序列协同优化方法在深海空间站结构系统设计中的应用
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摘要
深海空间站是一种新概念的大型载人深潜装备,它为人类更好的探测和开发海洋提供了一个广阔的平台。深海空间站的结构系统主要由耐压壳、外部结构和轻外壳等组成,是深海空间站最重要的分系统。在传统的设计方法中,耐压壳、外部结构和轻外壳等子系统是单独进行设计的,并且往往侧重于耐压壳的性能分析和评估,忽视了外部结构和轻外壳的设计。而后两者对于深海空间站的总体性能同样具有重要的影响。耐压壳、外部结构和轻外壳的设计又是相互依赖和相互影响的。因此,对于深海空间的结构系统,必须将其作为一个整体来进行设计。但这也带来了一个涉及结构力学和水动力学等多个学科内容的复杂工程系统的设计问题。从航空航天领域发展起来的多学科设计优化为解决这一难题提供了一条有效的途径。
本文作为国防科工委“十一五”重大基础研究专项的部分研究内容,对多学科设计优化在深海空间站结构系统设计中的应用进行了探索,利用本文提出的序列协同优化方法完成了结构系统的设计,重点对多学科设计优化方法、耐压壳结构设计和结构系统的协同优化进行了研究,主要完成了以下几个方面的内容:
(1)对多学科设计优化进行了综述,详细介绍了多学科设计优化提出的背景、研究概况及研究的主要内容,并对多学科设计优化方法进行了重点描述。
(2)详细介绍了协同优化方法的基本思想、框架结构、数学模型和灵敏度分析原理,对其优缺点进行了阐述,并分析了其产生计算困难的原因,同时还列举了几种常见的改进措施。通过对采用L1范数形式一致性约束的协同优化方法进行分析和改造,提出了序列协同优化方法(SCO)。其主要思想是,在系统级每一步迭代中对L1范数形式一致性约束进行改造,通过引入附加约束来去除一致性约束中的绝对值符号,消除了一致性约束的非光滑性,并有效的缩小了子系统优化问题的设计空间,大大降低了陷入局部最优解的概率。结合数值算例,本文将SCO与标准协同优化方法进行了比较。
(3)对多学科设计优化中的近似技术进行了研究,分别对试验设计方法及响应面、径向基神经网络和Kriging等近似方法作了详细介绍。结合数值算例和加筋板屈曲问题,采用三种近似方法建立了相应的近似模型,并通过误差分析,对近似模型的性能进行评估和比较。
(4)对多球交接耐压壳的结构优化问题进行了研究。详细介绍了多球交接耐压壳的结构形式和几何模型,利用非线性有限元方法和Kriging近似模型,并对其进行了结构优化。在对非线性有限元结果进行观察和分析的基础上,提出了多球交接耐压壳结构优化问题的简化计算公式,并针对不同材料进行了结构优化研究。此外,本文还对多球交接耐压壳的结构形式进行了推广,提出了几种新型的球壳交接方式。
(5)将深海空间站结构系统的多学科设计优化划分为耐压壳、外部结构、轻外壳和性能四个子系统,分别对各子系统进行了详细的研究,建立了相应的子系统分析模型,明确了各子系统的输入输出,编制了相应的计算机程序。
(6)建立了深海空间站结构系统的协同优化框架,对结构系统各组成部分的具体结构形状进行了介绍,利用序列协同优化方法和Kriging近似模型,对其进行了多学科设计优化,得到了优化结果。
本文的主要创新点有:
(1)首次将多学科设计优化方法应用于深海空间站结构系统的设计过程,建立了各子系统的数学模型并将其嵌入到协同优化的框架中,验证了多学科设计优化对于复杂深海结构物结构系统设计的适用性。
(2)在对协同优化方法深入研究和分析的基础上,首次提出了序列协同优化方法。通过对L1范数形式一致性约束进行改造,有效降低了子系统级优化问题的求解难度,消除了一致性约束的非光滑性,在一定程度上提高了协同优化的性能。
(3)通过对多球交接耐压壳的非线性有限元分析,指出多球交接耐压壳的两种典型破坏模式,并分析了造成破坏的原因。在此基础上,建立了多球交接耐压壳结构优化问题的简化公式。
多学科设计优化是一门新兴的学科,而它在复杂深海结构物(包括深海空间站)结构系统设计中的应用才刚刚起步,其研究还有待深入,这主要包括:
(1)本文虽然对序列协同优化方法进行了测试,但其理论分析还不够系统和全面,其收敛性能还有待于进一步的考察和证实。同时,对于L1范数形式一致性约束的其它方式的改造有可能会产生更好的效果,这也是今后研究工作一个思路。
(2)由于对深海空间站总体设计的信息掌握较少,本文对外部结构子系统进行了大量的假设和简化,仅对吊放工况进行了分析。在将来的研究中,应当将深海空间结构系统的设计与总体设计结合起来,作为一个整体进行详细的多学科设计优化。
(3)本文假设深海空间站的轻外壳具有水滴型回转体形状,并采用经验公式估算其水下运动阻力。在将来的研究中,可以采用CFD方法,对深海空间站的外部形状建立三维模型进行流场模拟。
(4)本文仅对协同优化方法进行了系统研究,但CSSO和BLISS等多学科设计优化方法同样具有较高的发展潜力和应用价值。对于这几种多学科设计优化方法究竟哪一种更适合复杂深海结构物的结构系统设计,也有待于进一步深入的研究。
(5)多学科设计优化的发展趋势是分布式和并行计算和设计,通过计算机网络,建立分布式、并行的MDO计算环境,将大型的分析软件集成在一起,对于复杂深海结构物的多学科设计优化设计将具有更重要的意义。
The deep sea space station is a new concept human occupied vehicle, which provides a broader platform for the exploration and exploitation of ocean. As the most important part of the deep sea space station, the structural system consists of pressure hull, exostructure and faring. Traditionally, the subspaces of pressure hull, exostructure and faring are designed independently. While the designers usually emphasized on the structural analysis and design of pressure hull, those of exostructure and faring were paid little attention. Nevertheless, the latter also have a great influence on the general performance of the deep sea space station. Further more, the design of the three subspaces interacts with each other. Therefore, the structural system should be treated as a whole in the design procedure, which results in a complex design problem involving several disciplines, such as structural mechanics and hydrodynamics. Multidisciplinary design optimization (MDO) emerged from the field of aeronautics and astronautics provides an effective way to settle the problem.
As a part of the project supported by the Commission of Science Technology and Industry for National defense, the dissertation explores the application of multidisciplinary design optimization in the structural system design of deep sea space station by using sequential collaborative optimization. Focused on the MDO methods, structural design of pressure hull and collaborative optimization of structural system, the dissertation mainly consists of the following aspects:
(1) A literature review referred to the theory of MDO is presented. As well as the history and development, the main contents of MDO are introduced in detail, among which the MDO methods are focused primarily.
