用户名: 密码: 验证码:
民用飞机气动外形数值优化设计面临的挑战与展望
详细信息    查看全文 | 推荐本文 |
  • 英文篇名:Challenges and prospects of numerical optimization design for large civil aircraft aerodynamic shape
  • 作者:周铸 ; 江涛 ; 高正红 ; 黄勇 ; 陈作斌 ; 余婧
  • 英文作者:ZHOU Zhu;HUANG Jiangtao;GAO Zhenghong;HUANG Yong;CHEN Zuobin;YU Jing;Computational Aerodynamics Institute,China Aerodynamics Research and Development Center;School of Aeronautics,Northwestern Polytechnical University;
  • 关键词:综合优化体系 ; 多学科优化 ; 耦合伴随系统 ; 气动/结构优化 ; 气动/声爆优化
  • 英文关键词:integrated optimization system;;multidisciplinary optimization;;coupled adjoint system;;aero-structural optimization;;aerodynamic/sonic boom optimization
  • 中文刊名:HKXB
  • 英文刊名:Acta Aeronautica et Astronautica Sinica
  • 机构:中国空气动力研究与发展中心计算空气动力研究所;西北工业大学航空学院;
  • 出版日期:2018-08-27 16:56
  • 出版单位:航空学报
  • 年:2019
  • 期:v.40
  • 基金:国家自然科学基金(11402288);; 国家重点研发计划(2016YFB0200704)~~
  • 语种:中文;
  • 页:HKXB201901005
  • 页数:22
  • CN:01
  • ISSN:11-1929/V
  • 分类号:69-90
摘要
系统回顾了气动外形优化的主要环节,对优化体系中学科分析、参数化建模、网格重构技术、敏度分析、优化算法、代理模型、目标函数/约束处理等各个环节的进展,及气动综合优化面临的挑战、基础科学问题进行了总结。结合课题组在优化体系建设上开展的研究工作,针对民用飞机气动外形综合设计的需求,提炼了工程型号对优化体系构建的具体要求。并对今后的研究工作以及未来发展方向进行了展望与建议。通过文章系统整理论述,希望能够为气动数值优化设计研究人员提供一些有意义的建议和参考,促进设计空气动力学、以及多学科优化技术的发展。
        A systematic review of major aspects of aerodynamic shape optimization is carried out,summarizing the progress in all aspects of system optimization,including the discipline analysis,parametric method,grid deformation technology,sensitivity analysis,optimization algorithm,surrogate model,objective function/constraint processing,basic subjects and challenges of aerodynamic optimization.Combined with the research works carried out by our research team on the construction of optimization system,this paper addresses the requirement of the integrated design of the aerodynamic configuration of civil aircraft,summarizing the specific requirements of engineering type for constructing an optimized system.Prospects and suggestions for future research are also illustrated.Through the systematic discussion of the article,we hope to provide some meaningful suggestions and references for the researchers of designing aerodynamic numerical optimization,promoting the development of design aerodynamics and multidisciplinary optimization technology.
引文
[1] MARTINS J R R A.A coupled-adjoint method for highfidelity.aero-structural optimization[D].Palo Alto:Stanford University,2002:79-87.
    [2] MADER C A,KENWAY G K W,MARTINS J R R A.Towards high-fidelity aerostructural optimization using a coupled adjoint approach:AIAA-2008-5968[R].Reston,VA:AIAA,2008.
    [3] LEOVIRIYAKIT K,JAMESON A.Case studies in aerostructural wing planform and section optimization:AIAA-2004-5372[R].Reston,VA:AIAA,2004.
    [4] MOHAMMD A Z,BREZILLON J.Shape optimization using the aerostructural coupled adjoint approach for viscous flows[C]∥Proceedings of Evolutionary and Deterministic for Design,Optimization and Control,2011.
    [5] MARCELET M,PETER J,CARRIER G.Sensitivity analysis of a strongly coupled aero-structural system using direct and adjoint methods:AIAA-2008-5863[R].Reston,VA:AIAA,2008.
    [6] GHAZLANE I,CARRIER G,DUMONT A,et al.Aerostructural adjoint method for flexible wing optimization:AIAA-2012-1924[R].Reston,VA:AIAA,2012.
    [7]白俊强,孙智伟,董建鸿,等.考虑机翼尾流影响的运输类飞机后体气动外形优化设计[J].空气动力学学报,2015,33(1):134-141.BAI J Q,SUN Z W,DONG J H,et al.After body aerodynamic optimization design of transport airplane considering wing wake flow[J].Acta Aerodynamica Sinica,2015,33(1):134-141(in Chinese).
