固体弹道导弹总体多目标设计优化研究
|
摘要
未来对先进弹道导弹武器系统的需求促进了导弹总体设计技术的不断发展。依托计算机软件平台的数字化设计是近年来导弹总体设计的研究热点,拥有广阔的应用前景。本文以固体弹道导弹的数字化设计为背景,重点研究了固体弹道导弹总体设计的分析模型、多目标优化方法和灵敏度分析方法、软件的设计与开发等问题,主要研究工作如下:
首先,对固体弹道导弹相关的固体推进、气动设计、轨迹等学科的分析模型抽象和各分系统工作过程仿真展开研究。根据不同阶段不同层次总体设计的需求,建立了导出和展开形式的固体弹道导弹质量方程;借鉴代理模型(Surrogate Models)的思想,将复杂的精确分析模型的计算放在优化过程外完成,建立了满足一定精度要求又适于优化迭代的固体火箭发动机简化分析模型;在分析弹道导弹基准外形的基础上,建立了基于Missile DATCOM简化气动工程估算模型;通过对主动段飞行程序参数的分析,建立了适于工程实践的弹道设计模型。总体设计分析模型的研究为后续章节提供了仿真模型
其次,开展了导弹总体设计的多目标优化研究。运用物理规划将导弹总体多目标设计问题处理成单目标问题,而后采用基于拉丁超立方设计和经典优化算法的混合优化算法对其优化。同时,对比研究了多目标遗传算法(NSGA-II算法)和罚函数处理的单目标遗传算法对导弹总体多目标设计的优化效果和效率。基于上述模型和算法实现的三级固体弹道导弹总体多目标设计算例的结果表明:基于物理规划和混合优化算法的导弹多目标设计优化效率高(耗费的计算机时与NSGA-II算法和单目标遗传算法比分别为1:38.75和1:17.5),且优化性能指标更好。
再次,引入基于正交试验设计的灵敏度分析方法对导弹总体多目标设计优化的结果进行了分析,得到了最优设计点附近各设计参数对射程等优化指标的灵敏度。
最后,设计开发了固体弹道导弹总体方案设计优化软件。分析了软件多样化、通用化的功能需求,安排了软件主要计算流程,采用面向对象技术搭建了软件基本框架。软件计算结果表明,该软件能够提供固有导弹构型优化设计、新建构型优化设计、各参数配置、多种优化算法、可变优化变量、可变约束以及数据结果输出等主要功能。
本文将现代优化技术、数据分析方法应用到固体弹道导弹多学科设计中,为飞行器优化设计领域提供了新的方法和思路。设计开发的固体弹道导弹总体设计软件有一定的应用价值。
The future needs of an advanced ballistic missile weapon promote the continuous development of missile design technology. With wide application prospects, missile digital design study is very popular in recent years. In this background, the thesis concentrates on the studies of the solid ballistic missile system design models, multi-object optimal algorithms, sensitivity analysis methods and missile system optimization design software development. The main work and achievements are summarized as follows:
Firstly, modeling and simulation of solid ballistic missile operating process are studied. According to requirement in different phase of missile system design, the synopsis missile mass equation and the detailed missile mass equation are been built; Using the idea of Surrogate Models, simplified solid rocket motor analysis model which is suit to optimize is been proposed; Aerodynamic engineering estimation model which based on Missile DATCOM and trajectory design and computing model are also been proposed after the analysis of classic ballistic missile configure and the missile power phase parameters. These studies provide the simulation models for follow-up chapters.
Secondly, the dissertation conducted ballistic missile system design multi-objective optimization studies. The missile design multi-objective problem is deal with using physical programming, then a hybrid optimization algorithm based on Latin hypercube design and classic optimal algorithm is proposed to optimize the missile design model. At the same time, the multi-objective genetic algorithm NSGA-II and a single-object genetic algorithm are applied to the missile system design optimization to compare the optimal results and affectivity. A 3 stage solid ballistic missile multi-object system design optimization case which based on upwards optimal algorithm is been studied. The comparison between NSGA-II’s result and other optimal methods’results show that the physical programming and hybrid optimal algorithm are more suitable and efficiency to solve the missile system design optimization problem.
