多学科设计优化在小水线面双体船中的研究与应用
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摘要
小水线面双体船(Small Water-Plane-Area Twin Hull ,SWATH)是上个世纪70年代出现的一种高性能船舶,其集成了潜艇、水翼艇和双体船的性能优点,是一种性能优异的新型船舶形式。
在实际工程中,SWATH的设计是一个涉及流体阻力、结构应力、推进动力和控制等方面的复杂问题,其设计过程是一项涵盖了多学科、多领域分析的综合系统工程。对于传统的设计方法,由于方法本身的单学科局限,使得在设计过程中造成SWATH多学科合理解的缺失,从而不能很好地满足工程技术发展的需求,或由于设计流程在学科之间的反复迭代导致设计周期过长。本文将多学科设计优化方法(Multidisciplinary Design Optimization,MDO)引入到SWATH的设计当中,以期克服现有设计方法所存在的不足。
本文探索了MDO方法在SWATH概念设计中的应用途径,以减少SWATH的每海里油耗量为总体目标,在协同优化(Collaborative Optimization,CO)算法的建立了系统级与学科级优化框架。在SWATH的概念设计中,主要将其分为外形阻力与结构两个子学科来进行综合考虑。在多学科模型构建过程中,详细研究了两个学科在SWATH设计中的分析方法,结合Solid Works、Fluent和ANSYS等造型和分析工具以及数值计算方法来获取各学科内设计参量的响应值。
由于在上述两个学科分析中,参数值和响应值之间的关系无法用精确的数学模型来表达,且模型过于复杂不易于进行优化。在本文中,引入了代理模型技术,在综合分析常用的三种代理模型优缺点的基础上,选取kriging模型来对参数值和响应值之间的关系进行高精度拟合。并将其融合于协同优化框架之中,在系统层面的最底层运用粒子群优化算法对目标进行优化。最后的结果表明计算性能良好,该方法使得SWATH的油耗率在原基础上减小了8.62%。
本文的研究工作将新的多学科设计优化方法引入到SWATH的概念设计之中,是SWATH设计方法一种新的尝试,它同时也为以后在SWATH或其它船舶设计研究当中有效运用多学科优化方法提供了有价值的参考。
Small Water-Plane-Area Twin Hull (SWATH) configuration was initially introduced in the early 20th century, which not only assimilates many strong points of submarine, hydrofoil and catamaran, but also overcomes their defects, respectively, thus it is a new type ship with high performance.
In practical engineering, SWATH design is a complex issue involved multidisciplinary knowledge (fluid resistance, structure stress, propellant power and so on), experts experience and coupling in multidiscipline. As the inherent defects, the traditional design methods can’t get the global optimal solutions and satisfy the needs, and the more iterations lead to too long design cycle. In this paper, the new design method, multidisciplinary design optimization (MDO), is introduced into solving the problems mentioned above.
The paper explores the application of MDO approach in the concept design of SWATH. Therefore, considering the minimization of the oil consumption as the design goal, the system and sub-disciplines analysis architecture is constructed with collaborative optimization. SWATH concept design mainly comprises the sub-disciplines, fluid resistance analysis and structural analysis, The analysis method in the two sub-disciplines have been deeply studied, besides, during the whole MDO process, the design variables and their response values are gained by the 3D model software (Solid Works, Fluent and ANSYS) and numerical methods. In the two disciplines, the relationships between the deisgn variables and response values can’t be easily defined by a mathematical model, consequently, they can’t be optimized conveniently. In order to solve this problem, the surrogate model is utilized to fit the expected mathematical model in the MDO process. In the paper, the features of three main kinds of surrogate models are compared and considering the characters of SWATH design, the kriging model is selected as the surrogate model to define the relationship of the design variables and their response values. At last, the objective function of the whole design system is optimized by Particle Swarm Optimization Algorithms with the whole framework combined the kriging model and Collaborate Optimization. The experiment result shows the oil consumption is decreased by 8.62% by the proposed approach.
The main work of the paper is to explore how to apply the MDO approach in the SWATH concept design, and make ship designers get the appropriate and high performance system level design results that satisfied the multidisciplinary design needs in practical engineering. At the same time, the work provides the valuable reference for research of MDO in ship design.
