CJA ENGLISH

导航

联系我们
学术质量   |
广告服务   |
期刊征订   |
English Version CJA

航空学报 >

2020 , Vol. 41 >Issue 5: 623404 - 623404

DOI: https://doi.org/10.7527/S1000-6893.2019.23404

飞行器气动外形数值优化与设计专栏

飞行器多学科耦合伴随体系的现状与发展趋势综述

  • 黄江涛 ,
  • 刘刚 ,
  • 高正红 ,
  • 周铸 ,
  • 陈作斌 ,
  • 江雄
展开
  • 1. 中国空气动力研究与发展中心, 绵阳 621000;
    2. 西北工业大学 航空学院, 西安 710072

收稿日期: 2019-08-26

  修回日期: 2019-09-10

  网络出版日期: 2019-10-10

基金资助

国家自然科学基金（11402288）；国家重点研发计划（2016YFB0200704）

收起

Current situation and development trend of multidisciplinary coupled adjoint system for aircraft

  • HUANG Jiangtao ,
  • LIU Gang ,
  • GAO Zhenghong ,
  • ZHOU Zhu ,
  • CHEN Zuobin ,
  • JIANG Xiong
Expand
  • 1. Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
    2. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received date: 2019-08-26

  Revised date: 2019-09-10

  Online published: 2019-10-10

Supported by

National Natural Science Foundation of China (11402288); National Key R&D Program of China (2016YFB0200704)

Fold

摘要

多学科耦合伴随方法具有多学科耦合灵敏度计算量与各个学科设计变量个数均基本无关等优点，是一个值得关注的发展方向。面向气动、电磁、声学、结构、红外等与飞行器设计息息相关的学科，针对多学科耦合伴随方法的优势、现状、难点以及未来发展趋势开展研究与论述，系统性地分析了单一学科、多学科伴随方法的核心内容、关键技术与发展现状，对边界条件处理、交叉学科雅克比推导以及大型稀疏矩阵存储处理、求解等关键技术进行系统讨论，针对典型的关键环节和基础科学问题，给出了研究思路与解决方案，并进一步展望了多学科耦合伴随理论与应用发展趋势。希望能够为从事多学科伴随优化方法与应用的研究人员提供有意义的参考，促进多学科耦合灵敏度这一基础科学问题以及基于高保真度分析手段的多学科优化（MDO）技术的发展。

关键词： 多学科耦合伴随方法; 多学科优化; 耦合灵敏度; 交叉雅克比; 不确定度分析

本文引用格式

黄江涛 , 刘刚 , 高正红 , 周铸 , 陈作斌 , 江雄 . 飞行器多学科耦合伴随体系的现状与发展趋势综述[J]. 航空学报, 2020 , 41(5) : 623404 -623404 . DOI: 10.7527/S1000-6893.2019.23404

Abstract

The multidisciplinary coupled adjoint system has many advantages, such as independence of multidisciplinary coupled sensitivity analysis from the number of design variables of various disciplines, and is thus an interesting development direction. This paper discusses the advantages, current situation, difficulties and future development trend of the multidisciplinary coupled adjoint system, including the disciplines of aerodynamics, structure, electromagnetism, acoustics, and infrared, which are closely related to aircraft design. The core contents, key technologies and current development situation of the single discipline and the multidisciplinary adjoint system are analyzed. The key technologies such as boundary condition processing, Jacobi derivation of multiple disciplines, and storage processing and solution of large sparse matrix are discussed systematically. The research ideas and solutions for respective key technologies and basic problems are given, and the development trend of multidisciplinary coupled adjoint theory and application is provided. Through this systematic discussion, we hope to provide meaningful suggestions for researchers engaged in multidisciplinary adjoint optimization and application, promote the research on multidisciplinary coupled system sensitivity, and the development of Multidisciplinary Optimization (MDO) technology based on high fidelity analysis.

