基于径向基函数网络的飞机机翼和翼梢小翼外形优化
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摘要
和一般的飞机相比,水陆两用飞机的长处在于适应性强,在水面和陆地机场都可起降,适用于海上巡逻、反潜、救援和森林灭火等任务。我国的国情是水域和岛屿众多,海岸线长达18000公里,岛屿岸线总长1.4万多公里。在我国,水陆两用飞机的应用前景十分广阔。
本文对水陆两用飞机机翼安装翼梢小翼的问题进行了研究。采用构建径向基函数网络(RBFN)的方法来对机翼和翼梢小翼的外形参数进行优化求解,主要分为以下四个步骤:第一,选定机翼和翼梢小翼的外形参数,利用改进的随机取点法选取输入样本点,建立基于径向基函数的机翼和翼梢小翼的近似模型。第二,设计了径向基函数输入样本点的迭代方法,构造了径向基函数优化网络。第三,对不同输入样本数量条件下的优化网络的优化性能进行了简单分析,为实例的优化提供了参考依据。最后针对本文的实例,目标函数为机翼诱导阻力最小,分别结合拟牛顿法和序列二次规划法,对有/无翼根弯矩约束的两种情况,进行了优化求解,取得满意的优化效果。计算结果表明,径向基函数网络方法在多变量函数拟合方面有着良好的性能,为工程应用提供一定的参考价值。
Amphibious aircraft has more adaptability than general aircraft, for it can take off and land on either land or water. It can be applied to the maritime patrol and anti-submarine, forest fire fighting and rescue missions, etc. China has numerous islands and waters. It has up to 18,000 km coastline, and it’s island shoreline is more than 14,000 km. Amphibious aircraft has very broad application in china.
An optimum method of the shape parameters for amphibious aircraft’s wing and wingtip is studied in this paper. Radial Base Function (RBF) is introduced to solve the problem. The methodology consists of major four steps. In the first, the shape parameters of wing and winglet are selected, with improved random selection method enter sample points are got, and the approximate model of wing and winglet is constructed by RBF. In the second step, the iteration of RBF’s enter sample points is designed. Firstly, the performances of RBF network with different numbers of enter sample points are studied. In the forth, optimization object is minimum of induced drag for wing,with/without the bending moment constrain at wing root,combined with sequence quadratic programming or quasi Newton methods,respectively. The results show that optimization effect is satisfied. Research for optimum design of wingtip can provide reference to engineering application.
本文对水陆两用飞机机翼安装翼梢小翼的问题进行了研究。采用构建径向基函数网络(RBFN)的方法来对机翼和翼梢小翼的外形参数进行优化求解,主要分为以下四个步骤:第一,选定机翼和翼梢小翼的外形参数,利用改进的随机取点法选取输入样本点,建立基于径向基函数的机翼和翼梢小翼的近似模型。第二,设计了径向基函数输入样本点的迭代方法,构造了径向基函数优化网络。第三,对不同输入样本数量条件下的优化网络的优化性能进行了简单分析,为实例的优化提供了参考依据。最后针对本文的实例,目标函数为机翼诱导阻力最小,分别结合拟牛顿法和序列二次规划法,对有/无翼根弯矩约束的两种情况,进行了优化求解,取得满意的优化效果。计算结果表明,径向基函数网络方法在多变量函数拟合方面有着良好的性能,为工程应用提供一定的参考价值。
Amphibious aircraft has more adaptability than general aircraft, for it can take off and land on either land or water. It can be applied to the maritime patrol and anti-submarine, forest fire fighting and rescue missions, etc. China has numerous islands and waters. It has up to 18,000 km coastline, and it’s island shoreline is more than 14,000 km. Amphibious aircraft has very broad application in china.
An optimum method of the shape parameters for amphibious aircraft’s wing and wingtip is studied in this paper. Radial Base Function (RBF) is introduced to solve the problem. The methodology consists of major four steps. In the first, the shape parameters of wing and winglet are selected, with improved random selection method enter sample points are got, and the approximate model of wing and winglet is constructed by RBF. In the second step, the iteration of RBF’s enter sample points is designed. Firstly, the performances of RBF network with different numbers of enter sample points are studied. In the forth, optimization object is minimum of induced drag for wing,with/without the bending moment constrain at wing root,combined with sequence quadratic programming or quasi Newton methods,respectively. The results show that optimization effect is satisfied. Research for optimum design of wingtip can provide reference to engineering application.
引文
[1]王武红,兰芝芳,叶树林,世界水上飞机手册,北京:航空工业出版社, 1992.
[2]宋兰珠,俄罗斯新型A—40“信天翁”水陆两用飞机,现代兵器, 1994, 11.
[3]徐华舫,空气动力学基础,北京航空学院出版社, 1986.
[4] Whitcomb R T, A design approach and selected wind-tunnel results at high subsonic speeds for wing-tip mounted winglets, NASA TND-8260, 1976.
