结构动力鲁棒优化设计方法综述
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摘要
如何提高结构动力学性能的鲁棒性,以减小各种不确定性因素对设计结果的影响是当前学术界和工程界研究和关注的热点问题之一。该文阐述了结构动力鲁棒优化设计的基本概念,从基于Taguchi的方法、基于多目标优化的方法和基于响应面建模的方法三个方面对结构动力鲁棒优化设计的研究进行了综述。以双转子为例,从结构的动力响应要求出发,采用响应面建模、多目标优化的方法进行了设计并与采用Taguchi方法得到的结果进行比较。结果表明,基于响应面建模、多目标优化的方法能够获得多个具有鲁棒性的设计方案,在处理具有不确定性的结构动力学问题时有着很大的应用潜力。最后,对当前方法和后续研究内容作了简要总结和展望。
How to improve the robustness of structural dynamic performance, and how to minimize the influence of various uncertainties on mean design are one of the hot issues both in academic and engineering fields. In this paper, the basic concept of structural dynamic robust optimization design is described. The robust optimization design methods of structural dynamics are reviewed from three aspects that are based on Taguchi method, multi-objective optimization and response surface methods. Taking a dual-rotor as an example, the dynamic robust optimization design is carried out by using the response surface modeling and multi-objective optimization methods. The results show that multiple robust optimization design schemes can be obtained based on response surface modeling and multi-objective optimization, and robust design methods have great potential for application in structural dynamics to deal with uncertain problems. Finally, the current research methods and future work are briefly summarized and prospected.
How to improve the robustness of structural dynamic performance, and how to minimize the influence of various uncertainties on mean design are one of the hot issues both in academic and engineering fields. In this paper, the basic concept of structural dynamic robust optimization design is described. The robust optimization design methods of structural dynamics are reviewed from three aspects that are based on Taguchi method, multi-objective optimization and response surface methods. Taking a dual-rotor as an example, the dynamic robust optimization design is carried out by using the response surface modeling and multi-objective optimization methods. The results show that multiple robust optimization design schemes can be obtained based on response surface modeling and multi-objective optimization, and robust design methods have great potential for application in structural dynamics to deal with uncertain problems. Finally, the current research methods and future work are briefly summarized and prospected.
引文
[1]陈建军,车建文,崔明涛,等.结构动力优化设计述评与展望[J].力学进展,2001,31(2):181-192.Chen Jianjun,Che Jianwen,Cui Mingtao,et al.A review on structural dynamic optimum design[J].Advances in Mechanics,2001,31(2):181-192.(in Chinese)
[2]Niordson F I.The optimum design of a vibrating beam[J].Quarterly of Applied Mathematics,1965,23(1):47-53.
[3]林家浩.结构动力优化设计发展综述[J].力学进展,1983,13(4):423-431.Lin Jiahao.Review on the development in structural dynamic optimum design[J].Advances in Mechanics,1983,13(4):423-431.(in Chinese)
[4]刘永泉,王德友,洪杰,等.航空发动机整机振动控制技术分析[J].航空发动机,2013,39(5):1-8.Liu Yongquan,Wang Deyou,Hong Jie,et al.Analysis of whole aeroengine vibration control technology[J].Aeroengine,2013,39(5):1-8.(in Chinese)
[5]Rao S S.Reliability-based optimization under random vibration environment[J].Computers&Structures,1981,14(5):345-355.
[6]Ziegel E R.Taguchi techniques for quality engineering[J].Technometrics,1989,39(1):109-110.
[7]Yamakawa H,Miyashita M.A study on robust structures.1st report:concept of robust structure and 1ts design method[J].Transactions of the Japan Society of Mechanical Engineers Series C,1991,57(544):3913-3918.
[8]Zang C,Friswell M I,Mottershead J E.A review of robust optimal design and its application in dynamics[J].Computers&Structures,2005,83(4/5):315-326.
[9]Beyer H G,Sendhoff B.Robust optimization-Acomprehensive survey[J].Computer Methods in Applied Mechanics&Engineering,2007,196(33/34):3190-3218.
[10]接婧.国际学术界对鲁棒性的研究[J].系统工程学报,2005,20(2):153-159.Jie Jing.Study of robustness in the world[J].Journal of Systems Engineering,2005,20(2):153-159.(in Chinese)
[11]张正福,王安麟,刘广军,等.基于Taguchi三次设计的微机械陀螺健壮性设计[J].上海交通大学学报,2008,42(2):249-252.Zhang Zhengfu,Wang Anlin,LIU GuanJun,et al.Robust design for micromachined gyroscope using Taguchi three-stage design[J].Journal of Shanghai Jiaotong University,2008,42(2):249-252.(in Chinese)
[12]谢晖,刘行,洪健程.基于Taguchi方法的车门结构稳健性优化[J].中国机械工程,2013,24(12):1676-1681.Xie Hui,Liu Xing,Hong Jiancheng.Robust Optimization of automotive door structure based on Taguchi's method[J].China Mechanical Engineering,2013,24(12):1676-1681.(in Chinese)
[13]张代胜,张旭,王浩,等.基于Taguchi方法的动力总成悬置系统稳健优化[J].汽车工程,2014,36(4):475-480.Zhang Daisheng,Zhang Xu,Wang Hao,et al.Robust optimization of powertrain mounting system based on Taguchi's method[J].Automotive Engineering,2014,36(4):475-480.(in Chinese)
[14]王淑红,武潇,高泽梅.Taguchi法在内嵌式永磁同步电动机中的应用[J].太原理工大学学报,2014,45(5):618-622.Wang Shuhong,Wu Xiao,Gao Zemei.Application of Taguchi method in interior permanent magnet synchronous motor[J].Journal of Taiyuan University of Technology,2014,45(5):618-622.(in Chinese)
[15]Cai D A,Xiu-Ping W U,Yang G P,et al.Design for structure parameters of composite frangible cover based on Taguchi’s method[J].Journal of Solid Rocket Technology,2016,39(6):797-802.