Key words： multidisciplinary coupled adjoint method; multidisciplinary optimization; coupled sensitivity; cross Jacobi; uncertainty analysis

参考文献

[1] JAMESON A. Aerodynamic design via control theory[J]. Journal of Scientific Computing, 1988, 3:233-260.
[2] GILES M B, DUTA M C. Algorithm developments for discrete adjoint methods[J]. AIAA Journal, 2003, 41(2):198-205.
[3] CARPENTIERI G. An adjoint-based shape-optimization method for aerodynamic design[D]. Delft:Delft Technische Universiteit,2009.
[4] AMOIGNON O, BERGGREN M.Adjoint of a median-dual finite-volume scheme application to transonic aerodynamic shape optimization[R]. Uppsala:Uppsala University,2006
[5] REUTHER J. Aerodynamic shape optimization using control theory[D]. Davis:University of California,1996.
[6] 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).
[7] 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).
[8] FANG X M, ZHANG Y F, CHEN H X. Transonic nacelle aerodynamic optimization based on hybrid genetic algorithm:AIAA-2016-3833[R]. Reston:AIAA, 2016.
[9] HAN Z H, XU C Z, ZHANG L, et al. Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids[J]. Chinese Journal of Aeronautics, 2020, 33(1):31-47.
[10] ZHANG Y, HAN Z H, ZHANG K S. Variable-fidelity expected improvement for efficient global optimization of expensive functions[J]. Structural and Multidisciplinary Optimization, 2018, 58(4):1431-1451.
[11] 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).
[12] 韩忠华,张瑜,许晨舟,等. 基于代理模型的大型民机机翼气动优化设计[J]. 航空学报,2019, 40(1):522398. HAN Z H, ZHANG Y, XU C Z, et al. Aerodynamic shape optimization of large civil aircraft wing using surrogate model[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522398(in Chinese).
[13] WALTHER B, NADARAJAH S. Constrained adjoint-based aerodynamic shape optimization of a single stage transonic compressor[J]. Journal of Turbomachinery, 2013, 135(2):021017.
[14] NIELSEN E J, ANDERSON W K. Recent improvements in aerodynamic design optimization on unstructrued meshes[J]. AIAA Journal, 2002,40(6):1155-1163.
[15] DWIGHT R P, BREZILLON J. Effect of various approximations of the discrete adjoint on gradient-based optimization:AIAA-2006-0690[R]. Reston:AIAA, 2006.
[16] CARRIER G, DESTARAG D. Gradient-based aerodynamic optimization with the elsA software:AIAA-2014-0568[R]. Reston:AIAA, 2014.
[17] QIN N, WONG W S,MOIGNE A L. Three-dimensional contour bumps for transonic wing drag reduction[J] Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering, 2008,222(5):619-629
[18] MARTINS J R R A. A coupled-adjoint method for high-fidelity[M]//Aero-structural Optimization. Stanford:Stanford University,2002.
[19] MADER C A, KENWAY G K W, MARTINS J R R A. Towards high-fidelity aerostructural optimization using a coupled adjoint approach[C]//12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Reston:AIAA, 2008.
[20] KASIDIT L, ANTONY J. Case studies in aero-structural wing planform and section optimization:AIAA-2004-5372[R]. Reston:AIAA, 2004.
[21] MOHAMMAD A, JOL B. Shape optimization using the aerostructural coupled adjoint approach for viscous flows[M]//Evolutionary and Deterministic Methods for Design, Optimization and Control, 2011
[22] MERYEM M, JACQUES P, G'ERALD C. Sensitivity analysis of a strongly coupled aero-structural system using direct and adjoint methods:AIAA-2008-5863[R]. Reston:AIAA, 2008.