在实际工程中,SWATH的设计是一个涉及流体阻力、结构应力、推进动力和控制等方面的复杂问题,其设计过程是一项涵盖了多学科、多领域分析的综合系统工程。对于传统的设计方法,由于方法本身的单学科局限,使得在设计过程中造成SWATH多学科合理解的缺失,从而不能很好地满足工程技术发展的需求,或由于设计流程在学科之间的反复迭代导致设计周期过长。本文将多学科设计优化方法(Multidisciplinary Design Optimization,MDO)引入到SWATH的设计当中,以期克服现有设计方法所存在的不足。
本文探索了MDO方法在SWATH概念设计中的应用途径,以减少SWATH的每海里油耗量为总体目标,在协同优化(Collaborative Optimization,CO)算法的建立了系统级与学科级优化框架。在SWATH的概念设计中,主要将其分为外形阻力与结构两个子学科来进行综合考虑。在多学科模型构建过程中,详细研究了两个学科在SWATH设计中的分析方法,结合Solid Works、Fluent和ANSYS等造型和分析工具以及数值计算方法来获取各学科内设计参量的响应值。
由于在上述两个学科分析中,参数值和响应值之间的关系无法用精确的数学模型来表达,且模型过于复杂不易于进行优化。在本文中,引入了代理模型技术,在综合分析常用的三种代理模型优缺点的基础上,选取kriging模型来对参数值和响应值之间的关系进行高精度拟合。并将其融合于协同优化框架之中,在系统层面的最底层运用粒子群优化算法对目标进行优化。最后的结果表明计算性能良好,该方法使得SWATH的油耗率在原基础上减小了8.62%。
本文的研究工作将新的多学科设计优化方法引入到SWATH的概念设计之中,是SWATH设计方法一种新的尝试,它同时也为以后在SWATH或其它船舶设计研究当中有效运用多学科优化方法提供了有价值的参考。
Small Water-Plane-Area Twin Hull (SWATH) configuration was initially introduced in the early 20th century, which not only assimilates many strong points of submarine, hydrofoil and catamaran, but also overcomes their defects, respectively, thus it is a new type ship with high performance.
In practical engineering, SWATH design is a complex issue involved multidisciplinary knowledge (fluid resistance, structure stress, propellant power and so on), experts experience and coupling in multidiscipline. As the inherent defects, the traditional design methods can’t get the global optimal solutions and satisfy the needs, and the more iterations lead to too long design cycle. In this paper, the new design method, multidisciplinary design optimization (MDO), is introduced into solving the problems mentioned above.
The paper explores the application of MDO approach in the concept design of SWATH. Therefore, considering the minimization of the oil consumption as the design goal, the system and sub-disciplines analysis architecture is constructed with collaborative optimization. SWATH concept design mainly comprises the sub-disciplines, fluid resistance analysis and structural analysis, The analysis method in the two sub-disciplines have been deeply studied, besides, during the whole MDO process, the design variables and their response values are gained by the 3D model software (Solid Works, Fluent and ANSYS) and numerical methods. In the two disciplines, the relationships between the deisgn variables and response values can’t be easily defined by a mathematical model, consequently, they can’t be optimized conveniently. In order to solve this problem, the surrogate model is utilized to fit the expected mathematical model in the MDO process. In the paper, the features of three main kinds of surrogate models are compared and considering the characters of SWATH design, the kriging model is selected as the surrogate model to define the relationship of the design variables and their response values. At last, the objective function of the whole design system is optimized by Particle Swarm Optimization Algorithms with the whole framework combined the kriging model and Collaborate Optimization. The experiment result shows the oil consumption is decreased by 8.62% by the proposed approach.
The main work of the paper is to explore how to apply the MDO approach in the SWATH concept design, and make ship designers get the appropriate and high performance system level design results that satisfied the multidisciplinary design needs in practical engineering. At the same time, the work provides the valuable reference for research of MDO in ship design.