Furthermore, Orthogonal experimental design is applied to analyze sensitivity of missile system design multi-objective optimization results. Sensitivity analysis of the design variables to range and other performance merits near the best design point are been studied.
In the end, a solid ballistic missile system optimization design software is developed. By analyzing the diversity and generalization requirements, the main calculation process is completed. Using object-oriented design methods, the basic framework of the system is proposed. The software results show that the system can provide both certain and new configuration missile design optimization and results output. It also can configure different design variables, parameters, constrains and optimal algorithms.
In this desertion, the application of modern optimal techniques and data analysis methods to solid ballistic missile multi-disciplinary design provides a new approach and ideas in vehicle design optimization domain. The system concept design software has some certain applied value in the system design of solid ballistic missiles.
首先,对固体弹道导弹相关的固体推进、气动设计、轨迹等学科的分析模型抽象和各分系统工作过程仿真展开研究。根据不同阶段不同层次总体设计的需求,建立了导出和展开形式的固体弹道导弹质量方程;借鉴代理模型(Surrogate Models)的思想,将复杂的精确分析模型的计算放在优化过程外完成,建立了满足一定精度要求又适于优化迭代的固体火箭发动机简化分析模型;在分析弹道导弹基准外形的基础上,建立了基于Missile DATCOM简化气动工程估算模型;通过对主动段飞行程序参数的分析,建立了适于工程实践的弹道设计模型。总体设计分析模型的研究为后续章节提供了仿真模型
其次,开展了导弹总体设计的多目标优化研究。运用物理规划将导弹总体多目标设计问题处理成单目标问题,而后采用基于拉丁超立方设计和经典优化算法的混合优化算法对其优化。同时,对比研究了多目标遗传算法(NSGA-II算法)和罚函数处理的单目标遗传算法对导弹总体多目标设计的优化效果和效率。基于上述模型和算法实现的三级固体弹道导弹总体多目标设计算例的结果表明:基于物理规划和混合优化算法的导弹多目标设计优化效率高(耗费的计算机时与NSGA-II算法和单目标遗传算法比分别为1:38.75和1:17.5),且优化性能指标更好。
再次,引入基于正交试验设计的灵敏度分析方法对导弹总体多目标设计优化的结果进行了分析,得到了最优设计点附近各设计参数对射程等优化指标的灵敏度。
最后,设计开发了固体弹道导弹总体方案设计优化软件。分析了软件多样化、通用化的功能需求,安排了软件主要计算流程,采用面向对象技术搭建了软件基本框架。软件计算结果表明,该软件能够提供固有导弹构型优化设计、新建构型优化设计、各参数配置、多种优化算法、可变优化变量、可变约束以及数据结果输出等主要功能。
本文将现代优化技术、数据分析方法应用到固体弹道导弹多学科设计中,为飞行器优化设计领域提供了新的方法和思路。设计开发的固体弹道导弹总体设计软件有一定的应用价值。
The future needs of an advanced ballistic missile weapon promote the continuous development of missile design technology. With wide application prospects, missile digital design study is very popular in recent years. In this background, the thesis concentrates on the studies of the solid ballistic missile system design models, multi-object optimal algorithms, sensitivity analysis methods and missile system optimization design software development. The main work and achievements are summarized as follows:
Firstly, modeling and simulation of solid ballistic missile operating process are studied. According to requirement in different phase of missile system design, the synopsis missile mass equation and the detailed missile mass equation are been built; Using the idea of Surrogate Models, simplified solid rocket motor analysis model which is suit to optimize is been proposed; Aerodynamic engineering estimation model which based on Missile DATCOM and trajectory design and computing model are also been proposed after the analysis of classic ballistic missile configure and the missile power phase parameters. These studies provide the simulation models for follow-up chapters.
