第2期 柳强，等：基于Kriging模型和NSGA-IⅡ的航空发动机管路卡箍布局优化 ·287· 参考文献： [D].武汉：华中科技大学，2015。 LI Yaohui.The Kriging-based global approximation and [1]何宇廷，杨少华，冯立富.飞机地面压力加油系统导管卡 simulation optimization methods[D].Wuhan:Huazhong 箍固定间距的确定刀.机械科学与技术，2000,19(5)： University of Science and Technology,2015. 726-728. [13】韩永志，高行山，李立州，等.基于Kriging模型的涡轮 HE Yuting,YANG Shaohua,FENG Lifu.On the determin- 叶片多学科设计优化).航空动力学报，2007,22(7)： ation of fixture intervals of pipe hoops of aircraft ground 1055-1059. pressure refueling system[J].Mechanical science and tech- HAN Yongzhi,GAO Hangshan,LI Lizhou,et al.Kriging nology,2000,19(5):726-728. model-based multidisciplinary design optimization for [2]顾文彬.舰船管路系统在振动环境下弹性支承的位置优 turbine blade[J].Journal of aerospace power,2007,22(7): 化研究D].上海：同济大学，2000. 1055-1059. 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[10]刘周.多目标遗传算法及其在管路卡箍布局优化设计 中的应用研究D]武汉：武汉理工大学，2014. LIU Zhou.Research on multi-objective genetical al- gorithm and its application in optimal design of piping 焦国帅，男，1993年生，硕士研究 clamp layout[D].Wuhan:Wuhan University of Techno- 1ogy,2014. 生，主要研究方向为多目标优化及其 [11]MCKAY M D,BECKMAN R J.CONOVER W J.A 应用、管路布局。 comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J].Technometrics,2000,42(1):55-61. [l2]李耀辉.基于Kriging模型的全局近似与仿真优化方法参考文献： 何宇廷, 杨少华, 冯立富. 飞机地面压力加油系统导管卡 箍固定间距的确定 [J]. 机械科学与技术, 2000, 19(5): 726–728. HE Yuting, YANG Shaohua, FENG Lifu. On the determin￾ation of fixture intervals of pipe hoops of aircraft ground pressure refueling system[J]. Mechanical science and tech￾nology, 2000, 19(5): 726–728. [1] 顾文彬. 舰船管路系统在振动环境下弹性支承的位置优 化研究 [D]. 上海: 同济大学, 2000. GU Wenbin. The position optimizing of ship’pipe system support under vibration excitation[D]. Shanghai: Tongji University, 2000. [2] ZHU Jihong, ZHANG Weihong. Maximization of structur￾al natural frequency with optimal support layout[J]. Struc￾tural and multidisciplinary optimization, 2006, 31(6): 462–469. [3] 尹泽勇, 陈亚农. 卡箍刚度的有限元计算与实验测定 [J]. 航空动力学报, 1999, 14(2): 179–182. YIN Zeyong, CHEN Yanong. Finite element analysis and experimental measurement of stiffness of hoop[J]. Journal of aerospace power, 1999, 14(2): 179–182. [4] WANG D, JIANG J S, ZHANG W H. Optimization of support positions to maximize the fundamental frequency of structures[J]. International journal for numerical meth￾ods in engineering, 2004, 61(10): 1584–1602. [5] WANG D. Optimization of support positions to minimize the maximal deflection of structures[J]. International journ￾al of solids and structures, 2004, 41(26): 7445–7458. [6] 智友海, 史向平. 飞机管路系统卡箍位置的可靠性优化 设计 [J]. 飞机设计, 2010, 30(6): 75–80. ZHI Youhai, SHI Xiangping. Reliability optimization designs of clamp's locations for airplane pipeline system[J]. Aircraft design, 2010, 30(6): 75–80. [7] 刘伟, 曹刚, 翟红波, 等. 