[16]郭一鸣,魏玉明,上官文斌.发动机曲轴橡胶扭转减振器稳健性优化匹配[J].华南理工大学学报(自然科学版),2017,45(2):75-83.Guo Yiming,Wei Yuming,Shangguan Wenbin.Robust optimal matching of rubber-type torsional vibration damper for engine crankshaft[J].Journal of South China University of Technology(Natural Science Edition),2017,45(2):75-83.(in Chinese)
[17]Song J,Dong F,Zhao J,et al.Optimal design of a permanent magnet linear synchronous motors based on Taguchi method[J].Iet Electric Power Applications,2017,11(1):41-48.
[18]孙光永,屈瑞飞,张慧乐,等.基于Taguchi与TOPSIS-熵的车门多目标离散稳健优化研究[J].现代制造工程,2018(3):11-18.Sun Guangyong,Qu Ruifei,Zhang Huile,et al.Robust optimization of automobile door structure based on Taguchi and TOPSIS-entropy[J].Modern Manufacturing Engineering,2018(3):11-18.(in Chinese)
[19]Zong Y,Mao J.Tolerance optimization design based on the manufacturing-costs of assembly quality[J].Procedia Cirp,2015,27:324-329.
[20]孙岩辉,洪军,刘志刚,等.考虑零部件制造误差的精密主轴几何回转精度计算方法[J].机械工程学报,2017,53(3):173-182.Sun Yanhui,Hong Jun,Liu Zhigang,et al.A calculating method for the geometric rotation accuracy of precision spindles considering the manufacturing errors of component parts[J].Journal of Mechanical Engineering,2017,53(3):173-182.(in Chinese)
[21]Mohan P,Haghighi P,Vemulapalli P,et al.Toward automatic tolerancing of mechanical assemblies:assembly analyses[J].Journal of Computing&Information Science in Engineering,2014,14(4):1-14.
[22]殷良伟,郭海丁.某型航空发动机封严篦齿盘异型螺栓孔公差设计分析[J].航空发动机,2017,43(5):85-90.Yin Liangwei,Guo Haiding.Analysis on dimension tolerance design of non-circular hole of labyrinth disk for an aeroengine[J].Aeroengine,2017,43(5):85-90.(in Chinese)
[23]杨隽,臧朝平,刘永泉,等.基于Taguchi方法的转子系统动力学容差设计[J].航空动力学报,2014,29(7):1583-1590.Yang Jun,Zang Chaoping,Liu Yongquan,et al.Taguchi-based tolerance design method for rotor dynamics[J].Journal of Aerospace Power,2014,29(7):1583-1590.(in Chinese)
[24]杨隽,臧朝平.基于遗传算法的不确定性结构动力学鲁棒设计[C]//中国力学大会2011暨钱学森诞辰100周年纪念大会,2011.Yang Jun,Zang Chaoping.Genetic algorithm based robust design in dynamics due to parameter uncertainty[C]//The Chinese Conference on Theoretical and Applied Mechanics-2001 in Memorial of Tsien Hsue-shen’s 100th Anniversary,2011.(in Chinese)
[25]岳伟,梅庆,张大义,等.高速可拆卸转子止口连接结构稳健性设计方法[J].航空动力学报,2017,32(7):1754-1761.Yue Wei,Mei Qing,Zhang Dayi,et al.Robust design method of Rabbet joint structure in high speed assemble rotor[J].Journal of Aerospace Power,2017,32(7):1754-1761.(in Chinese)
[26]洪杰,徐筱李,梁天宇,等.转子结构系统界面失效分析及稳健设计方法[J].航空动力学报,2018,33(3):649-656.Hong Jie,Xu Xiaoli,Liang Tianyu,et al.Interface failure analysis and robust design method in rotor structural system[J].Journal of Aerospace Power,2018,33(3):649-656.(in Chinese)
[27]Tsui K L.A critical look at Taguchi's modelling approach for robust design[J].Journal of Applied Statistics,1996,23(1):81-96.
[28]Chang H H.A data mining approach to dynamic multiple responses in Taguchi experimental design[J].Expert Systems with Applications,2008,35(3):1095-1103.
[29]Parkinson A,Sorensen C,Pourhassan N.A general approach for robust optimal design[J].Trans.asme JMech.design,1993,115(1):74-80.
[30]Zang C.Robust design of a two degree freedom system due to the parameter uncertainty[J].Chinese Journal of Mechanical Engineering,2008,21(6):30-35.
[31]肖方豪,蹇开林.鲁棒优化设计方法在结构动力学中的应用[J].工程力学,2007,24(增刊1):62-65.Xiao Fanghao,Jian Kailin.Application of Robust Optimal Design in Structural Dynamics[J].Engineering Mechanics,2007,24(suppl 1):62-65.(in Chinese)
[32]Marano G C,Greco R,Sgobba S.A comparison between different robust optimum design approaches:Application to tuned mass dampers[J].Probabilistic Engineering Mechanics,2010,25(1):108-118.
[33]Miguel L F F,Lopez R H.Robust design optimization of friction dampers for structural response control[J].Structural Control&Health Monitoring,2014,21(9):1240-1251.
[34]孙晓颖,李天娥,陆正争,等.平流层飞艇的多目标优化与决策[J].工程力学,2015(6):243-250.Sun Xiaoying,Li Tian’e,Lu Zhengzheng,et al.Multiobjective optimization and decision making of stratosphe re airships[J].Engineering Mechanics,2015(6):243-250.(in Chinese)
[35]Roy B K,Chakraborty S.Robust optimum design of base isolation system in seismic vibration control of structures under random system parameters[J].Structure&Infrastructure Engineering,2016,12(5):592-602.
[36]Dell'Elce L,Gourc E,Kerschen G.A robust equal-peak method for uncertain mechanical systems[J].Journal of Sound Vibration,2018,414:97-109.