Secondly, the dissertation conducted ballistic missile system design multi-objective optimization studies. The missile design multi-objective problem is deal with using physical programming, then a hybrid optimization algorithm based on Latin hypercube design and classic optimal algorithm is proposed to optimize the missile design model. At the same time, the multi-objective genetic algorithm NSGA-II and a single-object genetic algorithm are applied to the missile system design optimization to compare the optimal results and affectivity. A 3 stage solid ballistic missile multi-object system design optimization case which based on upwards optimal algorithm is been studied. The comparison between NSGA-II’s result and other optimal methods’results show that the physical programming and hybrid optimal algorithm are more suitable and efficiency to solve the missile system design optimization problem.
Furthermore, Orthogonal experimental design is applied to analyze sensitivity of missile system design multi-objective optimization results. Sensitivity analysis of the design variables to range and other performance merits near the best design point are been studied.
In the end, a solid ballistic missile system optimization design software is developed. By analyzing the diversity and generalization requirements, the main calculation process is completed. Using object-oriented design methods, the basic framework of the system is proposed. The software results show that the system can provide both certain and new configuration missile design optimization and results output. It also can configure different design variables, parameters, constrains and optimal algorithms.
In this desertion, the application of modern optimal techniques and data analysis methods to solid ballistic missile multi-disciplinary design provides a new approach and ideas in vehicle design optimization domain. The system concept design software has some certain applied value in the system design of solid ballistic missiles.
引文
[1]王铮,胡永强.固体火箭发动机[M].北京:宇航出版社, 1993
[2]穆立军,蔡远文.国外战略导弹的现状及发展趋势[J].兵工自动化, 2007, 24(4): 3-4
[3]康磊晶.武器系统研制技术的发展[J].战术导弹技术, 2001, 2(2): 1-8
[4] Y.P.Su M.J.Chiang, S.D.Chang. The Optimization of Solid Rocket Vehicles [R]. AIAA 83-1251,