引文
[1]徐蓉.小水线面双体船方案设计及稳性研究:[硕士学位论文]。上海:上海交通大学,2005
[2]李仲伟.小水线面双体船直接设计法:[硕士学位论文]。上海:上海交通大学,2005
[3]黄鼎良.小水线面双体船性能原理.第一版.北京:国防工业出版社,1993. 6-9
[4] Suzukik, H Ohtsubo. The optiminmal design of ship structure by multi-level optimization. Journal of Society of Naval of Japan, 1995, 178:405-411
[5] F Campana Emilio, Daniele Peri, Yusuke Tahara,et al. Shape optimization in ship hydrodynamics using computational fluid dynamics. Computer methods in applied mechanics and engineering, 2006, 196(1-3):634-651
[6] A Schmitza, E Besnard, H Hefazi. Automated hydrodynamic shape optimization using neural networks. Transactions-Society of Naval Architects and Marine Engineers, 2004, 112(17):429-441
[7]张少雄,喻之凯,向林浩.基于等强度板格稳定的船体结构优化设计研究.船海工程. 2008, 37(1):19-22
[8]刘文玺,黄德波.对排水式高速船双球首构形优化的初步研究.哈尔滨工程大学学报. 2007, 28(12):1316-1320
[9]符瑞白.某船双层底结构优化设计.广船科技, 2007, 3:8-10
[10]冯大奎.小水线面双体船阻力性能研究及船型优化:[硕士学位论文]。武汉:华中科技大学,2004
[11]朱海烨.小水线面双体船稳定鳍优化设计研究:[硕士学位论文]。哈尔滨:哈尔滨工程大学,2007
[12]李仲伟,吴有生,崔维成.基于有限元法的小水线面双体船结构优化.船舶力学, 2005, 9(2):99-108
[13]尹群,朱安庆,朱克强等.小水线面双体船结构优化.船舶工程, 2003, 25(4):31-3
[14]高丽,曾庆良,范文慧.多学科设计优化研究及发展趋势分析.工程设计学报, 2007,14(6):429-434
[15] Hajela P. Application of Global Sensitivity Equations in Multidisciplinary Aircraftynthesis. Journal of Aircraft, 1992.21, 27(12):1002-1010 [16] Kroo I. Multidisciplinary Optimization Methods for Aircraft Preliminary Design. AIAA-94-4325,1994 [17] Renaud J E.Improved Coordination in Nonhierarchical System Optimization. AIAA Journal, 1993.12, 31(12):2367-2373 [18] Sellar R S. Response Surface Based Concurrent Subspace Optimization for Multidisciplinary System Design. AIAA-96-0714, 1996 [19] Bolebaum C L. Formal and Heuristic System Decomposition in Structural Optimization. NASA/CR-4413,1991 [20] Braun R D. Use of the Collaborative Optimization Architecture for Launch Vehicle.AIAA-96-4018,1996 [21] SOBIESCZANSKI-SOBIESKI J. The sensitivity of complex internally coupled systems, AIAA Journal, 1990, 28(1):153-160 [22] SOBIESCZANSKI-SOBIESKI J. Multidisciplinary Aerospace Design Optimization: Survey Of Recent Developments. AIAA-1996-0711 [23] ABBOTT E A, SCOTT M L. The case for multidisciplinary design approach for smart fiber composite structures. Composite Structures, 2002, 58:349-362 [24]余雄庆.多学科设计优化算法及其在飞行器设计中的应用研究:[博士学位论文]。南京:南京航空航天大学,1996 [25]蔡苗.多学科设计优化分布式计算环境的研究:[硕士学位论文]。南京:南京航空航天大学,2003 [26]孙侠生.飞机结构多学科综合优化设计技术研究:[博士学位论文]。西安:西北工业大学,2000 [27]胡峪.飞机多学科设计优化及其应用研究:[博士学位论文]。西安:西北工业大学,2001 [28]李伟建.基于MEMS技术的微型飞机的多学科设计优化:[硕士学位论文]。西安:西北工业大学,2001 [29]郭健.多学科设计优化技术研究:[硕士学位论文]。西安:西北工业大学,2001. [30]宋寒冰.两级重复使用运载器的多学科优化设计:[硕士学位论文]。西安:西北上业大学,2002.
[31]陈琪锋.飞行器分布式协同进化多学科设计优化方法研究:[博士学位论文]。长沙:国防科技大学,2003.