    [8]王超,高正红.小展弦比薄机翼精细化气动优化设计研究[J].中国科学:技术科学,2015,45(6):643-653.WANG C,GAO Z H.Refined aerodynamic design optimization of a wing with small aspect ratio[J].Scientia Sinica Technologica,2015,45(6):643-653(in Chinese).
    [9]李彬,邓有奇,唐静,等.基于三维非结构混合网格的离散伴随优化方法[J].航空学报,2014,35(3):674-686.LI B,DENG Y Q,TANG J,et al.Discrete adjoint optimization method for 3Dunstructured grid[J].Acta Aeronauticaet Astronautica Sinica,2014,35(3):674-686(in Chinese).
    [10]左英桃,高正红,詹浩.基于N-S方程和离散共轭方法的气动设计方法研究[J].空气动力学学报,2009,27(1):67-72.ZUO Y T,GAO Z H,ZHAN H.Aerodynamic design method based on N-S equations and discrete adjoint approach[J].Acta Aerodynamica Sinica,2009,27(1):67-72(in Chinese).
    [11]熊俊涛,乔志德,杨旭东,等.基于黏性伴随方法的跨声速机翼气动优化设计[J].航空学报,2007,28(2):281-285.XIONG J T,QIAO Z D,YANG X D,et al.Optimum aerodynamic design of transonic wing based on viscous adjoint method[J].Acta Aeronautica et Astronautica Sinica,2007,28(2):281-285(in Chinese).
    [12] HICKS R M,HENNE P A.Wing design by numerical optimization[J].Journal of Aircraft,1978,15(7):407-412.
    [13]王建军,高正红.翼型参数化方法分析及改进[J].航空计算技术,2010,40(4):46-49.WANG J J,GAO Z H.Analysis and improvement of hickshenne airfoil parameterization method[J].Aeronautical Computing Technique,2010,40(4):46-49(in Chinese).
    [14] KULFAN B M.A universal parametric geometry representation method-‘CST’:AIAA-2007-0062[R].Reston,VA:AIAA,2007.
    [15]李静,高正红,黄江涛,等.基于CST参数化方法气动优化设计研究[J].空气动力学学报,2012,30(4):443-449.LI J,GAO Z H,HUANG J T,et al.Aerodynamic optimization system based on CST technique[J].Acta Aerodynamica Sinica,2012,30(4):443-449(in Chinese).
    [16] FARIN G.Curves and surfaces for computer aided geometric design[M].New York:Academic Press,1990.
    [17] PIEGL L,TILLER W.The NURBS book[M].Berlin Heidelberg:Springer-Verlag,1997.
    [18]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社,2000.ZHU X X.Free curve and surface modeling technology[M].Beijing:Science Press,2000(in Chinese).
    [19] SAMAREH J A.Aerodynamic shape optimization based on free-form deformation:AIAA-2004-4630[R].Reston,VA:AIAA,2004.
    [20]马晓永,范召林,吴文华,等.基于NURBS方法的机翼气动外形优化[J].航空学报,2011,32(9):1616-1621.MA X Y,FAN Z L,WU W H,et al.Aerodynamic shape optimization for wing based on NURBS[J].Acta Aeronautica et Astronautica Sinica,2011,32(9):1616-1621(in Chinese).
    [21] SEDERBERG T W,PARRY S R.Free-form deformation of solid geometric models[J].Computer Graphics,1986,20(4):151-160.
    [22] LI J,GAO Z H,HUANG J T,et al.Aerodynamic design optimization of nacelle/pylon position on aircraft[J].Chinese Journal of Aeronautics,2013,26(4):850-857
    [23] HUANG J T,ZHOU Z,GAO Z H.Aerodynamic manyobjective integrated optimization based on principle components analysis[J].Chinese Journal of Aeronautics,2017,30(4):1336-1348.
    [24] LIU X Q,QIN N,XIA N.Fast dynamic grid deformation based on Delaunay graph mapping[J].Journal of Computational Physics,2006,211(2):405-423.
    [25] BUHMANN M.Radial basis functions[M].Cambridge:Cambridge University Press,2005.
    [26] WENDLAND H.Fast evaluation of radial basis functions:Methods based on partition of unity[M]∥Approximation theory X:Wavelets,splines,and applications.Nashville:Vanderbilt University Press,2002:473-483.
