基于继承拉丁超立方采样与局部Kriging近似的可靠性设计优化
|
摘要
针对基于Kriging近似的可靠性设计优化样本最优配置问题,提出基于继承拉丁超立方采样与局部Kriging近似的可靠性设计优化方法。采用继承拉丁超立方样本构建Kriging近似,并求解最大可能失效点作为局部序列采样中心。针对有效概率约束构建基于Kriging近似误差、功能函数非线性度量及目标可靠度的局部序列采样区域。以重要抽样策略计算失效概率及灵敏度,并采用序列近似规划求解最优设计点。通过3个算例及机床横梁设计优化应用验证了所提方法的有效性。
To improve the sample configuration of Kriging-based Reliability-based Design Optimization(RBDO)methods,a novel method using Inherited Latin Hypercube Sampling(ILHS)and local Kriging approximation method was proposed.ILHS was used to ensure the accuracy of Kriging at the initial optimization phase,and the Most Probable Point(MPP)was calculated to be the center of a local sampling region for active probabilistic constraints.The local sampling region was determined according to the Kriging approximation error,performance function nonlinearity and target reliability.The important sampling combined with sequential approximation programming was used to calculate the optimal design.Two numerical examples and the application of box girder were used to demonstrate the effectiveness of proposed method.
To improve the sample configuration of Kriging-based Reliability-based Design Optimization(RBDO)methods,a novel method using Inherited Latin Hypercube Sampling(ILHS)and local Kriging approximation method was proposed.ILHS was used to ensure the accuracy of Kriging at the initial optimization phase,and the Most Probable Point(MPP)was calculated to be the center of a local sampling region for active probabilistic constraints.The local sampling region was determined according to the Kriging approximation error,performance function nonlinearity and target reliability.The important sampling combined with sequential approximation programming was used to calculate the optimal design.Two numerical examples and the application of box girder were used to demonstrate the effectiveness of proposed method.
引文
[1] YU Fanhua,LIU Renyun,ZHANG Yimin,et al.Intelligent algorithm for optimized dynamic reliability design of mechanic structure[J].Journal of Jilin University:Engineering and Technology,2016,46(4):1269-1275(in Chinese).[于繁华,刘仁云,张义民,等.机械结构动态可靠性设计的智能计算方法[J].吉林大学学报:工学版,2016,46(4):1269-1275.]
[2] CAO Libo,LIU Heng,WU Hequan.Reliability optimal design of B-pillar for a hybrid electric vehicle in side impact[J].Journal Of Automotive Safety And Engergy,2016,7(3):272-278(in Chinese).[曹立波,刘衡,武和全.某混合动力汽车侧面碰撞中B柱可靠性优化设计[J].汽车安全与节能学报,2016,7(3):272-278.]
[3] LIU Lingjun.Reliability optimization design of aero-engine blisk[D].Harbin:Harbin University of Science and Technology,2016(in Chinese).[刘令君.航空发动机整体叶盘可靠性优化设计[D].哈尔滨:哈尔滨理工大学,2016.]
[4] ZIO E.Reliability engineering:old problems and new challenges[J].Reliability Engineering&System Safety,2009,94(2):125-141.
[5] JIANG C,LU G Y,HAN X,et al.Some important issues on first-order reliability analysis with nonprobabilistic convex models[J],Journal of Mechanical Design,2014,136(3):252-261.
[6] LIM J,LEE B,LEE I.Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization[J].International Journal for Numerical Methods in Engineering,2015,100(10):773-792.
[7] LEE G,YOOK S,KANG K,et al.Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points[J].International Journal of Precision Engineering and Manufacturing,2012,13(9):1609-1618.
[8] RUBINSTEIN R Y.Simulation and the Monte Carlo method[M]//Simulation and the Monte Carlo method.New York,N.Y.,USA:John Wiley&Sons,2008:1-345.
[9] ECHARD B,GAYTON N,LEMAIRE M.AK-MCS:An active learning reliability method combining Kriging and Monte Carlo Simulation[J],.Structural Safety,2011,33(2):145-154.
[10] ECHARD B,GAYTON N,LEMAIRE M,et al.A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models[J],.Reliability Engineering&System Safety,2013,111(2):232-240.
[11] GONG Jinxin,HE Shiqin,ZHAO Guofan.Structural reliability analysis by importance directional simulation[J],Chinese journal of computational Mechanics,2003,20(6):655-661(in Chinese).[贡金鑫,何世钦,赵国藩.结构可靠度模拟的方向重要抽样法[J].计算力学学报,2003,20(6):655-661.]
[12] SONG Shufang,LU Zhenzhou,QIAO Hongwei.Subset simulation for structural reliability sensitivity analysis[J].Reliability Engineering&System Safety,2009,94(2):658-665.