[37]蒲利东,罗务揆,严泽洲.气动伺服弹性系统结构陷幅滤波器优化设计[J].工程力学,2018,35(4):235-241.Pu Lidong,Luo Wukui,Yan Zezhou.Optimal design for notch filter of aeroservoelastic systems[J].Engineering Mechanics,2018,35(4):235-241.(in Chinese)
[38]陈鑫,李爱群,徐庆阳,等.基于遗传算法的高耸结构环形TLD满意优化设计[J].工程力学,2016,33(6):77-84.Chen Xin,Li Aiqun,Xu Qingyang,et al.Satisfaction optimum design of ring-shape tld control for high-rise structure using genetic algorithm[J].Engineering Mechanics,2016,33(6):77-84.(in Chinese)
[39]王歆侃.基于容差模型的发动机悬置系统稳健优化设计[J].汽车科技,2012(4):16-19.Wang Yinkan.Robust optimal design of engine mounting system based on tolerance model[J].AUTOSU-TECH,2012(4):16-19.(in Chinese)
[40]陈新志,孙桓五,刘荣,等.基于容差模型的半挂汽车列车行驶平顺性优化[J].汽车技术,2014(4):48-52.Chen Xinzhi,Sun Hengwu,Liu Rong,et al.Ridie comfort optimization of semitrailer train based on tolerance model[J].Automobile Technology,2014(4):48-52.(in Chinese)
[41]Loyer B,Jezequel L.Robust design of a passive linear quarter car suspension system using a multi-objective evolutionary algorithm and analytical robustness indexes[J].Vehicle System Dynamics 2009,47(10):1253-1270.
[42]燕宁宁,董恩国.基于多目标优化的悬架系统空间结构稳健性研究[J].天津职业技术师范大学学报,2016,26(3):10-13.Yan Ningning,Dong Enguo.Research on robustness of spatial structure of suspension system based on multi-objective optimization[J].Journal of Tianjin University of Technology and Education,2016,26(3):10-13.(in Chinese)
[43]范政武,王铁,王永红,等.基于改进多目标粒子群算法的商用车悬架系统优化[J].振动与冲击,2018,37(15):216-224.Fan Zhengwu,Wang Tie,Wang Yonghong,et al.Commercial vehicle suspension system optimization base on improved multi-object particle swarm optimization[J].Journal of Vibration and Shock,2018,37(15):216-224.(in Chinese)
[44]傅超,任兴民,杨永锋,等.考虑参数不确定性的转子系统瞬态动平衡研究[J].动力学与控制学报,2017,15(5):453-458.Fu Chao,Ren Xingmin,Yang Yongfeng,et al.Transient dynamic balancing of rotor system with parameter uncertainties[J].Journal of Dynamics and Control,2017,15(5):453-458.(in Chinese)
[45]Gan C B,Wang Y H,Yang S X,et al.Nonparametric modeling and vibration analysis of uncertain Jeffcott rotor with disc offset[J].International Journal of Mechanical Sciences,2014,78(1):126-134.
[46]Ma Y,Liang Z,Chen M,et al.Interval analysis of rotor dynamic response with uncertain parameters[J].Journal of Sound&Vibration,2013,332(16):3869-3880.
[47]Ritto T G,Lopez R H,Sampaio R,et al.Robust optimization of a flexible rotor-bearing system using the Campbell diagram[J].Engineering Optimization,2011,43(1):77-96.
[48]Lopez R H,Ritto T G,Sampaio R,et al.A new algorithm for the robust optimization of rotor-bearing systems[J].Engineering Optimization,2014,46(8):1123-1138.
[49]Krack M,Panning L,Wallaschek J,et al.Robust design of friction interfaces of bladed disks with respect to parameter uncertainties[C]//ASME Turbo Expo 2012:Turbine Technical Conference and Exposition,2012:1193-1204.
[50]姚建尧,王建军,李其汉.失谐叶盘结构鲁棒性能分析[J].航空动力学报,2010,25(7):1634-1639.Yao Jianyao,Wang JianJun,Li Qihan.Robust performance analysis of mistuned bladed disks[J].Journal of Aerospace Power,2010,25(7):1634-1639.(in Chinese)
[51]段勇亮,臧朝平,Petrov E.P.主动失谐叶盘振动特性及鲁棒性研究[J].航空发动机,2015,41(6):6-10.Duan Yongliang,Zang Chaoping,Petrov E P.Research on vibration performance and robustness of bladed disks with intentional mistuning[J].Aeroengine,2015,41(6):6-10.(in Chinese)
[52]罗佑新,车晓毅,杨继荣,等.高维多目标灰色稳健优化设计及其Matlab实现[J].农业机械学报,2008,39(8):157-160.Luo Youxin,Che Xiaoyi,Yang Jirong,et al.Grey-robust optimal design of high-dimensional multi-objective and its achieving with Matlab[J].Transactions of the Chinese Society of Agricultural Machinery,2008,39(8):157-160.(in Chinese)
[53]郝芳芳,范小宁,智博.基于灵敏度附加目标函数的起重机主梁稳健优化设计[J].机械强度,2017(6):1385-1390.Hao Fangfang,Fan Xiaoning,Zhi Bo.Structure and robust optimization design based on additional objective function of the sensitivity[J].Journal of Mechanical Strength,2017(6):1385-1390.(in Chinese)
[54]Sundaresan S,IshiiK,Houser D R.A robust optimization procedure with variations on design variables and constraints[J].Advances in Design Automation,69(1):379-386.
[55]Petrov E P,Ewins D J.Analysis of the worst mistuning patterns in bladed disk assemblies[C].Asme Turbo Expo:Power for Land,Sea,&Air,2003:623-631.
[56]谭元球,臧朝平,周标,等.失谐叶盘受迫响应的灵敏度分析方法[J].航空学报,2017,38(12):187-197.Tan Yuanqiu,Zang Chaoping,Zhou Biao,et al.Sensitivity analysis method for forced reponse of mistuned bladed discs[J].Acta Aeronautica et Astronautic Sinica,2017,38(12):187-197.(in Chinese)
[57]Du X P,Chen W.Efficient uncertainty analysis methods for multidisciplinary robust design[J].AIAA J,2002,40(3):545-552.
[58]Liu S,Ma Y,Zhang D,et al.Studies on dynamic characteristics of the joint in the aero-engine rotor system[J].Mechanical Systems&Signal Processing,2012,29(5):120-136.
[59]Marano G C,Quaranta G.Robust optimum criteria for tuned mass dampers in fuzzy environments[J].Applied Soft Computing Journal,2009,9(4):1232-1243.
[60]Lievens K,Lombaert G,Roeck G D,et al.Robust design of a TMD for the vibration serviceability of a footbridge[J].Engineering Structures,2016,12(3):408-418.
[61]Khuri A I,Mukhopadhyay S.Response surface methodology[J].Wiley Interdisciplinary Reviews Computational Statistics,2010,2(2):128-149.