[5] Winglets for the Airlines, NASA 1994.
[6]朱自强,吴宗成,现代飞机设计空气动力学,北京:北京航空航天大学出版社,2005.
[7] Montoga L C, Flecbner S G, Jacobs P F, Effect of Winglets on A First-generation Jet Transport Wing. NASA TND-8474, 1977.
[8] Dees P, Stowell M, 737-800 Winglet Integration, Aerospace Engineering, 2001, 21(10): 29-32.
[9]方宝瑞,飞机气动布局设计,航空工业出版社, 1997.
[10] Mccormick B W, Aerodynamics, aeronautics and flight mechanics , New York: John Wiley & Sons, 1979.
[11]傅德熏,王翼云,计算空气动力学,宇航出版社, 1994.
[12] Rumsey C L. Ying S X, Prediction of high lift: review of present CFD capability, Progress in Aerospace Sciences, 2002(38): 145-180.
[13] Lawrence C. Montoya, KC-135 Winglet Flight Results , NASA, 81N 19011, 1981
[14]周仁良,翼梢小翼的气动特性计算和实验验证,航空学报, 1984, 9: 261-266.
[15]吴希拴,师小娟,王建培,无人机翼尖小翼参数优化及风洞试验研究,飞行力学, 2004, 3: 30-36.
[16] Bourdin P, Numerical predictions of wingtip effects on lift-induced drag, ICAS Congress Toronto, 2002.
[17] Jean-Luc, Hantrais-Gervois, Marc Rapin, Aerodynamic and Structural Behaviour of a Wing Equipped with a Winglet at Cruise, AIAA 2006-1489
[18] Neal Pfeiffer, Numerical winglet optimization, AIAA Paper 2004-0213, Jan, 2004.
[19] Mark D, AVL 3.26 User Primer. MIT Department of Aeronautics and Astronautics, 2006.
[20]阎平凡,张长水,人工神经网络与模拟进化计算,清华大学出版社, 2000.
[21] Frank R, Scattered data interpolation: test of some methods, Math. Comp., 1982, 38: 181– 200.
[22]王炜,吴耿锋,张博锋等,径向基函数(RBF)神经网络及其应用,地震, 2005 ,4: 19-25.
[23]刘君,郭正,飞行器部件空气动力学,国防科技大学出版社, 2007, 7.
[24] Powell M, Radial basis function for multivariable interpolation: a review, Numerical Analysis, Eds. D. Griffiths, G. Watson. Longman Scientific & Technical, 1987, 223-241.
[25] Jackson I, Convergence properties of radial basis functions, Cons. Approx., 1988, 4: 243-264.
[26]卢涛,陈德钊,径向基网络的研究进展和评述,计算机工程及应用, 2005. 4: 60-62.
[27] Chen S, et al, Orthogonal Least Square Learning Algorithm for RBF Networks, IEEE Trans NN, 1991, 2: 302-3.9.
[28] Wei Haikun, Xu Sixin, Song Wenzhong, An Evolutionary selecting Algorithm for Designing Minimal RBF nets, Control Theory & Applications, 2000, 17(4):604-608.
[29]李艳军,吴铁军,赵明旺,一种新的RBF神经网络非线性动态系统建模方法,系统工程理论与实践, 2001, 3:64-69.
[30]吴宗敏,函数的径向基表示,数学进展, 1998, 6: 202-208.
[31]袁亚湘,孙文瑜,最优化理论与方法,科学出版社,2003.
[32]宋坤,刘锐宁,李伟明, Visual C++开发技术大全,人民邮电出版社2007, 3.
[33] Al Stevens Clayton Walnum,标准C++宝典,林丽闽,别红霞等译,电子工业出版社, 2001, 2.
[34]彭国伦, FORTRAN95程序设计,中国电力出版社, 2002, 9.
[35] Schaback R, Error estimates and condition numbers for radian basis function inter- polation , Adv. Comput. Math., 1995, 3: 251– 264.
[36]张志涌,精通Matlab6.5,北京航空航天大学出版社,2003, 03.
[37] Krzysztof Kubrynski, Wing-Winglet Design Methodology for Low Speed Applications, AIAA 2003-215.
[38] John M. Kuhlman, Christopher K. Brown, Computational Design of Low Aspect Ratio Wing-winglet Configurations for Transonic Wind-Tunnel Tests, NASA-CR-181939, 1989.
[39] Leigh Ann Smith, Richard L Campbell, Effects of Winglets on the Drag of a Low-Aspect-Ratio Configuration, NASA 1996.
[40] Richard T, Whitcomb, A Design Approach and Selected Wing-tunnel Results at High Subsonic speeds for Wing-tip Mounted Winglets, NASA TND-8260, 1976.
[2]宋兰珠,俄罗斯新型A—40“信天翁”水陆两用飞机,现代兵器, 1994, 11.
[3]徐华舫,空气动力学基础,北京航空学院出版社, 1986.