(2) The basic concept, architecture, mathematical model and sensitivity analysis of Collaborative optimization (CO) are introduced. Both of the advantages and disadvantages of CO are analyzed, and several improvement methods are presented. On the basis of the study of L1 compatibility constraint function, the sequential collaborative optimization (SCO) is brought forward with the concept to remove the absolute label in the L1 compatibility constraint function by introducing additional constraints. SCO eliminates the non-smoothness of the compatibility constraint functions and reduces greatly the probability for subspace optimization problem to convergence to local optimum. Besides, the performance of SCO and CO is compared through two numerical examples.
(3) A brief introduction of approximation methods in the field of MDO, including design of experiments and approximation models, are given. The performance of three approximation model—response surface, Kriging and radial basis function network are compared through numerical examples by the method of error analysis.
(4) The structural optimization problem of multiple intersecting pressure hull is studied. Based on nonlinear finite element method and Kriging mode, the structural optimization is performed. Based on the analysis of nonlinear FEM results, the simplified equations are introduced and used to the structural optimization of multiple intersecting pressure hull of different materials. In addition, several new concepts of multiple intersecting pressure hull are put forward.
(5) The dissertation divides the structural design problem of deep sea space station into four subspaces including pressure hull, exostructure, fairing and performance. The mathematical models of all subspaces are set up, and the inputs and outputs of each model are defined. The relevant calculation programs are compiled.
(6) The collaborative optimization architecture of the structural system is established and each subspace is described in detail. Kriging model and the SCO method developed in the dissertation are applied to the MDO problem of structural system design then.
The main innovation researches of the dissertation can be concluded that:
(1) This is the first time to apply the theory of MDO into the structural system design of deep sea space station. Some mathematical models are established and the applicability of MDO for the design large engineering system is proved.
(2) Based on the study of collaborative optimization, the sequential collaborative optimization is developed. By the modifying L1 compatibility constraint function, SCO eliminates the non-smoothness of the compatibility constraint functions and greatly improved the general performance of CO.
(3) The collapse modes of multiple intersecting pressure hull are concluded through the analysis of nonlinear FEM results and the simplified equations are introduced to perform structural optimization then.
Multidisciplinary design optimization is an emerging discipline and its application in the structural system design for complex deep sea structures is getting start. However, there are many aspects of research should be deepen and they are:
(1) Although the sequential collaborative optimization has been tested by numerical examples, it convergence should be inspected and verified in theory. Besides, it is possible that the other kinds of modification for the L1 compatibility constraint function improve the performance better and this is a direction for further research.
(2) Because of the lack of detailed information about the overall design, the dissertation takes much assumption and simplification. In the future, the structural system design should be integrated with the overall design to perform multidisciplinary design optimization.
(3) The fairing of deep sea space station is assumed to have a form of tear-like revolving body. For the further research, it follows a rational line to use the CFD method to model the 3-D form of faring and take more accurate hydrodynamic analysis.
(4) Besides collaborative optimization, there are many other MDO methods with great potential, such as CSSO and BLISS. Which MDO method is more suitable for the structural system design of complex deep sea structures should be further studied.
(5) Distributed and parallel computation is the trend of MDO. It is meaningful to set up an distributed and parallel environment by integrating large-scale engineering software through computer network for the multidisciplinary design optimization of large ocean structures.
本文作为国防科工委“十一五”重大基础研究专项的部分研究内容,对多学科设计优化在深海空间站结构系统设计中的应用进行了探索,利用本文提出的序列协同优化方法完成了结构系统的设计,重点对多学科设计优化方法、耐压壳结构设计和结构系统的协同优化进行了研究,主要完成了以下几个方面的内容:
(1)对多学科设计优化进行了综述,详细介绍了多学科设计优化提出的背景、研究概况及研究的主要内容,并对多学科设计优化方法进行了重点描述。
(2)详细介绍了协同优化方法的基本思想、框架结构、数学模型和灵敏度分析原理,对其优缺点进行了阐述,并分析了其产生计算困难的原因,同时还列举了几种常见的改进措施。通过对采用L1范数形式一致性约束的协同优化方法进行分析和改造,提出了序列协同优化方法(SCO)。其主要思想是,在系统级每一步迭代中对L1范数形式一致性约束进行改造,通过引入附加约束来去除一致性约束中的绝对值符号,消除了一致性约束的非光滑性,并有效的缩小了子系统优化问题的设计空间,大大降低了陷入局部最优解的概率。结合数值算例,本文将SCO与标准协同优化方法进行了比较。
(3)对多学科设计优化中的近似技术进行了研究,分别对试验设计方法及响应面、径向基神经网络和Kriging等近似方法作了详细介绍。结合数值算例和加筋板屈曲问题,采用三种近似方法建立了相应的近似模型,并通过误差分析,对近似模型的性能进行评估和比较。
(4)对多球交接耐压壳的结构优化问题进行了研究。详细介绍了多球交接耐压壳的结构形式和几何模型,利用非线性有限元方法和Kriging近似模型,并对其进行了结构优化。在对非线性有限元结果进行观察和分析的基础上,提出了多球交接耐压壳结构优化问题的简化计算公式,并针对不同材料进行了结构优化研究。此外,本文还对多球交接耐压壳的结构形式进行了推广,提出了几种新型的球壳交接方式。
(5)将深海空间站结构系统的多学科设计优化划分为耐压壳、外部结构、轻外壳和性能四个子系统,分别对各子系统进行了详细的研究,建立了相应的子系统分析模型,明确了各子系统的输入输出,编制了相应的计算机程序。
(6)建立了深海空间站结构系统的协同优化框架,对结构系统各组成部分的具体结构形状进行了介绍,利用序列协同优化方法和Kriging近似模型,对其进行了多学科设计优化,得到了优化结果。
本文的主要创新点有:
(1)首次将多学科设计优化方法应用于深海空间站结构系统的设计过程,建立了各子系统的数学模型并将其嵌入到协同优化的框架中,验证了多学科设计优化对于复杂深海结构物结构系统设计的适用性。
(2)在对协同优化方法深入研究和分析的基础上,首次提出了序列协同优化方法。通过对L1范数形式一致性约束进行改造,有效降低了子系统级优化问题的求解难度,消除了一致性约束的非光滑性,在一定程度上提高了协同优化的性能。
(3)通过对多球交接耐压壳的非线性有限元分析,指出多球交接耐压壳的两种典型破坏模式,并分析了造成破坏的原因。在此基础上,建立了多球交接耐压壳结构优化问题的简化公式。
多学科设计优化是一门新兴的学科,而它在复杂深海结构物(包括深海空间站)结构系统设计中的应用才刚刚起步,其研究还有待深入,这主要包括:
(1)本文虽然对序列协同优化方法进行了测试,但其理论分析还不够系统和全面,其收敛性能还有待于进一步的考察和证实。同时,对于L1范数形式一致性约束的其它方式的改造有可能会产生更好的效果,这也是今后研究工作一个思路。
(2)由于对深海空间站总体设计的信息掌握较少,本文对外部结构子系统进行了大量的假设和简化,仅对吊放工况进行了分析。在将来的研究中,应当将深海空间结构系统的设计与总体设计结合起来,作为一个整体进行详细的多学科设计优化。
(3)本文假设深海空间站的轻外壳具有水滴型回转体形状,并采用经验公式估算其水下运动阻力。在将来的研究中,可以采用CFD方法,对深海空间站的外部形状建立三维模型进行流场模拟。
(4)本文仅对协同优化方法进行了系统研究,但CSSO和BLISS等多学科设计优化方法同样具有较高的发展潜力和应用价值。对于这几种多学科设计优化方法究竟哪一种更适合复杂深海结构物的结构系统设计,也有待于进一步深入的研究。
(5)多学科设计优化的发展趋势是分布式和并行计算和设计,通过计算机网络,建立分布式、并行的MDO计算环境,将大型的分析软件集成在一起,对于复杂深海结构物的多学科设计优化设计将具有更重要的意义。
The deep sea space station is a new concept human occupied vehicle, which provides a broader platform for the exploration and exploitation of ocean. As the most important part of the deep sea space station, the structural system consists of pressure hull, exostructure and faring. Traditionally, the subspaces of pressure hull, exostructure and faring are designed independently. While the designers usually emphasized on the structural analysis and design of pressure hull, those of exostructure and faring were paid little attention. Nevertheless, the latter also have a great influence on the general performance of the deep sea space station. Further more, the design of the three subspaces interacts with each other. Therefore, the structural system should be treated as a whole in the design procedure, which results in a complex design problem involving several disciplines, such as structural mechanics and hydrodynamics. Multidisciplinary design optimization (MDO) emerged from the field of aeronautics and astronautics provides an effective way to settle the problem.