[62]刘小川,马晓利,孙侠生,等.基于响应面方法的多支柱起落架着陆缓冲性能优化[J].振动工程学报,2010,23(3):305-309.Liu Xiaochuang,Ma Xiaoli,Sun Xiasheng,et al.Performance optimization of shock absorber for multi-strut landing gear based on RSM[J].Journal of Vibration Engineering,2010,23(3):305-309.(in Chinese)
[63]黄亚,于德介,吕辉,等.含不确定参数的盘式制动器稳定性分析[J].机械强度,2017(6):1371-1378.Huang Ya,Yu Dejie,Lu Hui,et al.Stability analysis of disc brake systems with uncertainty parameters[J].Journal of Mechanical Strength,2011,47(24):97-103.(in Chinese)
[64]刘承杰,李倩,罗鹏,等.基于响应面法的V带轮多目标优化设计[J].应用力学学报,2018,35(1):147-153.Liu Chenjie,Li Qian,Luo Peng,et al.Multi-objective optimization design of V-pulley based on response surface method[J].Chinese Journal of Applied Mechanics,2018,35(1):147-153.(in Chinese)
[65]柯婉頔,吴婧,杨森,等.基于响应面法和遗传算法的某SUV前悬优化[J].华中师范大学学报(自科版),2017,51(4):455-460.Ke Wandi,Wu Jing,Yang Sen,et al.Optimization of front suspension of sports utility vehicle based on response surface method and genetic algorithm[J].Journal of Central China Normal University(Nat.Sci.),2017,51(4):455-460.(in Chinese)
[66]Ghisu T,Parks G T,Jarrett J P,et al.Robust design optimization of gas turbine compression systems[J].Journal of Propulsion&Power,2011,27(2):282-295.
[67]Tosi G,Mucchi E,D’Ippolito R,et al.Dynamic behavior of pumps:an efficient approach for fast robust design optimization[J].Meccanica,2015,50(8):2179-2199.
[68]Stocki R,Szolc T,Tauzowski P,et al.Robust design optimization of the vibrating rotor-shaft system subjected to selected dynamic constraints[J].Mechanical Systems&Signal Processing,2012,29(29):34-44.
[69]崔杰,张维刚,常伟波,等.基于双响应面模型的碰撞安全性稳健性优化设计[J].机械工程学报,2011,47(24):97-103.Cui Jie,Zhang Weigang,Chang Weibo,et al.Robustness optimization for crash safety based on dual-response surface model[J].Journal of mechanical engineering,2011,47(24):97-103.(in Chinese)
[70]Shen D E,Braatz R D.Polynomial chaos-based robust design of systems with probabilistic uncertainties[J].AICh E Journal,2016.
[71]陈力波,黄才贵,谷音.基于改进响应面法的公路简支梁桥地震易损性分析[J].工程力学,2018(4):208-218.Chen Libo,Huang Caigui,Gu Yin.Seimic vulnerability analysis of simply supported highway bridges based on an improved response surface method[J].Engineering Mechanics,2018(4):208-218.(in Chinese)
[72]窦毅芳,刘飞,张为华.响应面建模方法的比较分析[J].工程设计学报,2007,14(5):359-363.Dou Yifang,Liu Fei,Zhang Weihua.Research on comparative analysis of response surface methods[J].Journal of Engineering Design,2007,14(5):359-363.(in Chinese)
[73]陈永亮,刘双,王汉涛,等.基于Kriging代理模型的主轴箱稳健设计[J].天津大学学报(自然科学与工程技术版),2011,44(12):1111-1117.Chen Yongliang,Liu Shuang,Wang Hantao,et al.Robust design of headstock based on kriging surrogate model[J].Journal of Tianjin University(Science and Technology),2011,44(12):1111-1117.(in Chinese)
[74]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 optimization for dynamic characteristics of mechanical structures based on double renewal kriging model[J].Joural of Mechanical Engineering,2014,50(3):165-173.(in Chinese)
[75]刘艳,白俊强,华俊,等.基于Stochastic Kriging的柔性机翼稳健性优化设计[J].西北工业大学学报,2015(6):906-912.Liu Yan,Bai Junqiang,Hua Jun,et al.Robust optimization of flexible wing using stochastic kriging surrogate model[J].Journal of Northwestern Polytechnical University,2015(6):906-912.(in Chinese)
[76]蒙文巩,马东立,楚亮.基于神经网络响应面的机翼气动稳健性优化设计[J].航空学报,2010,31(6):1134-1140.Meng Wengong,Ma Dongli,Chu Liang.Wing aerodynamic robustness optimization based on neural network response surface[J].Acta Aeronautica et Astronautic Sinica,2010,31(6):1134-1140.(in Chinese)
[77]顾松年,徐斌,荣见华,等.结构动力学设计优化方法的新进展[J].机械强度,2005,27(2):24-30.Gu Songnian,Xu Bin,Rong Jianhua,et al.Recent progresses on structural dynamic design methods[J].Journal of Mechanical Strength,2005,27(2):24-30.(in Chinese)
[78]Steenackers G,Guillaume P,Vanlanduit S.Robust optimization of an airplane component taking into account the uncertainty of the design parameters[J].Quality&Reliability Engineering International,2009,25(3):255-282.
[79]张军红,韩景龙.考虑不确定性的机翼气动弹性优化问题研究[C]//全国空气弹性学术交流会,2011.Zhang Junhong,Han Jinglong.Study on aeroelastic optimization of wing with uncertainty[C]//National Air Flexibility Academic Intercommunions,2011.(in Chinese)
[80]李焦赞,高正红.多目标进化算法和代理模型技术在气动稳健优化设计中的应用[J].空气动力学学报,2012,30(1):46-51.Li Jiaozan,Gao Zhenghong.The application of multi-objective evolutionary algorithm and surrogate model to aerodynamic robust optimization design[J].Acta Aerodynamica Sinica,2012,30(1):46-51.(in Chinese)
[81]孙岩.飞行器机翼气动/结构耦合优化设计研究[J].工程力学,2012(11):360-364.Sun Yan.Investigation on coupling aerodynamic and structural design optimization for aircraft airfoil[J].Engineering Mechanics,2012(11):360-364.(in Chinese)
[82]Jansen M,Lombaert G,Schevenels M,et al.Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis[J].Computer Methods in Applied Mechanics and Engineering,2015,285:452-467.