[5] M.Briggs P.K.A.Menon, R.N.Ballou. Application of Numerical Optimization Techniques for Design of Optimum Trajectory and Propulsion Subsystem Combination [R]. AIAA 87-0128,
[6] J.Burkhalter M.Anderson, R.Jenkins. Multi-Disciplinary Intelligent Systems App- roach to Solid Rocket Motor Design Part I: Single and Dual Goal Optimization [R]. AIAA 2001-3599,
[7] J.Burkhalter M.Anderson, R.Jenkins. Multi-Disciplinary Intelligent Systems App- roach to Solid Rocket Motor Design Part II: Multiple Goal Optimization [R]. AIAA 2001-3600,
[8]韩品尧.优化设计方法的综述以及在飞航导弹设计中的应用[J].战术导弹技术, 1987, 1(3): 26-33
[9]董春平.近程地对地战术导弹总体/发动机一体化设计优化[J].战术导弹技术, 1991, 2(2): 16-26
[10]王文平,余立凤,张鸿涛.战术导弹/固体发动机一体化设计[J].固体火箭技术, 1991, 14(3): 16-23
[11]方国尧,龚晓宏.固体发动机/导弹一体化设计[J].固体火箭技术, 1992, 15(3): 7-13
[12]陈万春,赵丽红,刘佳琪,黄俊仁.反战术弹道导弹总体优化设计研究[J].北京航空航天大学学报, 1999, 25(6): 660-664
[13]从治琪,文仲辉.超高速动能导弹总体参数的优化设计[J].弹箭与制导学报, 2001, 21(3): 9-13
[14]王和平,苏浩秦.巡航导弹总体参数优化方法研究[J].航空计算技术, 1999, 29(3): 25-28
[15]杨军,陈汝训,赵锡良.战术火箭/固体火箭发动机一体化优化设计[J].宇航学报, 1999, 20(1): 21-27
[16]颜力,吴先宇,陈小前,等.固体战略弹道导弹的多学科设计优化研究[J].宇航学报, 2006, 27(1): 170-174
[17]宣颖,张为华,张育林.基于物理规划的固体运载火箭多学科设计优化[J].宇航学报, 2009, 30(2): 669-674
[18]公茂果,焦李成.进化多目标优化算法研究[J].软件学报, 2009, (2): 271-289
[19] A.Messac. Physical Programming [J]. Effective Optimization for Computational Design, 1996, 34(1): 149-158
[20]赵淑海,邱洪泽,马自谦.基于PPGA-MPB的神经网络优化及应用[J].计算机工程与应用, 2006, 42(13): 73-76
[21]欧阳骏,杨峰,杨仕文. INSGA-II算法及其在天线综合中的应用[J].电子科技大学学报, 2008, 37(6): 886-889
[22] W. Adam, C. Tim,B. Ellen. Genetic algorithm and calculus of variations-based trajectory optimization technique [J]. Journal of Spacecraft and Rockets, 2003, 40(6): 882-888
[23] Chen Gang, Xu Min, Wan Zi-ming,等. RLV Reentry Trajectory Multi-objective Optimization Design Based on NSGA-II Algorithm [A]. In.AIAA Atmospheri Flight Mechanis Conferene and Exhibit [C]. San Francisco,California,USA, 2005. 1-6
[24] Ying Hu, Gang Chen, Zi-Ming Wan,等. Multi-Objective Pareto Collaborative Optimization And Its Application [A]. In.11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference [C]. Portsmouth,Virginia, 2006. 1-6
[25] Saqlaini Akhtar,He Linshu. An Efficient Evolutionary Multi-Objective Approach for Robust Design of Multi-Stage Space Launch Vehicle [A]. In.11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference [C]. Psrtsmouth,Virginia, 2006. 1-12