As a part of the project supported by the Commission of Science Technology and Industry for National defense, the dissertation explores the application of multidisciplinary design optimization in the structural system design of deep sea space station by using sequential collaborative optimization. Focused on the MDO methods, structural design of pressure hull and collaborative optimization of structural system, the dissertation mainly consists of the following aspects:
(1) A literature review referred to the theory of MDO is presented. As well as the history and development, the main contents of MDO are introduced in detail, among which the MDO methods are focused primarily.
(2) The basic concept, architecture, mathematical model and sensitivity analysis of Collaborative optimization (CO) are introduced. Both of the advantages and disadvantages of CO are analyzed, and several improvement methods are presented. On the basis of the study of L1 compatibility constraint function, the sequential collaborative optimization (SCO) is brought forward with the concept to remove the absolute label in the L1 compatibility constraint function by introducing additional constraints. SCO eliminates the non-smoothness of the compatibility constraint functions and reduces greatly the probability for subspace optimization problem to convergence to local optimum. Besides, the performance of SCO and CO is compared through two numerical examples.
(3) A brief introduction of approximation methods in the field of MDO, including design of experiments and approximation models, are given. The performance of three approximation model—response surface, Kriging and radial basis function network are compared through numerical examples by the method of error analysis.
(4) The structural optimization problem of multiple intersecting pressure hull is studied. Based on nonlinear finite element method and Kriging mode, the structural optimization is performed. Based on the analysis of nonlinear FEM results, the simplified equations are introduced and used to the structural optimization of multiple intersecting pressure hull of different materials. In addition, several new concepts of multiple intersecting pressure hull are put forward.
(5) The dissertation divides the structural design problem of deep sea space station into four subspaces including pressure hull, exostructure, fairing and performance. The mathematical models of all subspaces are set up, and the inputs and outputs of each model are defined. The relevant calculation programs are compiled.
(6) The collaborative optimization architecture of the structural system is established and each subspace is described in detail. Kriging model and the SCO method developed in the dissertation are applied to the MDO problem of structural system design then.
The main innovation researches of the dissertation can be concluded that:
(1) This is the first time to apply the theory of MDO into the structural system design of deep sea space station. Some mathematical models are established and the applicability of MDO for the design large engineering system is proved.
(2) Based on the study of collaborative optimization, the sequential collaborative optimization is developed. By the modifying L1 compatibility constraint function, SCO eliminates the non-smoothness of the compatibility constraint functions and greatly improved the general performance of CO.
(3) The collapse modes of multiple intersecting pressure hull are concluded through the analysis of nonlinear FEM results and the simplified equations are introduced to perform structural optimization then.
Multidisciplinary design optimization is an emerging discipline and its application in the structural system design for complex deep sea structures is getting start. However, there are many aspects of research should be deepen and they are:
(1) Although the sequential collaborative optimization has been tested by numerical examples, it convergence should be inspected and verified in theory. Besides, it is possible that the other kinds of modification for the L1 compatibility constraint function improve the performance better and this is a direction for further research.
(2) Because of the lack of detailed information about the overall design, the dissertation takes much assumption and simplification. In the future, the structural system design should be integrated with the overall design to perform multidisciplinary design optimization.
(3) The fairing of deep sea space station is assumed to have a form of tear-like revolving body. For the further research, it follows a rational line to use the CFD method to model the 3-D form of faring and take more accurate hydrodynamic analysis.
(4) Besides collaborative optimization, there are many other MDO methods with great potential, such as CSSO and BLISS. Which MDO method is more suitable for the structural system design of complex deep sea structures should be further studied.
(5) Distributed and parallel computation is the trend of MDO. It is meaningful to set up an distributed and parallel environment by integrating large-scale engineering software through computer network for the multidisciplinary design optimization of large ocean structures.
引文
[1]朱继懋.潜水器设计[M].上海:上海交通大学出版社. 1992.
[2]弗朗克.布什毕.载人潜水器[M].北京:海洋出版社. 1982.
[3] American Institute of Aeronautics and Astronautic. AIAA Technical Committee on Multidisciplinary Design Optimization (MDO) [Z]. White paper on current state of the art. Reston, Va, USA. 1991.
[4] Giesing J P, Barthelemy J M. A Summary of Industry MDO Applications and Needs[Z]. AIAA White Paper, 7th AIAA/ USAF/NASA/ ISSMO Symposium on Multidisciplinary Analysis and Optimization. 1998.
[5] Sobieszczanski-Sobieski J. A Linear Decomposition Method for Optimization Problem– Blueprint for Development[Z]. NASA Technical Memorandum 83248. 1982.
[6]刘蔚.多学科设计优化方法在7000米载人潜水器总体设计中的应用[D] : [博士论文].上海:上海交通大学. 2007
[7]操安喜.载人潜水器多学科设计优化方法及其应用研究[D]: [博士论文].上海:上海交通大学. 2008.
[8]胡志强.多学科设计优化技术在深水半潜式钻井平台概念设计中的应用研究[D]: [博士论文].上海:上海交通大学. 2008.
[9]余雄庆.多学科设计算法及其在飞机设计中的应用研究[D]: [博士论文].南京:南京航空航天大学. 1999.
[10]胡峪.飞机多学科设计优化及其应用研究[D]: [博士论文].西安:西北工业大学. 2001.
[11]陈琪锋.飞行器分布式协同进化多学科设计优化方法研究[D]: [博士论文].长沙:国防科学技术大学研究生院. 2003.