    [27] HUANG J T,GAO Z H,WANG C.A new grid deformation technology with high quality and robustness based on quaternion[J].Chinese Journal of Aeronautics,2014,27(5):1078-1085.
    [28]黄江涛,高正红,周铸,等.一种新型高鲁棒性动网格技术及应用[J].力学学报,2014,46(2):291-298.HUANG J T,GAO Z H,ZHOU Z,et al.A new highly robust grid deformation technique and its application[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):291-298(in Chinese).
    [29] SPEKREIJSE S P,BOERSTOEL J W.An algorithm to check the topological validity of multiblock domain decompositions:NLR-TP-98198[R].Greenwich,1998.
    [30] MARUYAMA D,BAILLY D,CARRIER G.High quality grid deformation using quaternions for orthogonality preservation[J].AIAA Journal,2012,52(12):2712-2729.
    [31] SMITH R E.Transfinite interpolation(TFI)generation systems[M]∥Handbook of grid generation.CRC Press,1999.
    [32] FARHAT C,DEGAND C,KOOBUS B,et al.Torsional springs for two-dimensional dynamic unstructured fluid grids[J].Computer Methods in Applied Mechanics and Engineering,1998,163(1):231-245.
    [33]王刚,雷博琪,叶正寅.一种基于径向基函数的非结构混合网格变形技术[J].西北工业大学学报,2011,29(5):783-788.WANG G,LEI B Q,YE Z Y.An efficient deformation technique for hybrid unstructured grid using radial basis functions[J].Journal of Northwestern Polytechnical University,2011,29(5):783-788(in Chinese).
    [34]陈宝林.最优化理论与算法[M].北京:清华大学出版社,2002:98-106.CHEN B L.Optimization theory and algorithm[M].Beijing:Tsinghua University Press,2002:98-106(in Chinese).
    [35]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1999.YUAN X Y,SUN W Y.Optimization theory and methods[M].Beijing:Science Press,1999(in Chinese).
    [36] HESTENS M R,STIEFEL E L.Methods of conjugate gradients for solving linear systems[J].Journal of Research of the National Bureau of Standards,1952,49(6):99-147.
    [37] KENNEDY J,EBERHART R.Particle swarm optimization[C]∥Proceedings of IEEE International Conference on Neural.Piscataway,NJ:IEEE Press,1995:1942-1948.
    [38] KIRKPATRICK S,GELATT C D,VECCHI M P.Optimization by simulated annealing[J].Science,1983,220:671-680.
    [39] HOLLAND J H.Adaptation in natural and artificial systems[M].MIT Press,1975.
    [40] PILLO G,GRIPPOL.A continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints[J].SIAM Journal on Control and Optimization,1984,23(1):1093-1096.
    [41] GLAD T,POLAK E.A multiplier method with automatic limitation of penalty growth[J].Mathematical Programming,1979,17:140-155.
    [42] LI X,ZHONG W T,SHAO Z J,et al.Applying extended automatic differentiation technique to process system optimization problems[J].American Control Conference,2001,5:4079-4084.
    [43] LOUIS B R.Automatic differentiation:Techniques and applications,Lecture Notes in Computer Science No.120[M].Berlin Heidelberg:Springer-Verlag,1981.
    [44] SOBIESZCZANSKI_SOBIESKI J.Sensitivity analysis and multidisciplinary optimization for aircraft design:Recent advance and results[J].Journal of Aircraft,1990,27(12):993-1001.
    [45]颜力,陈小前,王振国.飞行器多学科优化设计中的灵敏度分析方法研究[J].航空计算技术,2005,35(1):1-6.YAN L,CHEN X Q,WANG Z G.The study of sensitivity analysis in the multidisciplinary design optimization of flying vehicles[J].Aeronautical Computer Technique,2005,35(1):1-6(in Chinese).
    [46] NESTOR V Q,HAFTKA T,SHYY W,et al.Surrogate-based analysis and optimization[J].Progress in Aerospace Sciences,2005,41:1-28.
    [47] ALEXANDER I,KEANE A.Recent advances in surrogate-based optimization[J].Progress in Aerospace Sciences,2009,45:50-79.
    [48] LEDOUX S T,HERLING W W,FATTA G J.MDOPTA multidisciplinary design optimization system using higher order analysis codes:AIAA-2004-4567[R].Reston,VA:AIAA,2004.