发动机管路卡箍位置动力灵敏 度分析与优化设计 [J]. 航空动力学报, 2012, 27(12): 2756–2762. LIU Wei, CAO Gang, ZHAI Hongbo, et al. Sensitivity analysis and dynamic optimization design of supports’ pos￾itions for engine pipelines[J]. Journal of aerospace power, 2012, 27(12): 2756–2762. [8] 李鑫, 王少萍. 基于卡箍优化布局的飞机液压管路减振 分析 [J]. 振动与冲击, 2013, 32(1): 14–20. LI Xin, WANG Shaoping. Vibration control analysis for hydraulic pipelines in an aircraft based on optimized clamp layout[J]. Journal of vibration and shock, 2013, 32(1): 14–20. [9] 刘周. 多目标遗传算法及其在管路卡箍布局优化设计 中的应用研究 [D]. 武汉: 武汉理工大学, 2014. LIU Zhou. Research on multi-objective genetical al￾gorithm and its application in optimal design of piping clamp layout[D]. Wuhan: Wuhan University of Techno￾logy, 2014. [10] MCKAY M D, BECKMAN R J, CONOVER W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics, 2000, 42(1): 55–61. [11] [12] 李耀辉. 基于 Kriging 模型的全局近似与仿真优化方法 [D]. 武汉: 华中科技大学, 2015. LI Yaohui. The Kriging-based global approximation and simulation optimization methods[D]. Wuhan: Huazhong University of Science and Technology, 2015. 韩永志, 高行山, 李立州, 等. 基于 Kriging 模型的涡轮 叶片多学科设计优化 [J]. 航空动力学报, 2007, 22(7): 1055–1059. HAN Yongzhi, GAO Hangshan, LI Lizhou, et al. Kriging model-based multidisciplinary design optimization for turbine blade[J]. Journal of aerospace power, 2007, 22(7): 1055–1059. [13] 韩鼎, 郑建荣, 周骏彦. Kriging 模型并行加点策略的多 目标优化方法 [J]. 机械科学与技术, 2016, 35(11): 1715–1720. HAN Ding, ZHENG Jianrong, ZHOU Junyan. A multi￾objective optimization method using Kriging model and parallel point adding strategy[J]. Mechanical science and technology for aerospace engineering, 2016, 35(11): 1715–1720. [14] SACKS J, WELCH W J, MITCHELL T J, et al. Design and analysis of computer experiments[J]. Statistical sci￾ence, 1989, 4(4): 409–423. [15] 李小刚, 程锦, 刘振宇, 等. 基于双层更新 Kriging 模型 的机械结构动态特性稳健优化设计 [J]. 机械工程学报, 2014, 50(3): 165–173. LI Xiaogang, CHENG Jin, LIU Zhenyu, et al. Robust op￾timization for dynamic characteristics of mechanical structures based on double renewal Kriging model[J]. Journal of mechanical engineering, 2014, 50(3): 165–173. [16] 柳强, 王成恩. 基于 Kriging 模型的复杂产品管线敷设 顺序粒子群优化 [J]. 机械工程学报, 2011, 47(13): 140–146. LIU Qiang, WANG Cheng’en. Kriging model-based rout￾ing sequence planning for complex products by particle swarm optimization[J]. Journal of mechanical engineer￾ing, 2011, 47(13): 140–146. [17] DEB K, PRATAP A, AGARWAL S, et al. A fast and elit￾ist multiobjective genetic algorithm: NSGA-II[J]. IEEE transactions on evolutionary computation, 2002, 6(2): 182–197. [18] 作者简介： 柳强，男，1982 年生，副教授，主 要研究方向为多目标优化、近似模型 方法。 焦国帅，男，1993 年生，硕士研究 生，主要研究方向为多目标优化及其 应用、管路布局。 第 2 期 柳强，等：基于 Kriging 模型和 NSGA-II 的航空发动机管路卡箍布局优化 ·287·