
[79] WANG Z, LAN C E, BRANDON J M. Estimation of lateral-directional unsteady aerodynamic models from flight test data:AIAA-2002-4626[R]. Reston:AIAA, 2002.
[80] LAN C E, LI J, YAU W, et al. Longitudinal and lateral-directional coupling effects on nonlinear unsteady aerodynamic modeling from flight data:AIAA-2002-4804[R]. Reston:AIAA, 2002.
[81] PAN C, LAN C E. Estimation and analysis of unsteady aerodynamic models of a jet transport by a fuzzy logic algorithm using flight-data-recorder data:AIAA-2002-4494[R]. Reston:AIAA, 2002.
[82] WENG C T, HO C H, LAN C E. Aerodynamic model estimation and analysis for a jet transport in a landing accident:AIAA-2003-5699[R]. Reston:AIAA, 2003.
[83] LI J, LAN C E. Unsteady aerodynamic modeling of aircraft response to atmospheric turbulence:AIAA-2001-4017[R]. Reston:AIAA, 2001.
[84] 尹江辉, 刘昶. 一种非定常气动力的模糊逻辑模型[C]//中国2000年飞行力学与飞行试验学术年会论文集. 北京:中国航空学会, 2000:222-229. YIN J H, LIU C. Fuzzy logic model of unsteady aerodynamics[C]//Proceedings of Chinese Symposium on Flight Dynamics and Flight Tests. Beijing:Chinese Society of Aeronautics and Astronautics, 2000:222-229(in Chinese).
[85] 史志伟, 吴根兴. 多变量非线性非定常气动力的模糊逻辑模型[J]. 空气动力学学报, 2001, 19(1):103-108. SHI Z W, WU G X. Fuzzy logic model of nonlinear unsteady aerodynamics with multiple variables[J]. Acta Aerodynamica Sinica, 2001, 19(1):103-108(in Chinese).
[86] 刘志涛. 孙海生, 姜裕标, 等. 非线性非定常气动力的模糊逻辑建模方法[J]. 实验流体力学, 2005, 19(1):99-103. LIU Z T, SUN H S, JIANG Y B, et al. Fuzzy logic modeling of nonlinear unsteady aerodynamics[J]. Journal of Experiments in Fluid Mechanics, 2005, 19(1):99-103(in Chinese).
[87] 刘志涛. 大迎角非定常气动力试验和建模研究[D]. 绵阳:中国空气动力研究与发展中心, 2004. LIU Z T. Experiment and modeling of unsteady aerodynamics at high angles of attack[D]. Mianyang:China Aerodynamics Research and Development Center, 2004(in Chinese).
[88] 孔轶男, 何开锋, 钱伟祺, 等. 非定常气动力建模的模糊逻辑方法[C]//飞行力学与飞行试验学术交流年会论文集. 北京:中国航空学会, 2004:82-86. KONG Y N, HE K F, QIAN W Q, et al. Fuzzy logic method for unsteady aerodynamic modeling[C]//Proceedings of Chinese Symposium on Flight Dynamics and Flight Tests. Beijing:Chinese Society of Aeronautics and Astronautics, 2004:82-86(in Chinese).
[89] 孔轶男. 气动力建模的模糊逻辑方法[D]. 绵阳:中国空气动力研究与发展中心, 2005. KONG Y N. Fuzzy logic technique of aerodynamic modeling[D]. Mianyang:China Aerodynamics Research and Development Center, 2005(in Chinese).
[90] VAPNIK V. The nature of statistical learning theory[M]. New York:Springer-Verlag, 1995:161-206.
[91] SUYKENS J A K, VANDEWALLE J. Least squares support vector machine classifiers[J]. Neural Processing Letters, 1999, 9(3):293-300.
[92] CHEN Y L. Modeling of longitudinal unsteady aerodynamics at high angle-of-attack based on support vector machines[C]//Proceedings of the 8th International Conference on Natural Computation. New York:IEEE, 2012:431-435.
[93] WANG Q, QIAN W Q, HE K F. Unsteady aerodynamic modeling at high angles of attack using support vector machines[J]. Chinese Journal of Aeronautics, 2015, 28(3):659-668.4714[R], Reston: AIAA, 2002.
[67]Huang X Z.Nonlinear indicial response/internal state-space representation and its application on delta wing aerodynamics. AIAA 2003-3944[R], Reston: AIAA, 2003.
[68]Pashilkar A A.Unsteady Aerodynamic modeling at high Incidence for flight dynamic analysis. AIAA 2001-4079[R], Reston: AIAA, 2001.
[69]Pashilkar A A.Flow incidence rate model for unsteady aerodynamics at high angles of attack. AIAA 2001-2469[R], Reston: AIAA, 2001.