    [49]徐家宽,白俊强,黄江涛,等.考虑螺旋桨滑流影响的机翼气动优化设计[J].航空学报,2014,35(11):2910-2920.XU J K,BAI J Q,HUANG J T,et al.Aerodynamic optimization design of wing under the interaction of propeller slipstream[J].Acta Aeronautica et Astronautica Sinica,2014,35(11):2910-2920(in Chinese).
    [50]李静,高正红,赵轲.基于直接控制FFD参数化方法的跨声速层流翼身组合体稳健性设计[J].中国科学:技术科学,2015,45(9):964-974.LI J,GAO Z H,ZHAO K.Robust design of transonic laminar wingbody configuration based on direct manipulated FFD technique[J].Scientia Sinica Technologica,2015,45(9):964-974(in Chinese).
    [51]黄江涛,高正红,白俊强,等.基于任意空间属性FFD技术的融合式翼稍小翼稳健型气动优化设计[J].航空学报,2013,34(1):37-45.HUANG J T,GAO Z H,BAI J Q,et al.Study of robust winglet design based on arbitrary space shape FFD technique[J].Acta Aeronautica et Astronautica Sinica,2013,34(1):37-45(in Chinese).
    [52]王超,高正红.小展弦比薄机翼精细化气动优化设计研究[J].中国科学:技术科学,2015,45(6):643-653.WANG C,GAO Z H.Refined aerodynamic design optimization of a wing with small aspect ratio[J].Scientia Sinica Technologica,2015,45(6):643-653(in Chinese).
    [53] FANG X M,ZHANG Y F,CHEN H X.Transonic nacelle aerodynamic optimization based on hybrid genetic algorithm:AIAA-2016-3833[R].Reston,VA:AIAA,2016.
    [54] HAN Z H,ZHANG K S,LIU J,et al.Surrogate-based aerodynamic shape optimization with application to wind turbine airfoils:AIAA-2013-1108[R]. Reston,VA:AIAA,2013.
    [55] ZHANG K S,HAN Z H,LI W J,et al.Coupled aerodynamic and structural optimization of a subsonic-transport wing using surrogate model:AIAA-2008-0897[R].Reston,VA:AIAA,2008.
    [56]黄礼铿,高正红,张德虎.基于变可信度代理模型的气动优化[J].空气动力学学报,2013,31(6):783-788.HUANG L K,GAO Z H,ZHANG D H.Aerodynamic optimization based on multi-fidelity surrogate[J].Acta Aerodynamica Sinica,2013,31(6):783-788(in Chinese).
    [57]苏伟,白俊强.一种代理模型方法及其在气动优化设计中的应用[J].弹箭与制导学报,2008,28(3):199-202.SU W,BAI J Q.A surrogate-based optimization algorithm and its application to aerodynamic optimization design[J].Journal of Projectiles,Rockets,Missiles and Guidance,2008,28(3):199-202(in Chinese).
    [58]朱莉,高正红.基于神经网络的翼型优化设计方法研究[J].航空计算技术,2007,37(3):33-36.ZHU L,GAO Z H.Aerodynamic optimization design of airfoil based on neural networks[J].Aeronautical Computing Technique,2007,37(3):33-36(in Chinese).
    [59] HUANG J T,GAO Z K,ZHAO K,et al.Robust design of supercritical wing aerodynamic optimization considering fuselage interfering[J].Chinese Journal of Aeronautics,2010,23(5):523-528.
    [60]李焦赞,高正红.多目标进化算法和代理模型技术在气动稳健优化设计中的应用[J].空气动力学学报,2012,30(1):46-51.LI J Z,GAO Z H.The application of multi-objective evolutionary algorithm and surrogate model to aerodynamic robust optimization design[J].Acta Aerodynamica Sinica,2012,30(1):46-51(in Chinese).
    [61]孙智伟,白俊强,华俊,等.基于支持向量回归代理模型的气动力优化设计[J].航空工程进展,2015,6(2):149-159.SUN Z W,BAI J Q,HUA J,et al.Aerodynamic optimal design of surrogate models based on support vector regression[J].Advances in Aeronautical Science and Engineering,2015,6(2):149-159(in Chinese).
    [62] ZHANG K,HAN Z H.Support vector regression-based multidisciplinary design optimization in aircraft conceptual design:AIAA-2013-1160[R]. Reston,VA:AIAA,2013.