[32]卜广志,张宇文.使用多学科设计优化方法对鱼雷总体设计的建模思路研究.兵工学报,2005,26(2):163-166
[33] LIU W,CUI W C. Multidisciplinary design optimization(MDO):A promising tool for the design of HOV. Journal of Ship Mechanics, 2004, 8(6):95-110
[34]陈柏鸿.机械产品多学科综合优化设计中的建模、规划及求解策略:[博士学位论文]。武汉:华中科技大学,200l
[35]余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计仲的应用.航空学报,2000,21(1):1-6
[36] W L Neu, W H Mason, S Ni, et al. A Multidisciplinary Design Optimization Scheme for Containerships. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary analysis and Optimization 2000, 9, 6-8
[37] Sandipan, Ganguly. Algorithmic modifications to a multidisciplinary design optimization model of containerships:[Master's degree thesis]. Virginia: Virginia Polytechnic Institute and State University, 2002
[38] EF Campana, G Fasano, D Peri. Issues on Nonlinear Programming for Multidisciplinary Design Optimization (MDO)in Ship Design Framework. 8th Numerical Towing Tank Symposium, Varna, Bulgaria 2005.10, 2-4
[39] Nathan Andrew Good, Multi-objective design optimization considering uncertainty in a multi-disciplinary ship synthesis model:[ Master's degree thesis]. Virginia:Virginia Polytechnic Institute and State University, 2006
[40]苟鹏,刘蔚,崔维成.船舶结构多学科设计优化近似方法的比较.船舶力学, 2007, 11(6):913-923
[41]贾建东,姚卫星,吴德海.飞行器多学科优化设计技术概论.航空科学技术,2005, 6:21-25
[42] Xiong Qing Xu,Marc A Stelmack,Stephen M Batill. An Application of Concurrent Subspace Design(CSD) to the Preliminary Design of a Low Reynolds Number UAV. AlAA 98—4917.1998
[43]黎华.鱼雷总体多学设计优化技术研究:[硕士学位论文]。西安:西北工业大学,2007
[44] S Kodiyalam, J S Sobieski. Bi-Level Integrated System Synthesis with Response Surfaces. AIAA-99-1306-wip,1999
[45]龚春林.多学科设计优化技术研究:[硕士学位论文]。西安:西北工业大学,2004
[46] Kroo I M, Altus S, Braun R D, et al. Multidisciplinary optimization methods for aircraft preliminary design. AIAA 94- 4325- CP, 1994, 697- 707
[47]陈仁伍. MDO在空空导弹设计中的应用:[硕士学位论文]。西安:西北工业大学,2007
[48]许辉,邹早建.基于FLUENT软件的小水线面双体船粘性流数值模拟.武汉理工大学学报(交通科学与工程版),2004,28(1):9-10
[49]黄鼎良.小水线面双体船性能原理.第一版.北京:国防工业出版社,1993. 52-54
[50]许辉.小水线面双体船粘性数值模拟:[硕士学位论文]。武汉:武汉理工大学,2004
[51]黄鼎良.小水线面双体船性能原理.第一版.北京:国防工业出版社,1993. 21-42
[52]陆丛红,林焰,纪卓尚.船舶设计中的三维参数化技术.第一版.北京:国防工业出版社,2007,187-247
[53]余德海,宋保维,李家旺等.鱼雷多学科设计优化中的代理模型研究.机械科学与技术, 2008,2(27):184-187
[54]王家华、高余海、周叶.克立金地质绘图技术—计算机的模型和算法.第一版.北京:石油工业出版社,1999,1
[55] CHUNG HS, ALONSO JJ. Multiobjective Optimization Using Approximation Model-based Genetic Algorithms, AIAA-2004-4325
[56]张健,飞机多学科设计优化中的近似方法研究:[硕士学位论文]。西安:西北工业大学,2006
[57] J P Costa, L Pronzato, E Thierry. A comparison between kriging and radial basis function networks for nonlinear prediction. Dans Proc. NSIP'99, Antalya, June 1999
[58] V Cherkassky, D Gehring, F Mulier. Comparison of adaptive methods for function estimation from samples. IEEE Trans. on Neural Networks, 1996, 7(4):969-984
[59] Min-Soo KIM, HuiJe CHO, Soon-Geul LEE et al. DFSS and Robust Optimization Tool for Multibody System with Random Variables. Special Issue on The Third Asian Conference on Multibody Dynamics, 2006, 1:583-592