[13] SONG Shufang,LU Zhenzhou,ZHANG Weiwei,et al.Reliability and sensitivity analysis of transonic flutter using improved line sampling technique[J].Chinese Journal of Aeronautics,2009,22(5):513-519.
[14] LIU Zhan,ZHANG Jianguo,WANG Cancan,et al.An hybrid structure reliability method combining optimized Kriging and importance sampling[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1347-1355(in Chinese).[刘瞻,张建国,王灿灿,等.基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J].航空学报,2013,34(6):1347-1355.]
[15] WANG Jun,MA Yizhong,WANG Jianjun.Applications of importance sampling based on Kriging metamodel in structural reliability analysis[J],Computer Integrated Manufacturing Systems,2016,22(11):2643-2652(in Chinese).[王娟,马义中,汪建均.基于Kriging模型的重要性抽样在结构可靠性中的应用[J].计算机集成制造系统,2016,22(11):2643-2652.]
[16] XIAO NingCong,ZUO Mingj,ZHOU Chengning,et al.A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis[J].Reliability Engineering and System Safety,2018,169:330-338.
[17] LEE T H,JUNG J J.A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO:constraint boundary sampling[J].Computers&Structures,2008,86(3):1463-1476.
[18] BICHON B J,ELDRED M S,SWILER L P,et al.Efficient global reliability analysis for nonlinear implicit performance functions[J].AIAA Journal,2008,46(10):2459-2468.
[19] CHEN Zhenzhong,QIU Haobo,GAO Liang,et al.A local adaptive sampling method for reliability-based design optimization using Kriging model[J].Structural and Multidisciplinary Optimization,2014,49(3):401-416.
[20] CHEN Zhenzhong,PENG Siping,LI Xiaoke,et al.An important boundary sampling method for reliability-based design optimization using kriging model[J].Structural&Multidisciplinary Optimization,2015,52(1):55-70.
[21] LI Xiaoke,QIU Haobo,CHEN Zhenzhong,et al.A local Kriging approximation method using MPP for reliabilitybased design optimization[J].Computers&Structures,2016,162:102-115.
[22] XIAO Mi,GAO Liang,SHAO Xinyu,et al.A generalised collaborative optimisation method and its combination with kriging metamodels for engineering design[J].Journal of Engineering Design,2012,23(5):379-399.
[23] WANG G G.Adaptive response surface method using inherited latin hypercube design points[J].Journal of Mechanical Design,2003,125(2):210-220.
[24] LYU Zhenzhou,SONG Shufang,LI Hongshuang,et al.Reliability and reliability sensitivity analysis of structure[M].Beijing:Science Press,2009(in Chinese).[吕震宙,宋述芳,李洪双,等,结构机构可靠性及可靠性灵敏度分析[M].北京:科学出版社,2009.]
[25] YOUN B D,CHOI K K.An investigation of nonlinearity of reliability-based design optimization approaches[J].Journal of Mechanical Design,2004,126(3):881-890.
[26] WANG Yu,YU Xiongqing,Du Xiaoping.Improved reliability-based optimization with support vector machines and its application in aircraft wing design[J].Mathematical Problems in Engineering,2015,2015:3127-3141.
[27] CHEN Zhenzhong,QIU Haobo,GAO Liang,et al.An optimal shifting vector approach for efficient probabilistic design[J].Structural and Multidisciplinary Optimization,2013,47(6):905-920.
[28] HYEON JU B,CHAI LEE B.Reliability-based design optimization using a moment method and a kriging metamodel[J],Engineering Optimization,2008,40(5):421-438.
[2] CAO Libo,LIU Heng,WU Hequan.Reliability optimal design of B-pillar for a hybrid electric vehicle in side impact[J].Journal Of Automotive Safety And Engergy,2016,7(3):272-278(in Chinese).[曹立波,刘衡,武和全.某混合动力汽车侧面碰撞中B柱可靠性优化设计[J].汽车安全与节能学报,2016,7(3):272-278.]
[3] LIU Lingjun.Reliability optimization design of aero-engine blisk[D].Harbin:Harbin University of Science and Technology,2016(in Chinese).[刘令君.航空发动机整体叶盘可靠性优化设计[D].哈尔滨:哈尔滨理工大学,2016.]
[4] ZIO E.Reliability engineering:old problems and new challenges[J].Reliability Engineering&System Safety,2009,94(2):125-141.
[5] JIANG C,LU G Y,HAN X,et al.Some important issues on first-order reliability analysis with nonprobabilistic convex models[J],Journal of Mechanical Design,2014,136(3):252-261.
[6] LIM J,LEE B,LEE I.Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization[J].International Journal for Numerical Methods in Engineering,2015,100(10):773-792.