    [63]韩忠华.Kriging模型及代理优化算法研究进展[J].航空学报,2016,37(11):3197-3225.HAN Z H.Kriging surrogate model and its application to design optimization:A review of recent progress[J].Acta Aeronautica et Astronautica Sinica,2016,37(11):3197-3225(in Chinese).
    [64]张德虎,高正红,王明亮.基于变可信度模型差值的低可信度模型修正方法[J].西北工业大学学报,2011,29(2):176-182.ZHANG D H,GAO Z H,WANG M L.A new and better metamodel utilizing difference between high-and low-fidelity model[J].Journal of Northwestern Polytechnical University,2011,29(2):176-182(in Chinese).
    [65]张德虎,高正红,李焦赞,等.基于双层代理模型的无人机气动隐身综合设计[J].空气动力学学报,2013,31(3):394-400.ZHANG D H,GAO Z H,LI J Z,et al.Aerodynamic and stealth synthesis design optimization of UAV based on double-stage metamodel[J].Acta Aerodynamica Sinica,2013,31(3):394-400(in Chinese).
    [66] LIU J,HAN Z H,SONG W P.Efficient kriging-based aerodynamic design of transonic airfoils:Some key issues:AIAA-2012-0967[R].Reston,VA:AIAA,2012.
    [67] ZHANG Y,HAN Z H,SHI L X,et al.Multi-round surrogate-based optimization for benchmark aerodynamic design problems:AIAA-2016-1545[R]. Reston, VA:AIAA,2016.
    [68]李焦赞,高正红.多变量气动设计问题分层协同优化[J].航空学报,2013,34(1):58-65.LI J Z,GAO Z H. Multivariable aerodynamic design based on multilevel collaborative optimization[J].Acta Aeronautica et Astronautica Sinica,2013,34(1):58-65(in Chinese).
    [69] GAO Z H,ZHAO K,WANG C.Aerodynamic shape optimization of BWB aircraft based on multi-zone collaborative optimization design method:AIAA-2015-2878[R].Reston,VA:AIAA,2015.
    [70] WANG C,GAO Z H,ZHAO K,et al.HDMR-based surrogate model for high dimensional aerodynamic design problems:AIAA-2015-3094[R].Reston,VA:AIAA,2015.
    [71]左英桃,王晓鹏,陈云,等.一种高效的CFD/CSD耦合飞行器多学科优化设计方法[J].航空动力学报,2014,29(12):2898-2904.ZUO Y T,WANG X P,CHEN Y,et al.An efficient method for multidisciplinary design optimization of aircraft based on CFD/CSD coupling[J].Journal of Aerospace Power,2014,29(12):2898-2904(in Chinese).
    [72]李焦赞,高正红.基于几何不确定性的翼型多目标稳健优化设计[J].力学学报,2011,43(3):611-615.LI J Z,GAO Z H.Multiobjective optimization methodology for airfoil robust design under geometry uncertainty[J].Chinese Journal of Theoretical and Applied Mechanics,2011,43(3):611-615(in Chinese).
    [73]王波,GEA H,白俊强,等.基于Stochastic Kriging模型的不确定性序贯试验设计方法[J].工程设计学报,2016,23(6):530-536.WANG B,GEA H,BAI J Q,et al.The uncertaintybased sequential design of experiment method based on stochastic kriging metamodel[J].Chinese Journal of Engineering Design,2016,23(6):530-536(in Chinese).
    [74] SHI L X,HAN Z H,MUHAMMAD S,et al.Surrogatebased robust airfoil design under aleatory operating-conditions and geometric uncertainties:AIAA-2016-0810[R].Reston,VA:AIAA,2016.
    [75]郑传宇,黄江涛,周铸,等.飞翼翼型高维目标空间多学科综合优化设计[J].空气动力学学报,2017,35(4):588-597.ZHENG C Y,HUANG J T,ZHOU Z,et al.Multidisciplinary optimization design of high dimensional target space for flying wing airfoil[J].Acta Aerodynamica Sinica,2017,35(4):588-597(in Chinese).
    [76] TURK M,PENTLAND A.Eigenfaces for recognition[J].Journal of Cognitive Neuroscience,1991,3(1):71-86.
    [77] ZHANG D,ZHOU Z H.(2D)2 PCA:2-directional 2-dimensional PCA for efficient face representation and recog-nition[J].Neurocomputing,2005,69:224-231.