[83]邬晓敬,张伟伟,肖华,等.一种基于响应面的翼型鲁棒优化设计方法[J].工程力学,2015,32(2):250-256.Wu Xiaojing,Zhang Weiwei,Xiao Hua,et al.A robust aerodynamic design for airfoil based on response surface method[J].Engineering Mechanics,2015,32(2):250-256.(in Chinese)
[84]何大全,冯爱庆,王伟.基于CG法及Taguchi理论的气动力鲁棒性优化方法[J].飞行力学,2017(6):25-29.He Daquan,Feng Aiqing,Wang Wei.Robust aerodynamic optimization based on conjugate gradient algorithm and Taguchi's theory[J].Flight Dynamics,2017(6):25-29.(in Chinese)
[85]Changizi N,Kaboodanian H,Jalalpour M.Stress-based topology optimization of frame structures under geometric uncertainty[J].Computer Methods in Applied Mechanics&Engineering,2017,315:121-140.
[86]彭细荣,隋允康.基于ICM法的高层建筑大型支撑体系拓扑优化[J].工程力学,2017,34(5):17-22.Peng Xirong,Sui Yunkang.Topology optimization of mega braced systems of high-rise buildings based on ICM method[J].Engineering Mechanics,2017,34(5):17-22.(in Chinese)
[2]Niordson F I.The optimum design of a vibrating beam[J].Quarterly of Applied Mathematics,1965,23(1):47-53.
[3]林家浩.结构动力优化设计发展综述[J].力学进展,1983,13(4):423-431.Lin Jiahao.Review on the development in structural dynamic optimum design[J].Advances in Mechanics,1983,13(4):423-431.(in Chinese)
[4]刘永泉,王德友,洪杰,等.航空发动机整机振动控制技术分析[J].航空发动机,2013,39(5):1-8.Liu Yongquan,Wang Deyou,Hong Jie,et al.Analysis of whole aeroengine vibration control technology[J].Aeroengine,2013,39(5):1-8.(in Chinese)
[5]Rao S S.Reliability-based optimization under random vibration environment[J].Computers&Structures,1981,14(5):345-355.
[6]Ziegel E R.Taguchi techniques for quality engineering[J].Technometrics,1989,39(1):109-110.
[7]Yamakawa H,Miyashita M.A study on robust structures.1st report:concept of robust structure and 1ts design method[J].Transactions of the Japan Society of Mechanical Engineers Series C,1991,57(544):3913-3918.
[8]Zang C,Friswell M I,Mottershead J E.A review of robust optimal design and its application in dynamics[J].Computers&Structures,2005,83(4/5):315-326.
[9]Beyer H G,Sendhoff B.Robust optimization-Acomprehensive survey[J].Computer Methods in Applied Mechanics&Engineering,2007,196(33/34):3190-3218.
[10]接婧.国际学术界对鲁棒性的研究[J].系统工程学报,2005,20(2):153-159.Jie Jing.Study of robustness in the world[J].Journal of Systems Engineering,2005,20(2):153-159.(in Chinese)
[11]张正福,王安麟,刘广军,等.基于Taguchi三次设计的微机械陀螺健壮性设计[J].上海交通大学学报,2008,42(2):249-252.Zhang Zhengfu,Wang Anlin,LIU GuanJun,et al.Robust design for micromachined gyroscope using Taguchi three-stage design[J].Journal of Shanghai Jiaotong University,2008,42(2):249-252.(in Chinese)
[12]谢晖,刘行,洪健程.基于Taguchi方法的车门结构稳健性优化[J].中国机械工程,2013,24(12):1676-1681.Xie Hui,Liu Xing,Hong Jiancheng.Robust Optimization of automotive door structure based on Taguchi's method[J].China Mechanical Engineering,2013,24(12):1676-1681.(in Chinese)
[13]张代胜,张旭,王浩,等.基于Taguchi方法的动力总成悬置系统稳健优化[J].汽车工程,2014,36(4):475-480.Zhang Daisheng,Zhang Xu,Wang Hao,et al.Robust optimization of powertrain mounting system based on Taguchi's method[J].Automotive Engineering,2014,36(4):475-480.(in Chinese)
[14]王淑红,武潇,高泽梅.Taguchi法在内嵌式永磁同步电动机中的应用[J].太原理工大学学报,2014,45(5):618-622.Wang Shuhong,Wu Xiao,Gao Zemei.Application of Taguchi method in interior permanent magnet synchronous motor[J].Journal of Taiyuan University of Technology,2014,45(5):618-622.(in Chinese)
[15]Cai D A,Xiu-Ping W U,Yang G P,et al.Design for structure parameters of composite frangible cover based on Taguchi’s method[J].Journal of Solid Rocket Technology,2016,39(6):797-802.
[16]郭一鸣,魏玉明,上官文斌.发动机曲轴橡胶扭转减振器稳健性优化匹配[J].华南理工大学学报(自然科学版),2017,45(2):75-83.Guo Yiming,Wei Yuming,Shangguan Wenbin.Robust optimal matching of rubber-type torsional vibration damper for engine crankshaft[J].Journal of South China University of Technology(Natural Science Edition),2017,45(2):75-83.(in Chinese)
[17]Song J,Dong F,Zhao J,et al.Optimal design of a permanent magnet linear synchronous motors based on Taguchi method[J].Iet Electric Power Applications,2017,11(1):41-48.
[18]孙光永,屈瑞飞,张慧乐,等.基于Taguchi与TOPSIS-熵的车门多目标离散稳健优化研究[J].现代制造工程,2018(3):11-18.Sun Guangyong,Qu Ruifei,Zhang Huile,et al.Robust optimization of automobile door structure based on Taguchi and TOPSIS-entropy[J].Modern Manufacturing Engineering,2018(3):11-18.(in Chinese)
[19]Zong Y,Mao J.Tolerance optimization design based on the manufacturing-costs of assembly quality[J].Procedia Cirp,2015,27:324-329.
[20]孙岩辉,洪军,刘志刚,等.考虑零部件制造误差的精密主轴几何回转精度计算方法[J].机械工程学报,2017,53(3):173-182.Sun Yanhui,Hong Jun,Liu Zhigang,et al.A calculating method for the geometric rotation accuracy of precision spindles considering the manufacturing errors of component parts[J].Journal of Mechanical Engineering,2017,53(3):173-182.(in Chinese)
[21]Mohan P,Haghighi P,Vemulapalli P,et al.Toward automatic tolerancing of mechanical assemblies:assembly analyses[J].Journal of Computing&Information Science in Engineering,2014,14(4):1-14.