[26] Shinji Suzuki,Takeshi Yoshizawa. Multiobjective Trajectory Optimization by Goal Programming with Fuzzy Decisions [J]. Journal of Guidance ,Control and Dynamics, 1994, 17(2): 297-303
[27]王允良,李为吉.物理规划方法及其在飞机方案设计中的应用[J].航空学报, 2005, 26(5): 562-566
[28]杨青,邱苑华,汪亮.固体火箭发动机成本与性能双目标优化设计[J].北京航空航天大学学报, 2005, 31(5): 574-577
[29]陈刚,康兴无,闫桂荣,等.基于多目标多学科设计优化方法的再入弹道设计研究[J].宇航学报, 2008, 29(4): 1210-1215
[30]陈新民,余梦伦.基于功能分析法的导弹基准方案设计方法[J].导弹与航天运载技术, 2008, 296(4):
[31] A.M.西纽科夫.固体弹道式导弹[M].北京:国防工业出版社, 1984
[32]瓦弗洛缅也夫B N,邸晓华等译.弹道式导弹设计和试验[M].北京:国防工业出版社, 1977
[33]陈汝训.固体火箭发动机设计与研究(上) [M].北京:宇航出版社, 1991
[34]陈汝训.固体火箭发动机设计与研究(下) [M].北京:宇航出版社, 1991
[35]侯林法.复合固体推进剂[M].北京:宇航出版社, 1994
[36]侯世明.导弹总体设计与试验[M].北京:宇航出版社, 1996
[37]黄寿康.流体动力·弹道·载荷·环境[M].北京:宇航出版社, 1991
[38]刘新建.固体弹道导弹总体论证决策系统的质量模块、发动机模块研究[D].长沙:国防科技大学硕士学位论文, 1992
[39]青龙.固体火箭发动机总体优化设计[D].长沙:国防科技大学硕士学位论文, 2003
[40]丘哲明.固体火箭发动机材料与工艺[M].北京:宇航出版社, 1995
[41]田锡惠.导弹结构材料强度(上) [M].北京:宇航出版社, 1996
[42]田锡惠.导弹结构材料强度(下) [M].北京:宇航出版社, 1996
[43]王光林,蔡峨.固体火箭发动机设计[M].西安:西北工业大学出版社, 1994
[44]王和平,苏浩秦.巡航导弹总体参数优化方法研究[J].航空计算技术, 1999, 29(3): 25-28
[45]朱忠惠.推力矢量控制伺服系统[M].北京:宇航出版社, 1995
[46]贾沛然,陈克俊,何力.远程火箭弹道学[M].长沙:国防科大出版社, 1993
[47]董师颜,张兆良等.固体火箭发动机原理[M].北京:北京理工大学出版社, 1996
[48]龙乐豪.总体设计[M].北京:宇航出版社, 1989
[49]甘楚雄,刘冀湘.运载火箭和弹道导弹总体设计[M].北京:国防工业出版社, 1996
[50]昂海松.飞行器先进设计技术[M].北京:国防工业出版社, 2008
[51]方国尧,张中钦,张鸿涛等.固体火箭发动机总体优化设计[M].北京:北京航空航天大学出版社, 1988
[52]杨青.固体火箭发动机面向成本优化设计[D].西安:西北工业大学, 2003
[53]苗瑞生,居贤铭,吴甲生.导弹空气动力学[M].北京:国防工业出版社, 2006
[54]李晓斌,张为华.多学科设计优化中搜索策略研究[J].战术导弹技术, 2004, 2(1): 1-6
[55] Dougals C.Montgomery. Design and Analysis of Experiments [M].北京:人民邮电出版社, 2009
[56] R D Manteufel. Estimating the error in LHS predictions [R]. AIAA-2005-1820, 2005
[57]李凯斌.智能进化优化算法的研究与应用[D].杭州:浙江大学硕士学位论文, 2008
[58]王元有.固体火箭发动机设计[M].北京:国防工业出版社, 1984
[59]邱清盈,冯培恩.基于正交试验的灵敏度分析法[J].机械设计, 1997, 3(5): 4-7
[60] Zeigler B P. Object-Oriented simulation with hierarchical modular models [M]. London: Academic Press, 1990
[61] Zobrist G W. Object Oriented simulation, reusability, adaptability, maintainability [M]. IEEE Press, 1996
[62]张海藩.软件工程导论(第三版) [M].北京:清华大学出版社, 1998
[63]朱海滨.面向对象的原理与应用[M].长沙:国防科技大学出版社, 1998
[64]黄柯棣.系统仿真技术[M].长沙:国防科技大学出版社, 1998
[65] Stanley B. Lippman著,潘爱民、张丽译. C++ Primer中文版[M].北京:人民邮电出版社, 2006
[2]穆立军,蔡远文.国外战略导弹的现状及发展趋势[J].兵工自动化, 2007, 24(4): 3-4
[3]康磊晶.武器系统研制技术的发展[J].战术导弹技术, 2001, 2(2): 1-8