    [78] KIM K I,PARK S H,KIM H J.Kernel principal component analysis for texture classification[J].IEEE Signal Processing Letters,2001,8(2):39-41
    [79] PADULA S L,GUMBERT C R,LI W.Aerospace applications of optimization under uncertainty[J].Optimization and Engineering,2006,7(3):317-328.
    [80] WANG X,QIU Z,SOFFER D.Uncertainty-based design optimization in engineering:model,algorithm,and application[J].Journal of Applied Mathematics,2013(8):1-2.
    [81] HU X,CHEN X,PARKS G T,et al.Review of improved monte carlo methods in uncertainty-based design optimization for aerospace vehicles[J].Progress in Aerospace Sciences,2016,86:20-27.
    [82] LEE K H,PARK G J.Robust optimization considering tolerances of design variables[J].Computers&Structures,2001,79(1):77-86.
    [83] CHEN W,SAHAI A,MESSAC A,et al.Exploration of the effectiveness of physical programming in robust design[J].Journal of Mechanical Design,2000,122(2):155-163.
    [84] CHEN W,WIECEK M M,ZHANG J.Quality utility—A compromise programming approach to robust design[J].Journal of Mechanical Design,1999,121(2):179-187.
    [85] HU X,CHEN X,LATTARULO V,et al.Multidisciplinary optimization under high-dimensional uncertainty for small satellite system design[J].AIAA Journal,2016,54(5):1-10.
    [86] TU J,CHOI K K,PARK Y H.Design potential method for robust system parameter design[J].AIAA Journal,2001,39(4):667-677.
    [87] LI P,ARELLANO-GARCIA H, WOZNY G.Chance constrained programming approach to process optimization under uncertainty[J].Computers&Chemical Engineering,2008,32(1-2):25-45.
    [88] KROESE D P,TAIMRE T,BOTEV Z I.Handbook of monte carlo methods[M].New York:John Wiley&Sons,2013.
    [89] LIU W K,TED B,MANI A.Random field finite elements[J].International Journal for Numerical Methods in Engineering,1986,23(10):1831-1845.
    [90] YAO W,CHEN X,OOUYANG Q,et al.A reliabilitybased multidisciplinary design optimization procedure based on combined probability and evidence theory[J].Structural and Multidisciplinary Optimization,2013,48(2):339-354.
    [91] MCDONALD M,ZAMAN K,MAHADEVAN S.Representation and first-order approximations for propagation of aleatory and distribution parameter uncertainty[C]∥Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Reston,VA:AIAA,2009:4-7.
    [92] MAHADEVAN S,SMITH N.Efficient first-order reliability analysis of multidisciplinary systems[J].International Journal of Reliability and Safety,2006,1(1):137-154.
    [93] MAHADEVAN S,SMITH N L,ZANG T A.System risk assessment and allocation in conceptual design[M].Washington,D.C.:National Aeronautics and Space Administration,2003.
    [94] KEWLANI G,CRAWFORD J,IAGNEMMA K.A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty[J].Vehicle System Dynamics,2012,50(5):749-774.
    [95] XIU D B,HESTHAVEN J S.High-order collocation methods for differential equations with random inputs[J].Siam Journal on Scientific Computing,2005,27(3):1118-1139.
    [96]李润泽,张宇飞,陈海昕.“人在回路”思想在飞机气动优化设计中演变与发展[J].空气动力学学报,2017,35(4):529-543.LI R Z,ZHANG Y F,CHEN H X.Evolution and development of“man-in-loop”in aerodynamic optimization design[J].Acta Aerodynamica Sinica,2017,35(4):529-543(in Chinese).
    [97]黄江涛,刘刚,周铸,等.基于离散伴随方程求解灵敏度信息的若干问题研究[J].空气动力学学报,2017,35(4):554-562.HUANG J T,LIU G,ZHOU Z,et al.Investigation of gradient computation based on discrete adjoint method[J].Act Aerodynamica Sinica,2017,35(4):554-562(in Chinese).
    [98]黄江涛,周铸,刘刚,等.飞行器气动/结构多学科延迟耦合伴随系统数值研究[J].航空学报,2018,39(5):121731.HUANG J T,ZHOU Z,LIU G,et al.Numerical study of aero-structural multidisciplinary lagged coupled adjoint system for aircraft[J].Acta Aeronautica et Astronautica Sinica,2018,39(5):121731(in Chinese).
    [99] RALLABHANDI S K.Sonic boom adjoint methodology and its applications[C]∥Proceedings of the 29th AIAA Applied Aerodynamics Conference.Reston,VA:AIAA,2011.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700