[60] http://www.hudong.com/wiki/
[61] http://www.core.org.cn/NR/rdonlyres/Aeronautics-and-Astronautics/
[62]刘克龙,姚卫星.基于高精度模型的机翼气动结构多学科设计优化方法,中国科技论文在线. 2008,10(3):767-775
[65]Kennedy J, Eberhart R C. Particle swarm optimization. Proceedings of IEEE International Conference on Neutral Networks, Perth, Australia, 1995, 1942-1948
[2]李仲伟.小水线面双体船直接设计法:[硕士学位论文]。上海:上海交通大学,2005
[3]黄鼎良.小水线面双体船性能原理.第一版.北京:国防工业出版社,1993. 6-9
[4] Suzukik, H Ohtsubo. The optiminmal design of ship structure by multi-level optimization. Journal of Society of Naval of Japan, 1995, 178:405-411
[5] F Campana Emilio, Daniele Peri, Yusuke Tahara,et al. Shape optimization in ship hydrodynamics using computational fluid dynamics. Computer methods in applied mechanics and engineering, 2006, 196(1-3):634-651
[6] A Schmitza, E Besnard, H Hefazi. Automated hydrodynamic shape optimization using neural networks. Transactions-Society of Naval Architects and Marine Engineers, 2004, 112(17):429-441
[7]张少雄,喻之凯,向林浩.基于等强度板格稳定的船体结构优化设计研究.船海工程. 2008, 37(1):19-22
[8]刘文玺,黄德波.对排水式高速船双球首构形优化的初步研究.哈尔滨工程大学学报. 2007, 28(12):1316-1320
[9]符瑞白.某船双层底结构优化设计.广船科技, 2007, 3:8-10
[10]冯大奎.小水线面双体船阻力性能研究及船型优化:[硕士学位论文]。武汉:华中科技大学,2004
[11]朱海烨.小水线面双体船稳定鳍优化设计研究:[硕士学位论文]。哈尔滨:哈尔滨工程大学,2007
[12]李仲伟,吴有生,崔维成.基于有限元法的小水线面双体船结构优化.船舶力学, 2005, 9(2):99-108
[13]尹群,朱安庆,朱克强等.小水线面双体船结构优化.船舶工程, 2003, 25(4):31-3
[14]高丽,曾庆良,范文慧.多学科设计优化研究及发展趋势分析.工程设计学报, 2007,14(6):429-434
[15] Hajela P. Application of Global Sensitivity Equations in Multidisciplinary Aircraftynthesis. Journal of Aircraft, 1992.21, 27(12):1002-1010 [16] Kroo I. Multidisciplinary Optimization Methods for Aircraft Preliminary Design. AIAA-94-4325,1994 [17] Renaud J E.Improved Coordination in Nonhierarchical System Optimization. AIAA Journal, 1993.12, 31(12):2367-2373 [18] Sellar R S. Response Surface Based Concurrent Subspace Optimization for Multidisciplinary System Design. AIAA-96-0714, 1996 [19] Bolebaum C L. Formal and Heuristic System Decomposition in Structural Optimization. NASA/CR-4413,1991 [20] Braun R D. Use of the Collaborative Optimization Architecture for Launch Vehicle.AIAA-96-4018,1996 [21] SOBIESCZANSKI-SOBIESKI J. The sensitivity of complex internally coupled systems, AIAA Journal, 1990, 28(1):153-160 [22] SOBIESCZANSKI-SOBIESKI J. Multidisciplinary Aerospace Design Optimization: Survey Of Recent Developments. AIAA-1996-0711 [23] ABBOTT E A, SCOTT M L. The case for multidisciplinary design approach for smart fiber composite structures. Composite Structures, 2002, 58:349-362 [24]余雄庆.多学科设计优化算法及其在飞行器设计中的应用研究:[博士学位论文]。南京:南京航空航天大学,1996 [25]蔡苗.多学科设计优化分布式计算环境的研究:[硕士学位论文]。南京:南京航空航天大学,2003 [26]孙侠生.飞机结构多学科综合优化设计技术研究:[博士学位论文]。西安:西北工业大学,2000 [27]胡峪.飞机多学科设计优化及其应用研究:[博士学位论文]。西安:西北工业大学,2001 [28]李伟建.基于MEMS技术的微型飞机的多学科设计优化:[硕士学位论文]。西安:西北工业大学,2001 [29]郭健.多学科设计优化技术研究:[硕士学位论文]。西安:西北工业大学,2001. [30]宋寒冰.两级重复使用运载器的多学科优化设计:[硕士学位论文]。西安:西北上业大学,2002.
[31]陈琪锋.飞行器分布式协同进化多学科设计优化方法研究:[博士学位论文]。长沙:国防科技大学,2003.