[23] GHAZLANE I, CARRIER G, DUMONT A. Aerostructural adjoint method for flexible wing optimization:AIAA-2012-1924[R]. Reston:AIAA, 2012.
[24] KENWAY G K W, MARTINS J R R A. Multipoint high-fidelity aerostructural optimization of a transport aircraft configuration[J]. Journal of Aircraft, 2014, 51(1):144-160.
[25] 黄江涛, 刘刚, 周铸, 等. 基于离散伴随方程求解梯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]. Acta Aerodynamica Sinica, 2017, 35(4):554-562(in Chinese).
[26] LIOU M F, KIM H. Aerodynamic design of integrated propulsion-airframe configuration of the hybrid wingbody aircraft:AIAA-2017-3411[R]. Reston:AIAA, 2017.
[27] VINCENT P, SIVA N. Efficient reduced-radial basis function-based mesh deformation within an adjoint-based aerodynamic optimization framework[J]. Journal of Aircraft, 2016,53(6):1905-1921.
[28] LYU Z J, KENWAY G K W, MARTINS J R R A. Aerodynamic shape optimization investigations of the common research model wing benchmark[J]. AIAA Journal, 2015,53(4):968-984
[29] LEE B J, LIU M S. Optimizing a boundary-layer-ingestion offset inlet by discrete adjoint approach[J]. AIAA Journal, 2010,48(9):2008-2016.
[30] YI J, KIM C. Adjoint-based design optimization of vortex generator in an S-shaped subsonic inlet[J]. AIAA Journal, 2012,48(9):2492-2507.
[31] HEATHER K, FRANCISCO P. Adjoint-based optimization of a hypersonic inlet:AIAA-2015-3060[R]. Reston:AIAA, 2015.
[32] HEATH C M, GRAY J S. Aerodynamic shape optimization of a dual-stream supersonic plug nozzle[C]//53rd AIAA Aerospace Sciences Meeting. Reston:AIAA,2005.
[33] BENJAMIN W,SIVA N. Constrained adjoint-based aerodynamic shape optimization in a multistage turbomachinery environment:AIAA-2012-0062[R]. Reston:AIAA, 2012.
[34] 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).
[35] 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).
[36] 屈崑,李记超,蔡晋生.CFD数学模型的线性化方法及其应用[J]. 航空学报,2015,36(10):3218-3227. QU K, LI J C, CAI J S. Method of linearizing computational fluid dynamics model and its applications[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(10):3218-3227(in Chinese).
[37] 高宜胜,伍贻兆,夏健. 基于非结构网格离散型伴随方法的翼型优化[J]. 空气动力学学报, 2013,31(2):244-249. GAO Y S, WU Y Z, XIA J. A discrete adjoint-based approach for airfoil optimization on unstructured meshes[J]. Acta Aerodynamica Sinica, 2013, 31(2):244-249(in Chinese).
[38] 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 3D unstructured grid[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3):674-686(in Chinese).
[39] 黄江涛,周铸,高正红, 等. 大型民用飞机气动外形典型综合设计方法分析[J]. 航空学报, 2019,40(2):522369. HUANG J T, ZHOU Z, GAO Z H, et al. The analysis of a typical integrated design method for large civil aircraft aerodynamic optimization[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(2):522369(in Chinese).
[40] 黄江涛,周铸,余婧, 等. 考虑飞行器动力系统进排气效应的设计参数灵敏度分析研究[J]. 推进技术, 2019, 40(2):250-258. HUANG J T, ZHOU Z, YU J, et al. Sensitivity analysis of design variables considering intake and exhaust effe-cts[J]. Journal of Propulsion Technology, 2019, 40(2):250-258(in Chinese).
[41] 宋红超, 李鑫, 季路成. 基于离散型伴随方法的单边膨胀喷管优化设计研究[J]. 工程热物理学报, 2017,38(9):1849-1854. SONG H C, LI X, JI L C. Research on the optimization of unilateral expansion nozzle based on the discrete adjoint method[J]. Journal of Engineering Thermophysics, 2017,38(9):1849-1854(in Chinese).