[4] Y.P.Su M.J.Chiang, S.D.Chang. The Optimization of Solid Rocket Vehicles [R]. AIAA 83-1251,
[5] M.Briggs P.K.A.Menon, R.N.Ballou. Application of Numerical Optimization Techniques for Design of Optimum Trajectory and Propulsion Subsystem Combination [R]. AIAA 87-0128,
[6] J.Burkhalter M.Anderson, R.Jenkins. Multi-Disciplinary Intelligent Systems App- roach to Solid Rocket Motor Design Part I: Single and Dual Goal Optimization [R]. AIAA 2001-3599,
[7] J.Burkhalter M.Anderson, R.Jenkins. Multi-Disciplinary Intelligent Systems App- roach to Solid Rocket Motor Design Part II: Multiple Goal Optimization [R]. AIAA 2001-3600,
[8]韩品尧.优化设计方法的综述以及在飞航导弹设计中的应用[J].战术导弹技术, 1987, 1(3): 26-33
[9]董春平.近程地对地战术导弹总体/发动机一体化设计优化[J].战术导弹技术, 1991, 2(2): 16-26
[10]王文平,余立凤,张鸿涛.战术导弹/固体发动机一体化设计[J].固体火箭技术, 1991, 14(3): 16-23
[11]方国尧,龚晓宏.固体发动机/导弹一体化设计[J].固体火箭技术, 1992, 15(3): 7-13
[12]陈万春,赵丽红,刘佳琪,黄俊仁.反战术弹道导弹总体优化设计研究[J].北京航空航天大学学报, 1999, 25(6): 660-664
[13]从治琪,文仲辉.超高速动能导弹总体参数的优化设计[J].弹箭与制导学报, 2001, 21(3): 9-13
[14]王和平,苏浩秦.巡航导弹总体参数优化方法研究[J].航空计算技术, 1999, 29(3): 25-28
[15]杨军,陈汝训,赵锡良.战术火箭/固体火箭发动机一体化优化设计[J].宇航学报, 1999, 20(1): 21-27
[16]颜力,吴先宇,陈小前,等.固体战略弹道导弹的多学科设计优化研究[J].宇航学报, 2006, 27(1): 170-174
[17]宣颖,张为华,张育林.基于物理规划的固体运载火箭多学科设计优化[J].宇航学报, 2009, 30(2): 669-674
[18]公茂果,焦李成.进化多目标优化算法研究[J].软件学报, 2009, (2): 271-289
[19] A.Messac. Physical Programming [J]. Effective Optimization for Computational Design, 1996, 34(1): 149-158
[20]赵淑海,邱洪泽,马自谦.基于PPGA-MPB的神经网络优化及应用[J].计算机工程与应用, 2006, 42(13): 73-76
[21]欧阳骏,杨峰,杨仕文. INSGA-II算法及其在天线综合中的应用[J].电子科技大学学报, 2008, 37(6): 886-889
[22] W. Adam, C. Tim,B. Ellen. Genetic algorithm and calculus of variations-based trajectory optimization technique [J]. Journal of Spacecraft and Rockets, 2003, 40(6): 882-888
[23] Chen Gang, Xu Min, Wan Zi-ming,等. RLV Reentry Trajectory Multi-objective Optimization Design Based on NSGA-II Algorithm [A]. In.AIAA Atmospheri Flight Mechanis Conferene and Exhibit [C]. San Francisco,California,USA, 2005. 1-6
[24] Ying Hu, Gang Chen, Zi-Ming Wan,等. Multi-Objective Pareto Collaborative Optimization And Its Application [A]. In.11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference [C]. Portsmouth,Virginia, 2006. 1-6
[25] Saqlaini Akhtar,He Linshu. An Efficient Evolutionary Multi-Objective Approach for Robust Design of Multi-Stage Space Launch Vehicle [A]. In.11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference [C]. Psrtsmouth,Virginia, 2006. 1-12