[4] Whitcomb R T, A design approach and selected wind-tunnel results at high subsonic speeds for wing-tip mounted winglets, NASA TND-8260, 1976.
[5] Winglets for the Airlines, NASA 1994.
[6]朱自强,吴宗成,现代飞机设计空气动力学,北京:北京航空航天大学出版社,2005.
[7] Montoga L C, Flecbner S G, Jacobs P F, Effect of Winglets on A First-generation Jet Transport Wing. NASA TND-8474, 1977.
[8] Dees P, Stowell M, 737-800 Winglet Integration, Aerospace Engineering, 2001, 21(10): 29-32.
[9]方宝瑞,飞机气动布局设计,航空工业出版社, 1997.
[10] Mccormick B W, Aerodynamics, aeronautics and flight mechanics , New York: John Wiley & Sons, 1979.
[11]傅德熏,王翼云,计算空气动力学,宇航出版社, 1994.
[12] Rumsey C L. Ying S X, Prediction of high lift: review of present CFD capability, Progress in Aerospace Sciences, 2002(38): 145-180.
[13] Lawrence C. Montoya, KC-135 Winglet Flight Results , NASA, 81N 19011, 1981
[14]周仁良,翼梢小翼的气动特性计算和实验验证,航空学报, 1984, 9: 261-266.
[15]吴希拴,师小娟,王建培,无人机翼尖小翼参数优化及风洞试验研究,飞行力学, 2004, 3: 30-36.
[16] Bourdin P, Numerical predictions of wingtip effects on lift-induced drag, ICAS Congress Toronto, 2002.
[17] Jean-Luc, Hantrais-Gervois, Marc Rapin, Aerodynamic and Structural Behaviour of a Wing Equipped with a Winglet at Cruise, AIAA 2006-1489
[18] Neal Pfeiffer, Numerical winglet optimization, AIAA Paper 2004-0213, Jan, 2004.
[19] Mark D, AVL 3.26 User Primer. MIT Department of Aeronautics and Astronautics, 2006.
[20]阎平凡,张长水,人工神经网络与模拟进化计算,清华大学出版社, 2000.
[21] Frank R, Scattered data interpolation: test of some methods, Math. Comp., 1982, 38: 181– 200.
[22]王炜,吴耿锋,张博锋等,径向基函数(RBF)神经网络及其应用,地震, 2005 ,4: 19-25.
[23]刘君,郭正,飞行器部件空气动力学,国防科技大学出版社, 2007, 7.
[24] Powell M, Radial basis function for multivariable interpolation: a review, Numerical Analysis, Eds. D. Griffiths, G. Watson. Longman Scientific & Technical, 1987, 223-241.
[25] Jackson I, Convergence properties of radial basis functions, Cons. Approx., 1988, 4: 243-264.
[26]卢涛,陈德钊,径向基网络的研究进展和评述,计算机工程及应用, 2005. 4: 60-62.
[27] Chen S, et al, Orthogonal Least Square Learning Algorithm for RBF Networks, IEEE Trans NN, 1991, 2: 302-3.9.
[28] Wei Haikun, Xu Sixin, Song Wenzhong, An Evolutionary selecting Algorithm for Designing Minimal RBF nets, Control Theory & Applications, 2000, 17(4):604-608.
[29]李艳军,吴铁军,赵明旺,一种新的RBF神经网络非线性动态系统建模方法,系统工程理论与实践, 2001, 3:64-69.
[30]吴宗敏,函数的径向基表示,数学进展, 1998, 6: 202-208.
[31]袁亚湘,孙文瑜,最优化理论与方法,科学出版社,2003.
[32]宋坤,刘锐宁,李伟明, Visual C++开发技术大全,人民邮电出版社2007, 3.
[33] Al Stevens Clayton Walnum,标准C++宝典,林丽闽,别红霞等译,电子工业出版社, 2001, 2.
[34]彭国伦, FORTRAN95程序设计,中国电力出版社, 2002, 9.
[35] Schaback R, Error estimates and condition numbers for radian basis function inter- polation , Adv. Comput. Math., 1995, 3: 251– 264.
[36]张志涌,精通Matlab6.5,北京航空航天大学出版社,2003, 03.
[37] Krzysztof Kubrynski, Wing-Winglet Design Methodology for Low Speed Applications, AIAA 2003-215.
[38] John M. Kuhlman, Christopher K. Brown, Computational Design of Low Aspect Ratio Wing-winglet Configurations for Transonic Wind-Tunnel Tests, NASA-CR-181939, 1989.
[39] Leigh Ann Smith, Richard L Campbell, Effects of Winglets on the Drag of a Low-Aspect-Ratio Configuration, NASA 1996.
[40] Richard T, Whitcomb, A Design Approach and Selected Wing-tunnel Results at High Subsonic speeds for Wing-tip Mounted Winglets, NASA TND-8260, 1976.