[12] Sobieszczanski-Sobieski J, Barthelemy J F, Riley K M. Sensitivity of Optimum Solutions to Problem Parameters[J]. AIAA Journal. 1982, 20(9): 1291-1299.
[13] Schwabacher M. Multilevel simulation and numerical optimization of complex engineering designs[J]. AIAA Journal of Aircraft. 1998, 35: 1–23.
[14] Wrenn G A, Dovi A R. Multilevel Decomposition Approach to the Preliminary Sizing of a Transport Aircraft Wing[J]. AIAA Journal of Aircraft. 1988, 25(7):32–638.
[15] Azarm S, Li W. A Two-Level Decomposition Method For Design Optimization[J]. Engineering Optimization. 1988, 13: 211-224.
[16] Kirsch U. Two-level optimization of prestressed structures[J]. Engineering Structures. 1997, 19 (4): 309–317.
[17] Hutchison M G, Unger E R, Mason W H, Grossman B, Haftka R T. Variable-complexity aerodynamic optimization of an HSCT wing using structural wing-weight equations[J]. Journal of Aircraft 1994, 31(1): 110-116.
[18] Unger E R, Hutchison M G., Rais-Rohani M, Haftka R T, Grossman B. Variable-Complexity Multidisciplinary Design of a Transport Wing[J]. International Journal of System Automation: Research and Applications (SARA). 1992, 2(2): 87-113.
[19] Unger E R, Hutchinson M G., Rais-Rohani M, Haftka R T, Grossman B. Variable-complexity multidisciplinary design of a transport wing[J]. International Journal of System Automation: Research and Application. 1992, 2(2): 87-113.
[20] Barthelemy J F, Wrenn G., Dovi A, Coen P. Integrating aerodynamics and structures in the minimum weight design of a supersonic transport wing[R]. AIAA Paper 92-2372. 1992.
[21] Karpel M. Modal-Based Enhancement of integrated structural design optimization schemes[J]. Journal of Aircraft. 1998, 35 (3): 437– 444.
[22] Giunta A A, Dudley J M, Narducci R, Grossman B, Haftka R T, Mason W H, Watson L T. Noisy Aerodynamic Response and Smooth Approximations in HSCT Design[R]. AIAA Paper 94-4376. 1994.
[23] Toropov V V, Markine V L. The use of simplified numerical models as mid-range approximation[C]. 6th AIAA/USAF/NASA/ISSMO Symposium on multidisciplinary analysis and optimization. Bellevue, WA. 1996.
[24] Unal R, Lepsch R, Engelund W, Stanley D. Approximation model building and multidisciplinary design optimization using response surface methods[C]. Proc. 6th AIAA/NASA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, Part I . Bellevue, WA. 1996.
[25] Sacks J, Schiller S B, Welch W J. Design for computer experiments[J]. Technometrics. 1989, 31: 41–47.
[26] Sobieszczanski-Sobieski J. Sensitivity of complex, internally coupled systems[J]. AIAA Journal. 1990, 28(1): 153-162.
[27] Olds J. System sensitivity analysis applied to the conceptual design of a dual-fuel rocket SSTO[C]. Proc. 5th AIAA/NASA/USAF/ISSMO Symp. on Multidisciplinary Analysis and Optimization. Panama City Beach, FL. 1994.
[28] Haftka R T, Adelman H. Recent developments in structural sensitivity analysis[J]. Structural Optimization. 1989, 1: 137–151.
[29] Arslan A E, Carlson L A. Integrated determination of sensitivity derivatives for an aeroelastic transonic wing[J]. Journal of Aircraft. 1996, 33: 224–231.
[30] Sobieszczanski-Sobieski J, Barthelemy J F M, Riley K M. Sensitivity of optimum solutions to problems parameters[J]. AIAA Journal. 1992, 20: 1291–1299.
[31] Gage P. New approaches to optimization in aerospace conceptual design[R]. NASA CR-196695. 1995.
[32] Logan T R.: Strategy for multilevel optimization of aircraft[J]. Journal of Aircraft. 1990, 27: 1068–1072 .
[33] Balling R J, Sobieszczanski-Sobieski J. Optimization of Coupled Systems: A Critical Overview of Approaches[J]. AIAA Journal. 1996, 34(1): 6-17.
[34] Cramer E J, Frank P D, Shubin G R, Dennis J E, Lewis R M. On alternative problem formulation for multidisciplinary optimization[C]. Proceedings of the 4th AIAA/USAF/NASA/OAI symposium on multidisciplinary analysis and optimization. Cleveland, OH. 1992 .
[35] Cramer E J, Dennis J, Frank P, Lewis R, Shubin G. Problem formulation for multidisciplinary optimization[J]. SIAM Journal on Optimization. 1994, 4: 754-776.
[36] Sobieszczanski-Sobieski J. Optimization by decomposition: Step from hierarchic to non-hierarchic systems[C]. NASA TM 101494. Langley Research Center, Hampton, Virginia. 1988.
[37] Renaud J E, Gabriele G A. Improved Coordination in Nonhierarchic System Optimization[J]. AIAA Journal. 1993, 31(12): 2367-2373.
[38] Renaud J E, Gabriele G A. Sequential global approximation in non-hierarchic system decomposition and optimization[J]. Advances in Design Automation. 1991, 1:191-200.
[39] Renaud J E, Gabriele G A. Approximation in Non-hierarchical System Optimization[J]. AIAA Journal. 1994, 32: 198-205.
[40] Sellar R S, Stelmack M A, Batill SM, Renaud J E. Response surface approximations for discipline coordination in multidisciplinary design optimization[C]. 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference. Salt Lake City, Utha. 1996.
[41] Wujek B, Renaud J, Batill S, Johnson E, Brockman J. Design Flow Management and Multidisciplinary Design Optimization in Application to Aircraft Concept Sizing[R]. AIAA Paper 96-0713. 1996.
[42] Batill S B, Stelmack M A, Yu X Q. Multidisciplinary design optimization of an electric-powered unmanned air vehicle[J]. Aircraft Design. 1999, 2(1): 1-18.
[43] Wujek B, Renaud J E, Batill S M, Brockman J B. Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment[J]. Concurrent Engineering: Research and Applications (CERA). 1996, 4(4): 361-378.
[44]邢小楠,徐元铭,李烁,杨笑菡.神经网络响应面逼近在飞机总体优化设计中的应用[J].机械设计与研究. 2004, 20(1):60-71.
[45]张科施,李为吉,李响.飞机概念设计的多学科综合优化技术[J].西北工业大学学报. 2005, 23(1): 108-112.
[46] Stelmack M, Batill S M, Beck B, Flask D. Application of the Concurrent Subspace Design Framework to Aircraft Brake Component Design Optimizaiton[R]. AIAA Paper 98-2033. 1998.
[47] Yu X Q, Stelmack M, Batill S M. An Application of Concurrent Subspace Design(CSD) to the Preliminary Design of a Low-Reynolds Number UAV[R]. AIAA Paper 98-4917. 1998.