[22]殷良伟,郭海丁.某型航空发动机封严篦齿盘异型螺栓孔公差设计分析[J].航空发动机,2017,43(5):85-90.Yin Liangwei,Guo Haiding.Analysis on dimension tolerance design of non-circular hole of labyrinth disk for an aeroengine[J].Aeroengine,2017,43(5):85-90.(in Chinese)
[23]杨隽,臧朝平,刘永泉,等.基于Taguchi方法的转子系统动力学容差设计[J].航空动力学报,2014,29(7):1583-1590.Yang Jun,Zang Chaoping,Liu Yongquan,et al.Taguchi-based tolerance design method for rotor dynamics[J].Journal of Aerospace Power,2014,29(7):1583-1590.(in Chinese)
[24]杨隽,臧朝平.基于遗传算法的不确定性结构动力学鲁棒设计[C]//中国力学大会2011暨钱学森诞辰100周年纪念大会,2011.Yang Jun,Zang Chaoping.Genetic algorithm based robust design in dynamics due to parameter uncertainty[C]//The Chinese Conference on Theoretical and Applied Mechanics-2001 in Memorial of Tsien Hsue-shen’s 100th Anniversary,2011.(in Chinese)
[25]岳伟,梅庆,张大义,等.高速可拆卸转子止口连接结构稳健性设计方法[J].航空动力学报,2017,32(7):1754-1761.Yue Wei,Mei Qing,Zhang Dayi,et al.Robust design method of Rabbet joint structure in high speed assemble rotor[J].Journal of Aerospace Power,2017,32(7):1754-1761.(in Chinese)
[26]洪杰,徐筱李,梁天宇,等.转子结构系统界面失效分析及稳健设计方法[J].航空动力学报,2018,33(3):649-656.Hong Jie,Xu Xiaoli,Liang Tianyu,et al.Interface failure analysis and robust design method in rotor structural system[J].Journal of Aerospace Power,2018,33(3):649-656.(in Chinese)
[27]Tsui K L.A critical look at Taguchi's modelling approach for robust design[J].Journal of Applied Statistics,1996,23(1):81-96.
[28]Chang H H.A data mining approach to dynamic multiple responses in Taguchi experimental design[J].Expert Systems with Applications,2008,35(3):1095-1103.
[29]Parkinson A,Sorensen C,Pourhassan N.A general approach for robust optimal design[J].Trans.asme JMech.design,1993,115(1):74-80.
[30]Zang C.Robust design of a two degree freedom system due to the parameter uncertainty[J].Chinese Journal of Mechanical Engineering,2008,21(6):30-35.
[31]肖方豪,蹇开林.鲁棒优化设计方法在结构动力学中的应用[J].工程力学,2007,24(增刊1):62-65.Xiao Fanghao,Jian Kailin.Application of Robust Optimal Design in Structural Dynamics[J].Engineering Mechanics,2007,24(suppl 1):62-65.(in Chinese)
[32]Marano G C,Greco R,Sgobba S.A comparison between different robust optimum design approaches:Application to tuned mass dampers[J].Probabilistic Engineering Mechanics,2010,25(1):108-118.
[33]Miguel L F F,Lopez R H.Robust design optimization of friction dampers for structural response control[J].Structural Control&Health Monitoring,2014,21(9):1240-1251.
[34]孙晓颖,李天娥,陆正争,等.平流层飞艇的多目标优化与决策[J].工程力学,2015(6):243-250.Sun Xiaoying,Li Tian’e,Lu Zhengzheng,et al.Multiobjective optimization and decision making of stratosphe re airships[J].Engineering Mechanics,2015(6):243-250.(in Chinese)
[35]Roy B K,Chakraborty S.Robust optimum design of base isolation system in seismic vibration control of structures under random system parameters[J].Structure&Infrastructure Engineering,2016,12(5):592-602.
[36]Dell'Elce L,Gourc E,Kerschen G.A robust equal-peak method for uncertain mechanical systems[J].Journal of Sound Vibration,2018,414:97-109.
[37]蒲利东,罗务揆,严泽洲.气动伺服弹性系统结构陷幅滤波器优化设计[J].工程力学,2018,35(4):235-241.Pu Lidong,Luo Wukui,Yan Zezhou.Optimal design for notch filter of aeroservoelastic systems[J].Engineering Mechanics,2018,35(4):235-241.(in Chinese)
[38]陈鑫,李爱群,徐庆阳,等.基于遗传算法的高耸结构环形TLD满意优化设计[J].工程力学,2016,33(6):77-84.Chen Xin,Li Aiqun,Xu Qingyang,et al.Satisfaction optimum design of ring-shape tld control for high-rise structure using genetic algorithm[J].Engineering Mechanics,2016,33(6):77-84.(in Chinese)
[39]王歆侃.基于容差模型的发动机悬置系统稳健优化设计[J].汽车科技,2012(4):16-19.Wang Yinkan.Robust optimal design of engine mounting system based on tolerance model[J].AUTOSU-TECH,2012(4):16-19.(in Chinese)
[40]陈新志,孙桓五,刘荣,等.基于容差模型的半挂汽车列车行驶平顺性优化[J].汽车技术,2014(4):48-52.Chen Xinzhi,Sun Hengwu,Liu Rong,et al.Ridie comfort optimization of semitrailer train based on tolerance model[J].Automobile Technology,2014(4):48-52.(in Chinese)
[41]Loyer B,Jezequel L.Robust design of a passive linear quarter car suspension system using a multi-objective evolutionary algorithm and analytical robustness indexes[J].Vehicle System Dynamics 2009,47(10):1253-1270.