[70]Pashilkar A A.Flight dynamic analysis of the flow incidence rate model. AIAA 2002-0098[R], Reston: AIAA, 2002.
[71]Rokhsaz K, Steck J E.Use of neural network in control of high-alpha maneuvers[J].Journal of Guidance, Control, and Dynamics, 1993, 16(5):934-939
[72]Rokhsaz K, Steck J E.Application of artificial neural networks in nonlinear aerodynamics and aircraft design. Journal of Aerospace, 1993, 102: 1790-1798.
[73]Wang Q, Wu K Y, Zhang T J, et al.Aerodynamic modeling and parameter estimation from the QAR data of an airplane approaching high-altitude airport[J].Chinese Journal of Aeronautics, 2012, 25(3):361-371
[74]Wang Q, He K F, Qian W Q, et al.Unsteady aerodynamics modeling for flight dynamics application[J].ACTA Mechanica Sinica, 2012, 28(1):14-23
[75]龚正, 沈宏良.非定常气动力的结构自适应神经网络建模方法. 中国航空学会第22届飞行力学与飞行试验学术交流会论文集, 2006, 67-71.
[76]Wang Z, Lan C E, Brandon J M.Fuzzy logic modeling of nonlinear unsteady aerodynamics. AIAA 98-4351[R], Reston: AIAA, 1998.
[77]Wang Z, Lan C E, Brandon J M.Fuzzy logic modeling of lateral-directional unsteady aerodynamics. AIAA 99-4012[R], Reston: AIAA, 1998.
[78]Wang Z, Li J, Lan C E, et al.Estimation of unsteady aerodynamic models from flight test data. AIAA 2001-4017[R], Reston: AIAA, 2001.
[79]Wang Z, Lan C E, Brandon J M.Estimation of lateral-directional unsteady aerodynamic models from flight test data. AIAA 2002-4626[R], Reston: AIAA, 2002.
[80]Lan C E, Li J, Yau W, et al.Longitudinal and lateral-directinal coupling effects on nonlinear unsteady aerodynamic modeling from flight data. AIAA 2002-4804[R], Reston: AIAA, 2002.
[81]Pan C, Lan C E.Estimation and analysis of unsteady aerodynamic models of a jet transport by a fuzzy logic algorithm using flight-data-recorder data. AIAA 2002-4494[R], Reston: AIAA, 2002.
[82]Weng C-T, Ho C-H, Lan C E.Aerodynamic model estimation and analysis for a jet transport in a landing accident. AIAA 2003-5699[R], Reston: AIAA, 2003.
[83]Li J, Lan C E.Unsteady aerodynamic modeling of aircraft response to atmospheric turbulence. AIAA 2001-4017[R], Reston: AIAA, 2001.
[84]尹江辉, 刘昶.一种非定常气动力的模糊逻辑模型[C]. 中国2000年飞行力学与飞行试验学术年会论文集, 2000, 222-229.
[85]史志伟, 吴根兴.多变量非线性非定常气动力的模糊逻辑模型[J].空气动力学学报, 2001, 19(1):103-108
[86]刘志涛.孙海生, 姜裕标等非线性非定常气动力的模糊逻辑建模方法[J].实验流体力学, 2005, 19(1):99-103
[87] 刘志涛.大迎角非定常气动力试验和建模研究[D]. 绵阳: 中国空气动力研究与发展中心, 2004.
[88]孔轶男, 何开锋, 钱伟祺等:非定常气动力建模的模糊逻辑方法[C].飞行力学与飞行试验学术交流年会论文集, 2004, 82-86.
[89]孔轶男.气动力建模的模糊逻辑方法[D]. 绵阳: 中国空气动力研究与发展中心, 2005.
[90] Vapnik V.The nature of statistical learning theory[M]. New York: Springer-Verlag, 1995.
[91]Suykens J A K, Vandewalle J.Least squares support vector machine classifiers[J].Neural Processing Letters (S), 1999, 9(3):293-300
[92] Chen Y L.Modeling of longitudinal unsteady aerodynamics at high angle-of-attack based on support vector machines[C]. Proceedings of the 8th International Conference on Natural Computation, IEEE, 2012, 431-435.
[93]Wang Q, Qian W Q, He K F.Unsteady aerodynamic modeling at high angles of attack using support vector machines[J].Chinese Journal of Aeronautics, 2015, 28(3):659-668
[94]Murch A M, Foster J V.Recent NASA research on aerodynamic modeling of post-stall and spin dynamics of large transport airplanes. AIAA 2007-463[R], Reston: AIAA, 2007.

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