[48] Batill S B, Stelmack M A, Yu X Q. Multidisciplinary design optimization of an electric-powered unmanned air vehicle[J]. Aircraft Design. 1999, 2: 1-18.
[49] Lokanathan A N, Brockman J B, Renaud J. A Multidisciplinary Optimization Approach to Integrated Circuit Design[C]. Proceedings of Concurrent Engineering: A Global Perspective, CE95 Conference. McLean, Virginia. 1995 .
[50] Kroo I, Altus S, Braun R, Gage P, Sobieski I. Multidisciplinary optimization methods for aircraft preliminary design[R]. AIAA Paper 94-4325-cp. 1994.
[51] Sobieszczanski-Sobieski J, Agte J S, Sandusky J R. Bi-level integrated system synthesis (BLISS)[C]. Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. St Louis, Missouri. 1998.
[52] Kodiyalam S, Sobieszczanski-Sobieski J. Bi-level integrated system synthesis with response surface [J]. AIAA Journal. 2000, 38(8): 1479-1485.
[53] Sobieszczanski-Sobieski J, Altus T D, Phillips M, Sandusky R. Bi-Level Integrated System Synthesis for Concurrent and Distributed[J]. AIAA Journal. 2003, 41(10): 1996-2002.
[54] Altus T D. A response surface methodology for bi-level integrated system synthesis (BLISS)[R]. Hampton,Va.,USA:NASA Langley Research Center. 2002.
[55] Brown N, Olds J. Evaluation of Multidisciplinary Optimization (MDO) Technique. Applied to a Reusable Launch Vehicle[R]. AIAA Paper 2005-707. 2005.
[1] Kroo I, Altus S, Braun R, Gage P, Sobieski I. Multidisciplinary optimization methods for aircraft preliminary design[R]. AIAA Paper 94-4325-cp. 1994.
[2] Braun R D. Collaborative Optimization: An architecture for large-scale distributed design[D]: [PhD dissertation]. Stanford. 1996.
[3] Alexandrov N M, Lewis R M. Comparative properties of collaborative optimization and other approaches to mdo[R]. Technical Report ICASE Report No. 99-24. July 1999.
[4] Kroo I, Manning V. Collaborative Optimization: Status and Directions[R]. AIAA Paper 2000-4721. 2000.
[5] Braun R D, Moore A A, Kroo I M. Collaborative architecture for launch vehicle design[J]. Journal of Spacecraft and Rockets. 1997, 34(4): 478-486.
[6] Belegundu A D, Halberg E, Yukish M A. Attribute-Based Multidisciplinary Optimization of Undersea Vehicle[R]. AIAA Paper 2000-4865. 2000.
[7] Huque Z, Jahingir N. Application of Collaborative Optimization on a RBCC Inlet/Ejector System[R]. AIAA Paper 2002-3604. 2002.
[8] Kodiyalam S, Yuan C. Evaluation of Methods for Multidisciplinary Design Optimization Methods (MDO), Part II [R]. AIAA Paper NASA/CR-2000-210310. 2000.
[9] Alexandrova N M, Kodiyalam S, Initial Results of an MDO Method Evaluation Study[R]. AIAA Paper 98-4884. 1998.
[10] DeMiguel A, Murray W. An Analysis of Collaborative Optimization Methods [C]. in Eighth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization AIAA-2000-4720. Sept. 2000.
[11] Lin J G. Analysis and enhancement of collaborative optimization for multidisciplinary design [J]. AIAA Journal. 2004, 42(2): 348-360.
[12] Sobieski I P, Kroo I M. Collaborative Optimization Using Response Surface Estimation[J]. AIAA Journal. 2000, 38(10): 1931-1938.
[13]余雄庆,薛飞,穆雪飞,姚卫星,刘克龙,黄爱风.用遗传算法提高协同优化方法的可靠性[J].中国机械工程. 2003, 14(21): 1808-1811.
[14]韩明红. ICO多学科设计优化方法[J].北京航空航天学报. 2007, 33(8): 963-967.
[15] Sellar R S, Batill S M, Renaud J E. Response Surface Based, Concurrent Subspace Optimization for Multidisciplinary Design Optimization[C]. 34th Aerospace Sciences Meeting and Exhibit, Reno, NV. 1996.
[1] Golovidov O B, Mason W H, Grossman B, Watson L T, Haftka R T. Response Surface Approximations for Aerodynamic Parameters in High Speed Civil Transport Optimization[A]. Technical Report: TR-97-15. Virginia Polytechnic Institute and State University. 1997.
[2] Unal R, Lepsch R A, McMillin M L. Response surface model building and multidisciplinary optimization using D-optimal designs[C]. in: Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. 1998: 98–4759.
[3] Sobieski I P, Kroo I M. Collaborative Optimization Using Response Surface Estimation[J]. AIAA Journal. 2000, 38(10):1931~1938.
[4] McKay M D, Conover W J, Beckman R J. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code[J]. Technometrics. 1979,21: 239–245.
[5]张铁茂,丁建国.试验设计与数据处理[M].北京:兵器工业出版社. 1990: 190-195.
[6] Wang Y, Fang K T. A note on uniform distribution and experimental design[J]. Kexue Tongbao. 1981, 26: 485-489.
[7] Box G E P, Wilson K B. On the Experimental Attainment of Optimum Conditions[J]. Journal of the Royal Statistical Society, Series B (Methodological). 1951, 13(1): 1-45.
[8] Roberto V. Response surface methods for high dimensional structural design problems[D]:[Ph. D dissertation]. University of Florida. 2000.
[9] Sacks J, Schiller S B, Welch W J. Design for computer experiments[J]. Technometrics. 1989, 31: 41–47.
[10] Sacks J, Welch W J, Mitchell W J, Wynn H P. Design and analysis of computer experiments[J]. Statistical Science, 1989, 4(4):409–435.
[11] Welch W J, Buck R J, Sacks J, Wynn H P, Mitchell W J, Morris M D. Screening, predicting, and computer experiments[J]. Technometrics, 1992, 34: 15–25..
[12] Sasena M J. Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations[D]:[Ph.D dissertation]. University of Michigan. Ann Arbor, MI, USA, 2002.
[13] Etman L F P. Design and analysis of computer experiments: The method of sacks et al[R]. Technical Report WFW 94.098. Eindhoven University of Technology. 1994.
[14] Chen S, Cowan C F N, Grant P M. Orthogonal least squares learning algorithm for radial basis function networks[J]. IEEE Transactions on Neural Networks. 1991, 2(2): 302-309.
[15] Moody J E, Darken C J. Fast learning in networks of locally-tuned processing unit[J]. Neural Computation. 1989, 1(2): 281-294.
[16] Holcomb T, Morari M. Local training for radial basis function networks towards solving the hidden units problem[C]. Proceedings of the American Control Conference. Boston, MA, USA, 1991: 2331–2336.
[17] Cui W C. Buckling and Ultimate Strength Analysis of Stiffened Panels[J]. Journal of Ship Mechanics. 1998, 2(03): 41-61.