[42]燕宁宁,董恩国.基于多目标优化的悬架系统空间结构稳健性研究[J].天津职业技术师范大学学报,2016,26(3):10-13.Yan Ningning,Dong Enguo.Research on robustness of spatial structure of suspension system based on multi-objective optimization[J].Journal of Tianjin University of Technology and Education,2016,26(3):10-13.(in Chinese)
[43]范政武,王铁,王永红,等.基于改进多目标粒子群算法的商用车悬架系统优化[J].振动与冲击,2018,37(15):216-224.Fan Zhengwu,Wang Tie,Wang Yonghong,et al.Commercial vehicle suspension system optimization base on improved multi-object particle swarm optimization[J].Journal of Vibration and Shock,2018,37(15):216-224.(in Chinese)
[44]傅超,任兴民,杨永锋,等.考虑参数不确定性的转子系统瞬态动平衡研究[J].动力学与控制学报,2017,15(5):453-458.Fu Chao,Ren Xingmin,Yang Yongfeng,et al.Transient dynamic balancing of rotor system with parameter uncertainties[J].Journal of Dynamics and Control,2017,15(5):453-458.(in Chinese)
[45]Gan C B,Wang Y H,Yang S X,et al.Nonparametric modeling and vibration analysis of uncertain Jeffcott rotor with disc offset[J].International Journal of Mechanical Sciences,2014,78(1):126-134.
[46]Ma Y,Liang Z,Chen M,et al.Interval analysis of rotor dynamic response with uncertain parameters[J].Journal of Sound&Vibration,2013,332(16):3869-3880.
[47]Ritto T G,Lopez R H,Sampaio R,et al.Robust optimization of a flexible rotor-bearing system using the Campbell diagram[J].Engineering Optimization,2011,43(1):77-96.
[48]Lopez R H,Ritto T G,Sampaio R,et al.A new algorithm for the robust optimization of rotor-bearing systems[J].Engineering Optimization,2014,46(8):1123-1138.
[49]Krack M,Panning L,Wallaschek J,et al.Robust design of friction interfaces of bladed disks with respect to parameter uncertainties[C]//ASME Turbo Expo 2012:Turbine Technical Conference and Exposition,2012:1193-1204.
[50]姚建尧,王建军,李其汉.失谐叶盘结构鲁棒性能分析[J].航空动力学报,2010,25(7):1634-1639.Yao Jianyao,Wang JianJun,Li Qihan.Robust performance analysis of mistuned bladed disks[J].Journal of Aerospace Power,2010,25(7):1634-1639.(in Chinese)
[51]段勇亮,臧朝平,Petrov E.P.主动失谐叶盘振动特性及鲁棒性研究[J].航空发动机,2015,41(6):6-10.Duan Yongliang,Zang Chaoping,Petrov E P.Research on vibration performance and robustness of bladed disks with intentional mistuning[J].Aeroengine,2015,41(6):6-10.(in Chinese)
[52]罗佑新,车晓毅,杨继荣,等.高维多目标灰色稳健优化设计及其Matlab实现[J].农业机械学报,2008,39(8):157-160.Luo Youxin,Che Xiaoyi,Yang Jirong,et al.Grey-robust optimal design of high-dimensional multi-objective and its achieving with Matlab[J].Transactions of the Chinese Society of Agricultural Machinery,2008,39(8):157-160.(in Chinese)
[53]郝芳芳,范小宁,智博.基于灵敏度附加目标函数的起重机主梁稳健优化设计[J].机械强度,2017(6):1385-1390.Hao Fangfang,Fan Xiaoning,Zhi Bo.Structure and robust optimization design based on additional objective function of the sensitivity[J].Journal of Mechanical Strength,2017(6):1385-1390.(in Chinese)
[54]Sundaresan S,IshiiK,Houser D R.A robust optimization procedure with variations on design variables and constraints[J].Advances in Design Automation,69(1):379-386.
[55]Petrov E P,Ewins D J.Analysis of the worst mistuning patterns in bladed disk assemblies[C].Asme Turbo Expo:Power for Land,Sea,&Air,2003:623-631.
[56]谭元球,臧朝平,周标,等.失谐叶盘受迫响应的灵敏度分析方法[J].航空学报,2017,38(12):187-197.Tan Yuanqiu,Zang Chaoping,Zhou Biao,et al.Sensitivity analysis method for forced reponse of mistuned bladed discs[J].Acta Aeronautica et Astronautic Sinica,2017,38(12):187-197.(in Chinese)
[57]Du X P,Chen W.Efficient uncertainty analysis methods for multidisciplinary robust design[J].AIAA J,2002,40(3):545-552.
[58]Liu S,Ma Y,Zhang D,et al.Studies on dynamic characteristics of the joint in the aero-engine rotor system[J].Mechanical Systems&Signal Processing,2012,29(5):120-136.
[59]Marano G C,Quaranta G.Robust optimum criteria for tuned mass dampers in fuzzy environments[J].Applied Soft Computing Journal,2009,9(4):1232-1243.
[60]Lievens K,Lombaert G,Roeck G D,et al.Robust design of a TMD for the vibration serviceability of a footbridge[J].Engineering Structures,2016,12(3):408-418.
[61]Khuri A I,Mukhopadhyay S.Response surface methodology[J].Wiley Interdisciplinary Reviews Computational Statistics,2010,2(2):128-149.
[62]刘小川,马晓利,孙侠生,等.基于响应面方法的多支柱起落架着陆缓冲性能优化[J].振动工程学报,2010,23(3):305-309.Liu Xiaochuang,Ma Xiaoli,Sun Xiasheng,et al.Performance optimization of shock absorber for multi-strut landing gear based on RSM[J].Journal of Vibration Engineering,2010,23(3):305-309.(in Chinese)
[63]黄亚,于德介,吕辉,等.含不确定参数的盘式制动器稳定性分析[J].机械强度,2017(6):1371-1378.Huang Ya,Yu Dejie,Lu Hui,et al.Stability analysis of disc brake systems with uncertainty parameters[J].Journal of Mechanical Strength,2011,47(24):97-103.(in Chinese)
[64]刘承杰,李倩,罗鹏,等.基于响应面法的V带轮多目标优化设计[J].应用力学学报,2018,35(1):147-153.Liu Chenjie,Li Qian,Luo Peng,et al.Multi-objective optimization design of V-pulley based on response surface method[J].Chinese Journal of Applied Mechanics,2018,35(1):147-153.(in Chinese)
[65]柯婉頔,吴婧,杨森,等.基于响应面法和遗传算法的某SUV前悬优化[J].华中师范大学学报(自科版),2017,51(4):455-460.Ke Wandi,Wu Jing,Yang Sen,et al.Optimization of front suspension of sports utility vehicle based on response surface method and genetic algorithm[J].Journal of Central China Normal University(Nat.Sci.),2017,51(4):455-460.(in Chinese)
[66]Ghisu T,Parks G T,Jarrett J P,et al.Robust design optimization of gas turbine compression systems[J].Journal of Propulsion&Power,2011,27(2):282-295.