[42] 张朝磊, 厉海涛,丰镇平. 基于离散伴随方法的透平叶栅气动优化[J]. 工程热物理学报, 2012, 33(1):47-50. ZHANG C L, LI H T, FENG Z P. Aerodynamic optimization design of turbomachinery cascade based on discrete adjoint method[J]. Journal of Engineering Thermophysics, 2012,33(1):47-50(in Chinese).
[43] 唐方明,余佳,李伟伟, 等. 采用排间界面静压约束伴随方法的多级压气机叶片优化[J]. 航空动力学报, 2015,30(8):1869-1874. TANG F M, YU J, LI W W, et al. Blade shape optimization of multistage compressor using adjoint method with static pressure constraint at interfaces between rows[J]. Journal of Aerospace Power, 2015,30(8):1869-1874(in Chinese).
[44] 刘浩,张雷,李霄琳. 基于伴随方法的叶片三维气动外形优化设计[J]. 中南大学学报(自然科学版), 2016,47(2):436-442. LIU H, ZHANG L, LI X L. Three dimensional aerodynamic shape optimum design for blade based on adjoint method[J]. Journal of Central South University (Science and Technology), 2016,47(2):436-442(in Chinese).
[45] 马灿,苏欣荣,袁新.单级跨音压气机非定常伴随气动优化[J]. 工程热物理学报,2017,38(3):504-508. MA C, SU X R, YUAN X. Unsteady adjoint aerodynamic optimization of a transonic compressor stage[J]. Journal of Engineering Thermophysics, 2017,38(3):504-508(in Chinese).
[46] LUO J Q, LIU F. Multi-objective design optimization of a transonic compressor rotor using an adjoint equation method:AIAA-2013-2732[R]. Reston:AIAA, 2012.
[47] 阮颖铮. 雷达截面与隐身技术[M]. 北京:国防工业出版社, 1998. RUAN Y Z. Radar cross section and stealth technology[M]. Beijing:National Defense Industry Press, 1998(in Chinese)
[48] 李洁, 刘战合, 王英,等. 飞行器目标RCS计算方法适用性研究[J]. 战术导弹技术, 2012(1):38-42. LI J, LIU Z H, WANG Y, et al. Research on the applicability of the approach for calculating the RCS of aircraft target[J]. Tactical Missile Technology, 2012(1):38-42(in Chinese).
[49] GAO Z H, WANG M L. An efficient algorithm for calculating aircraft RCS based on the geometrical characterist-ics[J]. Chinese Journal of Aeronautics, 2008, 21(4):296-303.
[50] GEORGIEVA N K, GLAVIC S, BAKR M H, et al. Feasible adjoint sensitivity technique for EM design optimization[J]. IEEE Transactions on Microwave Theory & Techniques, 2002, 50(12):2751-2758.
[51] NIKOLOVA N K, SAFIAN R, SOLIMAN E A, et al. Accelerated gradient based optimization using adjoint sensitivities[J]. IEEE Transactions on Antennas & Propagation, 2004, 52(8):2147-2157.
[52] ZHOU L, HUANG J T. Radar cross section gradient calculation based on adjoint equation of method of moment[C]//Asia-Pacific International Symposium on Aerospace Technology, 2018.
[53] 张玉, 赵勋旺, 陈岩. 计算电磁学中的超大规模并行矩量法[M]. 西安:西安电子科技大学出版社, 2016. ZHANG Y, ZHAO X W, CHEN Y. Hyper-large-scale parallel method of moment in computational electromagnetics[M]. Xi'an:Xidian University Press, 2006(in Chinese).
[54] 宋文萍, 余雷, 韩忠华. 飞机机体气动噪声计算方法综述[J]. 航空工程进展, 2010(2):125-131. SONG W P, YU L, HAN Z H. Status of investigation on airframe noise computation[J]. Advances in Aeronautical Science and Engineering, 2010(2):125-131(in Chinese).
[55] 李晓东, 江旻, 高军辉, 等. 计算气动声学进展与展望[J]. 中国科学:物理学力学天文学, 2014, 44(3):234-248. LI X D, JIANG M, GAO J H, et al. Progress and prospective of computational aeroacoustics[J]. Scientia Sinica:Physica, Mechanica & Astronomica, 2014,44(3):234-248(in Chinese).
[56] RALLABHANDI S K. Advanced sonic boom prediction using augmented Burger's equation:AIAA-2011-1278[R]. Reston:AIAA, 2011.
[57] 钱炜祺,何开锋. 三维稳态热传导逆问题反演算法研究[J]. 力学学报,2008, 40(5):611-618. QIAN W Q, HE K F. Inverse estimation of heat source term in three-dimensional transient heat condution problem[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5):611-618.