[32]卜广志,张宇文.使用多学科设计优化方法对鱼雷总体设计的建模思路研究.兵工学报,2005,26(2):163-166
[33] LIU W,CUI W C. Multidisciplinary design optimization(MDO):A promising tool for the design of HOV. Journal of Ship Mechanics, 2004, 8(6):95-110
[34]陈柏鸿.机械产品多学科综合优化设计中的建模、规划及求解策略:[博士学位论文]。武汉:华中科技大学,200l
[35]余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计仲的应用.航空学报,2000,21(1):1-6
[36] W L Neu, W H Mason, S Ni, et al. A Multidisciplinary Design Optimization Scheme for Containerships. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary analysis and Optimization 2000, 9, 6-8
[37] Sandipan, Ganguly. Algorithmic modifications to a multidisciplinary design optimization model of containerships:[Master's degree thesis]. Virginia: Virginia Polytechnic Institute and State University, 2002
[38] EF Campana, G Fasano, D Peri. Issues on Nonlinear Programming for Multidisciplinary Design Optimization (MDO)in Ship Design Framework. 8th Numerical Towing Tank Symposium, Varna, Bulgaria 2005.10, 2-4
[39] Nathan Andrew Good, Multi-objective design optimization considering uncertainty in a multi-disciplinary ship synthesis model:[ Master's degree thesis]. Virginia:Virginia Polytechnic Institute and State University, 2006
[40]苟鹏,刘蔚,崔维成.船舶结构多学科设计优化近似方法的比较.船舶力学, 2007, 11(6):913-923
[41]贾建东,姚卫星,吴德海.飞行器多学科优化设计技术概论.航空科学技术,2005, 6:21-25
[42] Xiong Qing Xu,Marc A Stelmack,Stephen M Batill. An Application of Concurrent Subspace Design(CSD) to the Preliminary Design of a Low Reynolds Number UAV. AlAA 98—4917.1998
[43]黎华.鱼雷总体多学设计优化技术研究:[硕士学位论文]。西安:西北工业大学,2007
[44] S Kodiyalam, J S Sobieski. Bi-Level Integrated System Synthesis with Response Surfaces. AIAA-99-1306-wip,1999
[45]龚春林.多学科设计优化技术研究:[硕士学位论文]。西安:西北工业大学,2004
[46] Kroo I M, Altus S, Braun R D, et al. Multidisciplinary optimization methods for aircraft preliminary design. AIAA 94- 4325- CP, 1994, 697- 707
[47]陈仁伍. MDO在空空导弹设计中的应用:[硕士学位论文]。西安:西北工业大学,2007
[48]许辉,邹早建.基于FLUENT软件的小水线面双体船粘性流数值模拟.武汉理工大学学报(交通科学与工程版),2004,28(1):9-10
[49]黄鼎良.小水线面双体船性能原理.第一版.北京:国防工业出版社,1993. 52-54
[50]许辉.小水线面双体船粘性数值模拟:[硕士学位论文]。武汉:武汉理工大学,2004
[51]黄鼎良.小水线面双体船性能原理.第一版.北京:国防工业出版社,1993. 21-42
[52]陆丛红,林焰,纪卓尚.船舶设计中的三维参数化技术.第一版.北京:国防工业出版社,2007,187-247
[53]余德海,宋保维,李家旺等.鱼雷多学科设计优化中的代理模型研究.机械科学与技术, 2008,2(27):184-187
[54]王家华、高余海、周叶.克立金地质绘图技术—计算机的模型和算法.第一版.北京:石油工业出版社,1999,1
[55] CHUNG HS, ALONSO JJ. Multiobjective Optimization Using Approximation Model-based Genetic Algorithms, AIAA-2004-4325
[56]张健,飞机多学科设计优化中的近似方法研究:[硕士学位论文]。西安:西北工业大学,2006
[57] J P Costa, L Pronzato, E Thierry. A comparison between kriging and radial basis function networks for nonlinear prediction. Dans Proc. NSIP'99, Antalya, June 1999
[58] V Cherkassky, D Gehring, F Mulier. Comparison of adaptive methods for function estimation from samples. IEEE Trans. on Neural Networks, 1996, 7(4):969-984
[59] Min-Soo KIM, HuiJe CHO, Soon-Geul LEE et al. DFSS and Robust Optimization Tool for Multibody System with Random Variables. Special Issue on The Third Asian Conference on Multibody Dynamics, 2006, 1:583-592
[60] http://www.hudong.com/wiki/
[61] http://www.core.org.cn/NR/rdonlyres/Aeronautics-and-Astronautics/
[62]刘克龙,姚卫星.基于高精度模型的机翼气动结构多学科设计优化方法,中国科技论文在线. 2008,10(3):767-775
[65]Kennedy J, Eberhart R C. Particle swarm optimization. Proceedings of IEEE International Conference on Neutral Networks, Perth, Australia, 1995, 1942-1948