[67]Tosi G,Mucchi E,D’Ippolito R,et al.Dynamic behavior of pumps:an efficient approach for fast robust design optimization[J].Meccanica,2015,50(8):2179-2199.
[68]Stocki R,Szolc T,Tauzowski P,et al.Robust design optimization of the vibrating rotor-shaft system subjected to selected dynamic constraints[J].Mechanical Systems&Signal Processing,2012,29(29):34-44.
[69]崔杰,张维刚,常伟波,等.基于双响应面模型的碰撞安全性稳健性优化设计[J].机械工程学报,2011,47(24):97-103.Cui Jie,Zhang Weigang,Chang Weibo,et al.Robustness optimization for crash safety based on dual-response surface model[J].Journal of mechanical engineering,2011,47(24):97-103.(in Chinese)
[70]Shen D E,Braatz R D.Polynomial chaos-based robust design of systems with probabilistic uncertainties[J].AICh E Journal,2016.
[71]陈力波,黄才贵,谷音.基于改进响应面法的公路简支梁桥地震易损性分析[J].工程力学,2018(4):208-218.Chen Libo,Huang Caigui,Gu Yin.Seimic vulnerability analysis of simply supported highway bridges based on an improved response surface method[J].Engineering Mechanics,2018(4):208-218.(in Chinese)
[72]窦毅芳,刘飞,张为华.响应面建模方法的比较分析[J].工程设计学报,2007,14(5):359-363.Dou Yifang,Liu Fei,Zhang Weihua.Research on comparative analysis of response surface methods[J].Journal of Engineering Design,2007,14(5):359-363.(in Chinese)
[73]陈永亮,刘双,王汉涛,等.基于Kriging代理模型的主轴箱稳健设计[J].天津大学学报(自然科学与工程技术版),2011,44(12):1111-1117.Chen Yongliang,Liu Shuang,Wang Hantao,et al.Robust design of headstock based on kriging surrogate model[J].Journal of Tianjin University(Science and Technology),2011,44(12):1111-1117.(in Chinese)
[74]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 optimization for dynamic characteristics of mechanical structures based on double renewal kriging model[J].Joural of Mechanical Engineering,2014,50(3):165-173.(in Chinese)
[75]刘艳,白俊强,华俊,等.基于Stochastic Kriging的柔性机翼稳健性优化设计[J].西北工业大学学报,2015(6):906-912.Liu Yan,Bai Junqiang,Hua Jun,et al.Robust optimization of flexible wing using stochastic kriging surrogate model[J].Journal of Northwestern Polytechnical University,2015(6):906-912.(in Chinese)
[76]蒙文巩,马东立,楚亮.基于神经网络响应面的机翼气动稳健性优化设计[J].航空学报,2010,31(6):1134-1140.Meng Wengong,Ma Dongli,Chu Liang.Wing aerodynamic robustness optimization based on neural network response surface[J].Acta Aeronautica et Astronautic Sinica,2010,31(6):1134-1140.(in Chinese)
[77]顾松年,徐斌,荣见华,等.结构动力学设计优化方法的新进展[J].机械强度,2005,27(2):24-30.Gu Songnian,Xu Bin,Rong Jianhua,et al.Recent progresses on structural dynamic design methods[J].Journal of Mechanical Strength,2005,27(2):24-30.(in Chinese)
[78]Steenackers G,Guillaume P,Vanlanduit S.Robust optimization of an airplane component taking into account the uncertainty of the design parameters[J].Quality&Reliability Engineering International,2009,25(3):255-282.
[79]张军红,韩景龙.考虑不确定性的机翼气动弹性优化问题研究[C]//全国空气弹性学术交流会,2011.Zhang Junhong,Han Jinglong.Study on aeroelastic optimization of wing with uncertainty[C]//National Air Flexibility Academic Intercommunions,2011.(in Chinese)
[80]李焦赞,高正红.多目标进化算法和代理模型技术在气动稳健优化设计中的应用[J].空气动力学学报,2012,30(1):46-51.Li Jiaozan,Gao Zhenghong.The application of multi-objective evolutionary algorithm and surrogate model to aerodynamic robust optimization design[J].Acta Aerodynamica Sinica,2012,30(1):46-51.(in Chinese)
[81]孙岩.飞行器机翼气动/结构耦合优化设计研究[J].工程力学,2012(11):360-364.Sun Yan.Investigation on coupling aerodynamic and structural design optimization for aircraft airfoil[J].Engineering Mechanics,2012(11):360-364.(in Chinese)
[82]Jansen M,Lombaert G,Schevenels M,et al.Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis[J].Computer Methods in Applied Mechanics and Engineering,2015,285:452-467.
[83]邬晓敬,张伟伟,肖华,等.一种基于响应面的翼型鲁棒优化设计方法[J].工程力学,2015,32(2):250-256.Wu Xiaojing,Zhang Weiwei,Xiao Hua,et al.A robust aerodynamic design for airfoil based on response surface method[J].Engineering Mechanics,2015,32(2):250-256.(in Chinese)
[84]何大全,冯爱庆,王伟.基于CG法及Taguchi理论的气动力鲁棒性优化方法[J].飞行力学,2017(6):25-29.He Daquan,Feng Aiqing,Wang Wei.Robust aerodynamic optimization based on conjugate gradient algorithm and Taguchi's theory[J].Flight Dynamics,2017(6):25-29.(in Chinese)
[85]Changizi N,Kaboodanian H,Jalalpour M.Stress-based topology optimization of frame structures under geometric uncertainty[J].Computer Methods in Applied Mechanics&Engineering,2017,315:121-140.
[86]彭细荣,隋允康.基于ICM法的高层建筑大型支撑体系拓扑优化[J].工程力学,2017,34(5):17-22.Peng Xirong,Sui Yunkang.Topology optimization of mega braced systems of high-rise buildings based on ICM method[J].Engineering Mechanics,2017,34(5):17-22.(in Chinese)
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