[26] Shinji Suzuki,Takeshi Yoshizawa. Multiobjective Trajectory Optimization by Goal Programming with Fuzzy Decisions [J]. Journal of Guidance ,Control and Dynamics, 1994, 17(2): 297-303
[27]王允良,李为吉.物理规划方法及其在飞机方案设计中的应用[J].航空学报, 2005, 26(5): 562-566
[28]杨青,邱苑华,汪亮.固体火箭发动机成本与性能双目标优化设计[J].北京航空航天大学学报, 2005, 31(5): 574-577
[29]陈刚,康兴无,闫桂荣,等.基于多目标多学科设计优化方法的再入弹道设计研究[J].宇航学报, 2008, 29(4): 1210-1215
[30]陈新民,余梦伦.基于功能分析法的导弹基准方案设计方法[J].导弹与航天运载技术, 2008, 296(4):
[31] A.M.西纽科夫.固体弹道式导弹[M].北京:国防工业出版社, 1984
[32]瓦弗洛缅也夫B N,邸晓华等译.弹道式导弹设计和试验[M].北京:国防工业出版社, 1977
[33]陈汝训.固体火箭发动机设计与研究(上) [M].北京:宇航出版社, 1991
[34]陈汝训.固体火箭发动机设计与研究(下) [M].北京:宇航出版社, 1991
[35]侯林法.复合固体推进剂[M].北京:宇航出版社, 1994
[36]侯世明.导弹总体设计与试验[M].北京:宇航出版社, 1996
[37]黄寿康.流体动力·弹道·载荷·环境[M].北京:宇航出版社, 1991
[38]刘新建.固体弹道导弹总体论证决策系统的质量模块、发动机模块研究[D].长沙:国防科技大学硕士学位论文, 1992
[39]青龙.固体火箭发动机总体优化设计[D].长沙:国防科技大学硕士学位论文, 2003
[40]丘哲明.固体火箭发动机材料与工艺[M].北京:宇航出版社, 1995
[41]田锡惠.导弹结构材料强度(上) [M].北京:宇航出版社, 1996
[42]田锡惠.导弹结构材料强度(下) [M].北京:宇航出版社, 1996
[43]王光林,蔡峨.固体火箭发动机设计[M].西安:西北工业大学出版社, 1994
[44]王和平,苏浩秦.巡航导弹总体参数优化方法研究[J].航空计算技术, 1999, 29(3): 25-28
[45]朱忠惠.推力矢量控制伺服系统[M].北京:宇航出版社, 1995
[46]贾沛然,陈克俊,何力.远程火箭弹道学[M].长沙:国防科大出版社, 1993
[47]董师颜,张兆良等.固体火箭发动机原理[M].北京:北京理工大学出版社, 1996
[48]龙乐豪.总体设计[M].北京:宇航出版社, 1989
[49]甘楚雄,刘冀湘.运载火箭和弹道导弹总体设计[M].北京:国防工业出版社, 1996
[50]昂海松.飞行器先进设计技术[M].北京:国防工业出版社, 2008
[51]方国尧,张中钦,张鸿涛等.固体火箭发动机总体优化设计[M].北京:北京航空航天大学出版社, 1988
[52]杨青.固体火箭发动机面向成本优化设计[D].西安:西北工业大学, 2003
[53]苗瑞生,居贤铭,吴甲生.导弹空气动力学[M].北京:国防工业出版社, 2006
[54]李晓斌,张为华.多学科设计优化中搜索策略研究[J].战术导弹技术, 2004, 2(1): 1-6
[55] Dougals C.Montgomery. Design and Analysis of Experiments [M].北京:人民邮电出版社, 2009
[56] R D Manteufel. Estimating the error in LHS predictions [R]. AIAA-2005-1820, 2005
[57]李凯斌.智能进化优化算法的研究与应用[D].杭州:浙江大学硕士学位论文, 2008
[58]王元有.固体火箭发动机设计[M].北京:国防工业出版社, 1984
[59]邱清盈,冯培恩.基于正交试验的灵敏度分析法[J].机械设计, 1997, 3(5): 4-7
[60] Zeigler B P. Object-Oriented simulation with hierarchical modular models [M]. London: Academic Press, 1990
[61] Zobrist G W. Object Oriented simulation, reusability, adaptability, maintainability [M]. IEEE Press, 1996
[62]张海藩.软件工程导论(第三版) [M].北京:清华大学出版社, 1998
[63]朱海滨.面向对象的原理与应用[M].长沙:国防科技大学出版社, 1998
[64]黄柯棣.系统仿真技术[M].长沙:国防科技大学出版社, 1998
[65] Stanley B. Lippman著,潘爱民、张丽译. C++ Primer中文版[M].北京:人民邮电出版社, 2006