[58] KOUHI M, HOUZEAUX G. Implementation of discrete adjoint method for parameter sensitivity analysis in chemically reacting flows:AIAA-2016-1909[R].Reston:AIAA,2016.
[59] ABU-ZURAYK M. An aeroelastic coupled adjoint approach for multi-point design in viscous-flows[D].Braunschweig:DLR, 2016.
[60] ABU-ZURAYK M, BREZILLON J. Shape optimization using the aerostructural coupled adjoint approach for viscous flows[M]//Evolutionary and Deterministic Methods for Design, Optimization and Control, 2011.
[61] 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:AIAA, 2008.
[62] MVLLE L, VERSTRAETE T. Multidisciplinary adjoint optimization of trubomachinery components including aerodynamic and stress performance:AIAA-2017-4083[R]. Reston:AIAA, 2017.
[63] MISHRA A, MANI K. Time dependent adjoint-based optimization for coupled fluid-structure problems[J]. Journal of Computational Physics, 2015, 292:253-271.
[64] 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).
[65] HUANG J T, YU J, GAO Z H, et al. Multi-disciplinary optimization of large civil aircraft using a coupled aero-structural adjoint approach[C]//Asia-Pacific International Symposium on Aerospace Technology, 2018.
[66] FABIANO E, MISHRA A, MAVRIPLIS D. Time-dependent aero-acoustic adjoint-based shape optimization of helicopter rotors in forward flight:AIAA-2016-1910[R]. Reston:AIAA, 2016.
[67] 邱昇. 基于伴随方法、梯度增强Kriging方法的涡扇发动机进气道减噪高效优化方法[J].科学技术与工程,2018,18(19):289-295. QIU S.Efficient noise reduction optimization of turbofan engine intake based on the adjoint method and gradient enhanced Kriging method[J].Science Technology and Engineering, 2018, 18(19):289-295(in Chinese).
[68] THOMAS C. Extrapolation of sonic boom pressure signatures by the waveform parameter method:NASA TN D-6832[R]. Washington, D.C.:NASA,1972.
[69] PLOTKIN K J. Computer models for sonic boom analysis:PCBoom4, CABoom, BooMap, COR-Boom[M]. New York:Wyle, 2002.
[70] NADARAJAH S K, JAMESON A, ALONSO J J. Sonic boom reduction using an adjoint method for wing-body configurations in supersonic flow:AIAA-2002-5547[R]. Reston:AIAA, 2002.
[71] RALLABHANDI S K. Sonic boom adjoint methodology and its applications:AIAA-2011-3497[R]. Reston:AIAA, 2011.
[72] 冯晓强,李占科,宋笔锋. 超声速客机低音爆布局反设计技术研究[J]. 航空学报,2011, 32(11):1980-1986. FENG X Q, LI Z K, SONG B F. A research on inverse design method of a lower sonic boom supersonic aircraft configuration[J]. Acta Aeronautic et Atronautica Sinica, 2011, 32(11):1980-1986(in Chinese).
[73] 冯晓强,李占科,宋笔锋. 超声速飞机低音爆布局混合优化方法研[J]. 航空学报,2013,34(8):1768-1777. FENG X Q, LI Z K, SONG B F. Hybrid optimization approach research or low sonic boom supersonic aircraft configuration[J]. Acta Aeronautic et Atronautica Sinica, 2013,34(8):1768-1777(in Chinese).
[74] 王刚,马博平,雷知锦, 等. 典型标模音爆的数值预测与分析[J]. 航空学报,2018,39(1):121458. WANG G,MA B P, LEI Z J, et al. Simulation and analysis for sonic boom on several bench mark cases[J]. Acta Aeronautic et Atronautica Sinica, 2018,39(1):121458(in Chinese).
[75] 张绎典, 黄江涛, 高正红. 基于增广Burgers方程的音爆远场计算及应用[J]. 航空学报, 2018, 39(7):122039. ZHANG Y D, HUANG J T, GAO Z H. Far field simulation and applications of sonic boom based on augmented Burgers equation[J]. Acta Aeronautic et Atronautica Sinica, 2018, 39(7):122039(in Chinese).
[76] 黄江涛, 张绎典, 高正红. 基于流场/声爆耦合伴随方程的超声速公务机声爆优化[J]. 航空学报, 2019,40(5):122505. HUANG J T, ZHANG Y D, GAO Z H. The supersonic jet sonicboom optimization based on flow/sonicboom coupled adjoint equations[J]. Acta Aeronautic et Atronautica Sinica, 2019,40(5):122505(in Chinese).