[1] Garland C. Design and fabrication of deep-diving submersible pressure hulls[J]. SNAME Transactions. 1968, 76: 161–179.
[2] Leon G F. Intersecting titanium spheres for deep submersibles[J]. Journal of the Engineering Mechanics Division. 1971, 97(3): 981-1006.
[3] Hall J C, Leon G F, Kelly J J. Deep submergence design of intersecting composite spheres[G]. In Composites—Design, Manufacture and Applications, SAMPE, 1991: 2F1–2F12.
[4] Liang C C, Shiah S W, Jen C Y, Chen H W. Optimum Design of Multiple Intersecting Spheres Deep-Submerged Pressure Hull[J]. Ocean Engineering. 2004, 31: 177-199.
[5]陆蓓,刘涛,崔维成.深海载人潜水器耐压球壳极限强度研究[J].船舶力学. 2004, 8(1): 51-58.
[6] Krenzke M A, Kiernan T J. The effect of initial imperfections on the collapse strength of deep spherical shells[R]. David Taylor Model Basin Report No.1757. Bethesda, Md., Feb. 1965.
[7]张允真,曹富新.弹性力学及其有限元法[M].北京:中国铁道出版社. 1983: 141.
[8] ABS. Rules for Building and Classing Underwater Vehicles, Systems and Hyperbaric Facilities[S]. 2002.
[9] Liang C C, Teng T L, Lai W H. A study of diving depth on deep-diving submersible vehicle[J]. International Journal of Pressure Vessels and Piping. 1998, 75: 447-457.
[1] ABS. Rules for building and classing underwater vehicles, systems and hyperbaric Facilities[S]. 2002.
[2]朱继懋.潜水器设计[M].上海:上海交通大学出版社. 1992:126.
[3]刘涛.大深度潜水器结构分析与设计研究[D]:[博士论文].无锡:中国船舶科学研究中心. 2001.
[4]中国船级社.潜水系统和潜水器入级与建造规范[S]. 1996.
[5] Korean Register of Shipping. Rules for the classification of underwater vehicles[S]. 2005.
[6]叶彬.载人潜水器载体框架结构设计研究[D]:[硕士论文] .无锡:中国船舶科学研究中心. 2006.
[7]姜次平,邵世明.船舶阻力[M].上海:上海交通大学出版社. 1985:211.
[8] Hoerner S F. Fluid Dynamic Drag[M]. Brick Town, New Jersey. 1965.
[1] Nystrom J W. Treatise on Parabolic Construction of Ships and Other Marine Engineering Subjects[R]. 1863.
[2] Hoerner S F. Fluid Dynamic Drag[M]. Brick Town, New Jersey. 1965.
[3]沈国鉴.潜艇设计原理[M].上海:上海交通大学出版社. 1988:58.
[2]弗朗克.布什毕.载人潜水器[M].北京:海洋出版社. 1982.
[3] American Institute of Aeronautics and Astronautic. AIAA Technical Committee on Multidisciplinary Design Optimization (MDO) [Z]. White paper on current state of the art. Reston, Va, USA. 1991.
[4] Giesing J P, Barthelemy J M. A Summary of Industry MDO Applications and Needs[Z]. AIAA White Paper, 7th AIAA/ USAF/NASA/ ISSMO Symposium on Multidisciplinary Analysis and Optimization. 1998.
[5] Sobieszczanski-Sobieski J. A Linear Decomposition Method for Optimization Problem– Blueprint for Development[Z]. NASA Technical Memorandum 83248. 1982.
[6]刘蔚.多学科设计优化方法在7000米载人潜水器总体设计中的应用[D] : [博士论文].上海:上海交通大学. 2007
[7]操安喜.载人潜水器多学科设计优化方法及其应用研究[D]: [博士论文].上海:上海交通大学. 2008.
[8]胡志强.多学科设计优化技术在深水半潜式钻井平台概念设计中的应用研究[D]: [博士论文].上海:上海交通大学. 2008.
[9]余雄庆.多学科设计算法及其在飞机设计中的应用研究[D]: [博士论文].南京:南京航空航天大学. 1999.
[10]胡峪.飞机多学科设计优化及其应用研究[D]: [博士论文].西安:西北工业大学. 2001.
[11]陈琪锋.飞行器分布式协同进化多学科设计优化方法研究[D]: [博士论文].长沙:国防科学技术大学研究生院. 2003.
[12] Sobieszczanski-Sobieski J, Barthelemy J F, Riley K M. Sensitivity of Optimum Solutions to Problem Parameters[J]. AIAA Journal. 1982, 20(9): 1291-1299.
[13] Schwabacher M. Multilevel simulation and numerical optimization of complex engineering designs[J]. AIAA Journal of Aircraft. 1998, 35: 1–23.
[14] Wrenn G A, Dovi A R. Multilevel Decomposition Approach to the Preliminary Sizing of a Transport Aircraft Wing[J]. AIAA Journal of Aircraft. 1988, 25(7):32–638.
[15] Azarm S, Li W. A Two-Level Decomposition Method For Design Optimization[J]. Engineering Optimization. 1988, 13: 211-224.
[16] Kirsch U. Two-level optimization of prestressed structures[J]. Engineering Structures. 1997, 19 (4): 309–317.
[17] Hutchison M G, Unger E R, Mason W H, Grossman B, Haftka R T. Variable-complexity aerodynamic optimization of an HSCT wing using structural wing-weight equations[J]. Journal of Aircraft 1994, 31(1): 110-116.
[18] Unger E R, Hutchison M G., Rais-Rohani M, Haftka R T, Grossman B. Variable-Complexity Multidisciplinary Design of a Transport Wing[J]. International Journal of System Automation: Research and Applications (SARA). 1992, 2(2): 87-113.
[19] Unger E R, Hutchinson M G., Rais-Rohani M, Haftka R T, Grossman B. Variable-complexity multidisciplinary design of a transport wing[J]. International Journal of System Automation: Research and Application. 1992, 2(2): 87-113.
[20] Barthelemy J F, Wrenn G., Dovi A, Coen P. Integrating aerodynamics and structures in the minimum weight design of a supersonic transport wing[R]. AIAA Paper 92-2372. 1992.
[21] Karpel M. Modal-Based Enhancement of integrated structural design optimization schemes[J]. Journal of Aircraft. 1998, 35 (3): 437– 444.
[22] Giunta A A, Dudley J M, Narducci R, Grossman B, Haftka R T, Mason W H, Watson L T. Noisy Aerodynamic Response and Smooth Approximations in HSCT Design[R]. AIAA Paper 94-4376. 1994.
[23] Toropov V V, Markine V L. The use of simplified numerical models as mid-range approximation[C]. 6th AIAA/USAF/NASA/ISSMO Symposium on multidisciplinary analysis and optimization. Bellevue, WA. 1996.
[24] Unal R, Lepsch R, Engelund W, Stanley D. Approximation model building and multidisciplinary design optimization using response surface methods[C]. Proc. 6th AIAA/NASA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, Part I . Bellevue, WA. 1996.