[7] LEE G,YOOK S,KANG K,et al.Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points[J].International Journal of Precision Engineering and Manufacturing,2012,13(9):1609-1618.
[8] RUBINSTEIN R Y.Simulation and the Monte Carlo method[M]//Simulation and the Monte Carlo method.New York,N.Y.,USA:John Wiley&Sons,2008:1-345.
[9] ECHARD B,GAYTON N,LEMAIRE M.AK-MCS:An active learning reliability method combining Kriging and Monte Carlo Simulation[J],.Structural Safety,2011,33(2):145-154.
[10] ECHARD B,GAYTON N,LEMAIRE M,et al.A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models[J],.Reliability Engineering&System Safety,2013,111(2):232-240.
[11] GONG Jinxin,HE Shiqin,ZHAO Guofan.Structural reliability analysis by importance directional simulation[J],Chinese journal of computational Mechanics,2003,20(6):655-661(in Chinese).[贡金鑫,何世钦,赵国藩.结构可靠度模拟的方向重要抽样法[J].计算力学学报,2003,20(6):655-661.]
[12] SONG Shufang,LU Zhenzhou,QIAO Hongwei.Subset simulation for structural reliability sensitivity analysis[J].Reliability Engineering&System Safety,2009,94(2):658-665.
[13] SONG Shufang,LU Zhenzhou,ZHANG Weiwei,et al.Reliability and sensitivity analysis of transonic flutter using improved line sampling technique[J].Chinese Journal of Aeronautics,2009,22(5):513-519.
[14] LIU Zhan,ZHANG Jianguo,WANG Cancan,et al.An hybrid structure reliability method combining optimized Kriging and importance sampling[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1347-1355(in Chinese).[刘瞻,张建国,王灿灿,等.基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J].航空学报,2013,34(6):1347-1355.]
[15] WANG Jun,MA Yizhong,WANG Jianjun.Applications of importance sampling based on Kriging metamodel in structural reliability analysis[J],Computer Integrated Manufacturing Systems,2016,22(11):2643-2652(in Chinese).[王娟,马义中,汪建均.基于Kriging模型的重要性抽样在结构可靠性中的应用[J].计算机集成制造系统,2016,22(11):2643-2652.]
[16] XIAO NingCong,ZUO Mingj,ZHOU Chengning,et al.A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis[J].Reliability Engineering and System Safety,2018,169:330-338.
[17] LEE T H,JUNG J J.A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO:constraint boundary sampling[J].Computers&Structures,2008,86(3):1463-1476.
[18] BICHON B J,ELDRED M S,SWILER L P,et al.Efficient global reliability analysis for nonlinear implicit performance functions[J].AIAA Journal,2008,46(10):2459-2468.
[19] CHEN Zhenzhong,QIU Haobo,GAO Liang,et al.A local adaptive sampling method for reliability-based design optimization using Kriging model[J].Structural and Multidisciplinary Optimization,2014,49(3):401-416.
[20] CHEN Zhenzhong,PENG Siping,LI Xiaoke,et al.An important boundary sampling method for reliability-based design optimization using kriging model[J].Structural&Multidisciplinary Optimization,2015,52(1):55-70.
[21] LI Xiaoke,QIU Haobo,CHEN Zhenzhong,et al.A local Kriging approximation method using MPP for reliabilitybased design optimization[J].Computers&Structures,2016,162:102-115.
[22] XIAO Mi,GAO Liang,SHAO Xinyu,et al.A generalised collaborative optimisation method and its combination with kriging metamodels for engineering design[J].Journal of Engineering Design,2012,23(5):379-399.
[23] WANG G G.Adaptive response surface method using inherited latin hypercube design points[J].Journal of Mechanical Design,2003,125(2):210-220.
[24] LYU Zhenzhou,SONG Shufang,LI Hongshuang,et al.Reliability and reliability sensitivity analysis of structure[M].Beijing:Science Press,2009(in Chinese).[吕震宙,宋述芳,李洪双,等,结构机构可靠性及可靠性灵敏度分析[M].北京:科学出版社,2009.]
[25] YOUN B D,CHOI K K.An investigation of nonlinearity of reliability-based design optimization approaches[J].Journal of Mechanical Design,2004,126(3):881-890.
[26] WANG Yu,YU Xiongqing,Du Xiaoping.Improved reliability-based optimization with support vector machines and its application in aircraft wing design[J].Mathematical Problems in Engineering,2015,2015:3127-3141.
[27] CHEN Zhenzhong,QIU Haobo,GAO Liang,et al.An optimal shifting vector approach for efficient probabilistic design[J].Structural and Multidisciplinary Optimization,2013,47(6):905-920.
[28] HYEON JU B,CHAI LEE B.Reliability-based design optimization using a moment method and a kriging metamodel[J],Engineering Optimization,2008,40(5):421-438.