[77] SILVA W A, SANETRIKY M D, CHWALOWSKIZ P. Using FUN3D for aeroelastic, sonic boom, and AeroPropulsoServoElastic (APSE) analyses of a supersonic configuration[C]//Dynamics Specialists Conference, 2015.
[78] MANI K, MAVRIPLIS D J. Adjoint-based sensitivity formulation for fully coupled unsteady aeroelasticity problems[J]. AIAA Journal, 2009, 47(8):1902-1915.
[79] BERAN P, STANFORD B, SCHROCK C. Uncertainty quantification in aeroelasticity[J]. Annual Review of Fluid Mechanics, 2017, 49:361-386.
[80] RODERICK O, ANITESCU M, FISCHER P. Polynomial regression approaches using derivative information for uncertainty quantification[J]. Nuclear Science and Engineering, 2010, 164(2):122-139.
[81] ALLEN M, MAUTE K. Reliability-based shape optimization of structures undergoing fluid-structure interaction phenomena[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(30-33):3472-3495.
[82] ALLEN M, MAUTE K. Reliability-based design optimization of aeroelastic structures[J]. Structural and Multidisciplinary Optimization, 2004, 27(4):228-242.
[83] STANFORD B, BERA P. Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization[J]. Journal of Fluids and Structures, 2013, 36:111-123.
[84] MANI K, MAVRIPLIS D J. Unsteady discrete adjoint formulation for two-dimensional flow problems with deforming meshes[J]. AIAA Journal, 2008, 46(6):1351-1364.
[85] NIKBAY M, KURUT M N. Reliability based multidisciplinary optimization of aeroelastic systems with structural and aerodynamic uncertainties[J]. Journal of Aircraft, 2013, 50(3):708-715.
[86] STANFORD B, BERAN P. Minimum-mass panels under probabilistic aeroelastic flutter constraints[J]. Finite Elements in Analysis and Design, 2013, 70-71:15-26.
[87] VERHOOSEL C V, SCHOLCZ T P, HULSHOFF J, et al. Uncertainty and reliability analysis of fluid-structure stability boundaries[J]. AIAA Journal, 2009, 47(1):91-104.
[88] MANAN A, COOPER J. Design of composite wings including uncertainties:A probabilistic approach[J]. Journal of Aircraft, 2009, 46(2):601-607.
[89] SCARTH C, COOPER J E, WEAVER P M. et al. Uncertainty quantification of aeroelastic stability of composite plate wings using lamination parameters[J]. Composite Structures, 2014, 116:84-93.
[90] HOSDER S, WALTERS R, BALCH M. Efficient uncertainty quantification applied to the aeroelastic analysis of a transonic wing[C]//46th AIAA Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 2008.
[91] MISSOUM S, DRIBUSCH C, BERAN P. Reliability-based design optimization of nonlinear aeroelasticity problems[J]. Journal of Aircraft, 2010, 47(3):992-998.
[92] XIU D B, KARNIADAKIS G E. The Wiener-Askey polynomial chaos for stochastic differential equations[J]. Siam Journal on Scientific Computing, 2002, 24(2):619-644.
[93] KESHAVARZZADEH V, MEIDANI H, TORTORELLI D A. Gradient based design optimization under uncertainty via stochastic expansion methods[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 306:47-76.
[94] ZHAO H, GAO Z, XU F, et al. Review of robust aerodynamic design optimization for air vehicles[J]. Archives of Computational Methods in Engineering, 2019, 26(3):685-732.
Options
文章导航

/

〈 〉

地址：北京市海淀区北四环中路辅路238号柏彦大厦

邮政编码：100083

E-mail：hkxb@buaa.edu.cn

关于我们

期刊社服务

专业学科

封面文章

友情链接

版权所有 © 航空学报编辑部

版权所有 © 2011航空学报杂志社

主管单位：中国科学技术协会 主办单位：中国航空学会 北京航空航天大学