[25] Sacks J, Schiller S B, Welch W J. Design for computer experiments[J]. Technometrics. 1989, 31: 41–47.
[26] Sobieszczanski-Sobieski J. Sensitivity of complex, internally coupled systems[J]. AIAA Journal. 1990, 28(1): 153-162.
[27] Olds J. System sensitivity analysis applied to the conceptual design of a dual-fuel rocket SSTO[C]. Proc. 5th AIAA/NASA/USAF/ISSMO Symp. on Multidisciplinary Analysis and Optimization. Panama City Beach, FL. 1994.
[28] Haftka R T, Adelman H. Recent developments in structural sensitivity analysis[J]. Structural Optimization. 1989, 1: 137–151.
[29] Arslan A E, Carlson L A. Integrated determination of sensitivity derivatives for an aeroelastic transonic wing[J]. Journal of Aircraft. 1996, 33: 224–231.
[30] Sobieszczanski-Sobieski J, Barthelemy J F M, Riley K M. Sensitivity of optimum solutions to problems parameters[J]. AIAA Journal. 1992, 20: 1291–1299.
[31] Gage P. New approaches to optimization in aerospace conceptual design[R]. NASA CR-196695. 1995.
[32] Logan T R.: Strategy for multilevel optimization of aircraft[J]. Journal of Aircraft. 1990, 27: 1068–1072 .
[33] Balling R J, Sobieszczanski-Sobieski J. Optimization of Coupled Systems: A Critical Overview of Approaches[J]. AIAA Journal. 1996, 34(1): 6-17.
[34] Cramer E J, Frank P D, Shubin G R, Dennis J E, Lewis R M. On alternative problem formulation for multidisciplinary optimization[C]. Proceedings of the 4th AIAA/USAF/NASA/OAI symposium on multidisciplinary analysis and optimization. Cleveland, OH. 1992 .
[35] Cramer E J, Dennis J, Frank P, Lewis R, Shubin G. Problem formulation for multidisciplinary optimization[J]. SIAM Journal on Optimization. 1994, 4: 754-776.
[36] Sobieszczanski-Sobieski J. Optimization by decomposition: Step from hierarchic to non-hierarchic systems[C]. NASA TM 101494. Langley Research Center, Hampton, Virginia. 1988.
[37] Renaud J E, Gabriele G A. Improved Coordination in Nonhierarchic System Optimization[J]. AIAA Journal. 1993, 31(12): 2367-2373.
[38] Renaud J E, Gabriele G A. Sequential global approximation in non-hierarchic system decomposition and optimization[J]. Advances in Design Automation. 1991, 1:191-200.
[39] Renaud J E, Gabriele G A. Approximation in Non-hierarchical System Optimization[J]. AIAA Journal. 1994, 32: 198-205.
[40] Sellar R S, Stelmack M A, Batill SM, Renaud J E. Response surface approximations for discipline coordination in multidisciplinary design optimization[C]. 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference. Salt Lake City, Utha. 1996.
[41] Wujek B, Renaud J, Batill S, Johnson E, Brockman J. Design Flow Management and Multidisciplinary Design Optimization in Application to Aircraft Concept Sizing[R]. AIAA Paper 96-0713. 1996.
[42] Batill S B, Stelmack M A, Yu X Q. Multidisciplinary design optimization of an electric-powered unmanned air vehicle[J]. Aircraft Design. 1999, 2(1): 1-18.
[43] Wujek B, Renaud J E, Batill S M, Brockman J B. Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment[J]. Concurrent Engineering: Research and Applications (CERA). 1996, 4(4): 361-378.
[44]邢小楠,徐元铭,李烁,杨笑菡.神经网络响应面逼近在飞机总体优化设计中的应用[J].机械设计与研究. 2004, 20(1):60-71.
[45]张科施,李为吉,李响.飞机概念设计的多学科综合优化技术[J].西北工业大学学报. 2005, 23(1): 108-112.
[46] Stelmack M, Batill S M, Beck B, Flask D. Application of the Concurrent Subspace Design Framework to Aircraft Brake Component Design Optimizaiton[R]. AIAA Paper 98-2033. 1998.
[47] Yu X Q, Stelmack M, Batill S M. An Application of Concurrent Subspace Design(CSD) to the Preliminary Design of a Low-Reynolds Number UAV[R]. AIAA Paper 98-4917. 1998.
[48] Batill S B, Stelmack M A, Yu X Q. Multidisciplinary design optimization of an electric-powered unmanned air vehicle[J]. Aircraft Design. 1999, 2: 1-18.
[49] Lokanathan A N, Brockman J B, Renaud J. A Multidisciplinary Optimization Approach to Integrated Circuit Design[C]. Proceedings of Concurrent Engineering: A Global Perspective, CE95 Conference. McLean, Virginia. 1995 .
[50] Kroo I, Altus S, Braun R, Gage P, Sobieski I. Multidisciplinary optimization methods for aircraft preliminary design[R]. AIAA Paper 94-4325-cp. 1994.
[51] Sobieszczanski-Sobieski J, Agte J S, Sandusky J R. Bi-level integrated system synthesis (BLISS)[C]. Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. St Louis, Missouri. 1998.
[52] Kodiyalam S, Sobieszczanski-Sobieski J. Bi-level integrated system synthesis with response surface [J]. AIAA Journal. 2000, 38(8): 1479-1485.
[53] Sobieszczanski-Sobieski J, Altus T D, Phillips M, Sandusky R. Bi-Level Integrated System Synthesis for Concurrent and Distributed[J]. AIAA Journal. 2003, 41(10): 1996-2002.
[54] Altus T D. A response surface methodology for bi-level integrated system synthesis (BLISS)[R]. Hampton,Va.,USA:NASA Langley Research Center. 2002.
[55] Brown N, Olds J. Evaluation of Multidisciplinary Optimization (MDO) Technique. Applied to a Reusable Launch Vehicle[R]. AIAA Paper 2005-707. 2005.
[1] Kroo I, Altus S, Braun R, Gage P, Sobieski I. Multidisciplinary optimization methods for aircraft preliminary design[R]. AIAA Paper 94-4325-cp. 1994.
[2] Braun R D. Collaborative Optimization: An architecture for large-scale distributed design[D]: [PhD dissertation]. Stanford. 1996.
[3] Alexandrov N M, Lewis R M. Comparative properties of collaborative optimization and other approaches to mdo[R]. Technical Report ICASE Report No. 99-24. July 1999.
[4] Kroo I, Manning V. Collaborative Optimization: Status and Directions[R]. AIAA Paper 2000-4721. 2000.
[5] Braun R D, Moore A A, Kroo I M. Collaborative architecture for launch vehicle design[J]. Journal of Spacecraft and Rockets. 1997, 34(4): 478-486.
[6] Belegundu A D, Halberg E, Yukish M A. Attribute-Based Multidisciplinary Optimization of Undersea Vehicle[R]. AIAA Paper 2000-4865. 2000.
[7] Huque Z, Jahingir N. Application of Collaborative Optimization on a RBCC Inlet/Ejector System[R]. AIAA Paper 2002-3604. 2002.
[8] Kodiyalam S, Yuan C. Evaluation of Methods for Multidisciplinary Design Optimization Methods (MDO), Part II [R]. AIAA Paper NASA/CR-2000-210310. 2000.
[9] Alexandrova N M, Kodiyalam S, Initial Results of an MDO Method Evaluation Study[R]. AIAA Paper 98-4884. 1998.
[10] DeMiguel A, Murray W. An Analysis of Collaborative Optimization Methods [C]. in Eighth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization AIAA-2000-4720. Sept. 2000.
[11] Lin J G. Analysis and enhancement of collaborative optimization for multidisciplinary design [J]. AIAA Journal. 2004, 42(2): 348-360.
[12] Sobieski I P, Kroo I M. Collaborative Optimization Using Response Surface Estimation[J]. AIAA Journal. 2000, 38(10): 1931-1938.
[13]余雄庆,薛飞,穆雪飞,姚卫星,刘克龙,黄爱风.用遗传算法提高协同优化方法的可靠性[J].中国机械工程. 2003, 14(21): 1808-1811.
[14]韩明红. ICO多学科设计优化方法[J].北京航空航天学报. 2007, 33(8): 963-967.
[15] Sellar R S, Batill S M, Renaud J E. Response Surface Based, Concurrent Subspace Optimization for Multidisciplinary Design Optimization[C]. 34th Aerospace Sciences Meeting and Exhibit, Reno, NV. 1996.
[1] Golovidov O B, Mason W H, Grossman B, Watson L T, Haftka R T. Response Surface Approximations for Aerodynamic Parameters in High Speed Civil Transport Optimization[A]. Technical Report: TR-97-15. Virginia Polytechnic Institute and State University. 1997.
[2] Unal R, Lepsch R A, McMillin M L. Response surface model building and multidisciplinary optimization using D-optimal designs[C]. in: Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. 1998: 98–4759.
[3] Sobieski I P, Kroo I M. Collaborative Optimization Using Response Surface Estimation[J]. AIAA Journal. 2000, 38(10):1931~1938.
[4] McKay M D, Conover W J, Beckman R J. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code[J]. Technometrics. 1979,21: 239–245.
[5]张铁茂,丁建国.试验设计与数据处理[M].北京:兵器工业出版社. 1990: 190-195.
[6] Wang Y, Fang K T. A note on uniform distribution and experimental design[J]. Kexue Tongbao. 1981, 26: 485-489.
[7] Box G E P, Wilson K B. On the Experimental Attainment of Optimum Conditions[J]. Journal of the Royal Statistical Society, Series B (Methodological). 1951, 13(1): 1-45.
[8] Roberto V. Response surface methods for high dimensional structural design problems[D]:[Ph. D dissertation]. University of Florida. 2000.
[9] Sacks J, Schiller S B, Welch W J. Design for computer experiments[J]. Technometrics. 1989, 31: 41–47.
[10] Sacks J, Welch W J, Mitchell W J, Wynn H P. Design and analysis of computer experiments[J]. Statistical Science, 1989, 4(4):409–435.
[11] Welch W J, Buck R J, Sacks J, Wynn H P, Mitchell W J, Morris M D. Screening, predicting, and computer experiments[J]. Technometrics, 1992, 34: 15–25..
[12] Sasena M J. Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations[D]:[Ph.D dissertation]. University of Michigan. Ann Arbor, MI, USA, 2002.
[13] Etman L F P. Design and analysis of computer experiments: The method of sacks et al[R]. Technical Report WFW 94.098. Eindhoven University of Technology. 1994.
[14] Chen S, Cowan C F N, Grant P M. Orthogonal least squares learning algorithm for radial basis function networks[J]. IEEE Transactions on Neural Networks. 1991, 2(2): 302-309.
[15] Moody J E, Darken C J. Fast learning in networks of locally-tuned processing unit[J]. Neural Computation. 1989, 1(2): 281-294.
[16] Holcomb T, Morari M. Local training for radial basis function networks towards solving the hidden units problem[C]. Proceedings of the American Control Conference. Boston, MA, USA, 1991: 2331–2336.
[17] Cui W C. Buckling and Ultimate Strength Analysis of Stiffened Panels[J]. Journal of Ship Mechanics. 1998, 2(03): 41-61.
[1] Garland C. Design and fabrication of deep-diving submersible pressure hulls[J]. SNAME Transactions. 1968, 76: 161–179.
[2] Leon G F. Intersecting titanium spheres for deep submersibles[J]. Journal of the Engineering Mechanics Division. 1971, 97(3): 981-1006.
[3] Hall J C, Leon G F, Kelly J J. Deep submergence design of intersecting composite spheres[G]. In Composites—Design, Manufacture and Applications, SAMPE, 1991: 2F1–2F12.
[4] Liang C C, Shiah S W, Jen C Y, Chen H W. Optimum Design of Multiple Intersecting Spheres Deep-Submerged Pressure Hull[J]. Ocean Engineering. 2004, 31: 177-199.
[5]陆蓓,刘涛,崔维成.深海载人潜水器耐压球壳极限强度研究[J].船舶力学. 2004, 8(1): 51-58.
[6] Krenzke M A, Kiernan T J. The effect of initial imperfections on the collapse strength of deep spherical shells[R]. David Taylor Model Basin Report No.1757. Bethesda, Md., Feb. 1965.
[7]张允真,曹富新.弹性力学及其有限元法[M].北京:中国铁道出版社. 1983: 141.
[8] ABS. Rules for Building and Classing Underwater Vehicles, Systems and Hyperbaric Facilities[S]. 2002.
[9] Liang C C, Teng T L, Lai W H. A study of diving depth on deep-diving submersible vehicle[J]. International Journal of Pressure Vessels and Piping. 1998, 75: 447-457.
[1] ABS. Rules for building and classing underwater vehicles, systems and hyperbaric Facilities[S]. 2002.
[2]朱继懋.潜水器设计[M].上海:上海交通大学出版社. 1992:126.
[3]刘涛.大深度潜水器结构分析与设计研究[D]:[博士论文].无锡:中国船舶科学研究中心. 2001.
[4]中国船级社.潜水系统和潜水器入级与建造规范[S]. 1996.
[5] Korean Register of Shipping. Rules for the classification of underwater vehicles[S]. 2005.
[6]叶彬.载人潜水器载体框架结构设计研究[D]:[硕士论文] .无锡:中国船舶科学研究中心. 2006.
[7]姜次平,邵世明.船舶阻力[M].上海:上海交通大学出版社. 1985:211.
[8] Hoerner S F. Fluid Dynamic Drag[M]. Brick Town, New Jersey. 1965.
[1] Nystrom J W. Treatise on Parabolic Construction of Ships and Other Marine Engineering Subjects[R]. 1863.
[2] Hoerner S F. Fluid Dynamic Drag[M]. Brick Town, New Jersey. 1965.
[3]沈国鉴.潜艇设计原理[M].上海:上海交通大学出版社. 1988:58.