面向零件轻量化设计的自适应动态Kriging模型及应用
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摘要
机械零件轻量化对提高装备运行性能、降低成本具有重要作用。针对传统基于Kriging模型的全局优化方法在处理零件轻量化问题时,收敛速度慢、优化效率低、精度差等问题,提出一种自适应动态Kriging模型。采用复相关系数R2检验实现Kriging模型的全局动态更新,以Pareto解中各目标函数最小值为特征点,通过特征点加权计算理想特征点位置,在理想点附近选取可行解完成样本局部更新,实现Kriging模型的动态自适应性。以数值算例和FT(N)-2800注塑机模板为例,验证了所提方法的有效性。
Lightweight design of mechanical parts plays an important role in improving equipment performance and reducing cost.To improve convergence,optimization efficiency for the parts lightweight design of traditional Kriging method,an adaptively dynamic Kriging model was proposed.The multiple correlation coefficient was utilized to achieve the goal of overall update of Kriging model,and the minimums of each objective from the Pareto solutions were utilized to search for the optimal characteristic point.Then the local update of Kriging model was achieved by the feasible solutions near the optimal characteristic point.Numerical test cases and a platen of FT(N)-2800 injection machine were given to demonstrate the effectiveness of the proposed method.
Lightweight design of mechanical parts plays an important role in improving equipment performance and reducing cost.To improve convergence,optimization efficiency for the parts lightweight design of traditional Kriging method,an adaptively dynamic Kriging model was proposed.The multiple correlation coefficient was utilized to achieve the goal of overall update of Kriging model,and the minimums of each objective from the Pareto solutions were utilized to search for the optimal characteristic point.Then the local update of Kriging model was achieved by the feasible solutions near the optimal characteristic point.Numerical test cases and a platen of FT(N)-2800 injection machine were given to demonstrate the effectiveness of the proposed method.
引文
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[2]LI Baotong,HONG Jun,LIU Zhifeng.Stiffness design of machine tool structures by a biologically inspired topology optimization method[J].International Journal of Machine Tools and Manufacture,2014,84:33-44.
[3]ZHU Jihong,ZHANG Weihong,XIA Liang.Topology optimization in aircraft and aerospace structures design[J].Archives of Computational Methods in Engineering,2016,23(4):595-622.
[4]ORME M E,GSCHWEITL M,FERRARI M,et al.Designing for additive manufacturing:lightweighting through topology optimization enables lunar spacecraft[J].Journal of Mechanical Design,2017,139(10):100905.
[5]REN Bin,ZHANG Shuyou,TAN Jianrong.Structural scheme optimization design for the stationary platen of a precision plastic injection molding machine[J].Chinese Journal of Mechanical Engineering,2014,27(4):714-721.
[6]WU Tong,LIU Kai,ANDRES T.Multiphase thermomechanical topology optimization of functionally fraded lattice injection molds[C]//Proceedings of ASME 2016International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.New York,N.Y.,USA:ASME,2016:V02AT03A036-V02AT03A046.
[7]SUN S H.Optimum topology design for the stationary platen of a plastic injection machine[J].Computers in Industry,2004,55(2):147-158.
[8]XIE Ran,LAN Fengchong,CHEN Jiqing,et al.Multi-objective optimization method in car-body structure light-weight design with reliability requirement[J].Journal of mechanical engineering,2011,47(4):117-124(in Chinese).[谢然,兰凤崇,陈吉清,等.满足可靠性要求的轻量化车身结构多目标优化方法[J].机械工程学报,2011,47(4):117-124.]
[9]HOU S J,Li Q,LONG S Y,YANG X J,et al.Multiobjective optimization of multi-cell sections for the crashworthiness design[J].International Journal of Impact Engineering,2008,35(11):1355-1367.
[10]FONSECA C M,FLEMING P J.Genetic Algorithms for Multiobjective Optimization:Formulation Discussion and Generalization[EB/OL].[2017-08-10]https://pdfs.semanticscholar.org/11ec/6378801e6f8a800260b565439ff1cd9c5f5a.pdf.
[11]ZITZLER E,LAUMANNS M,THIELE L.SPEA2:Improving the strength Pareto evolutionary algorithm[EB/OL].[2017-08-10].https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/145755/eth-24689-01.pdf.
[12]DEB K,PRATAP A,AGARWAL S,et al.A fast and elitist multi-objective genetic algorithm:NSGA-Ⅱ[J].IEEE Transactions on Evolutionary Computation,2002,6(2):182-197.
[13]COELLO C A,PULIDO G T,LECHUGA M S.Handing multiple objectives with particle swarm optimization[J].IEEE Transactions on Evolutionary Computations,2004,8(3):256-279.
[14]SAKATA S,ASHIDA F,ZAKO M.An efficient algorithm for Kriging approximation and optimization with large-scale sampling data[J].Computer Methods in Applied Mechanics and Engineering,2004,193(3):385-404.
[15]LEE K H,KANG D H.A robust optimization using the statistics based on Kriging meta model[J].Journal of Mechanical Science and Technology,2006,20(8):1169-1182.
[16]KLEIJNEN J P C.Kriging meta modeling in simulation:a review[J].European Journal of Operational Research,2009,192(3):707-716.
[17]CHENG Jin,LIU Zhenyu,WU Zhenyu,et al.Robust optimization of structural dynamic characteristics based on adaptive Kriging model and CNSGA[J].Structural and Multidisciplinary Optimization,2015,51(2):423-437.
[18]LI Xiaogang,CHENG Jin,LIU Zhenyu.Robust optimization for dynamic characteristics of mechanical structures based on double renewal Kriging model[J].Journal of Mechanical Engineering,2014,50(3):165-173(in Chinese).[李小刚,程锦,刘振宇.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.]
[19]PENG Lei,LIU Li,LONG Teng.Optimization strategy using dynamic radial basis function meta-model[J].Journal of Mechanical Engineering,2011,47(7):164-170(in Chinese).[彭磊,刘莉,龙腾.基于动态径向基函数代理模型的优化策略[J].机械工程学报,2011,47(7):164-170.]
[20]WANG Chenen,HUANG Zhangjun.Kriging response surface method based on Gauss function and trust region update approach[J].Computer Integrated Manufacturing Systems,2011,17(4):740-746(in Chinese).[王成恩,黄章俊.基于高斯函数和信赖域更新策略的Kriging响应面法[J].计算机集成制造系统,2011,17(4):740-746.]
[21]HUANG Zhangjun,WANG Chenen.Turbine discs optimization design based on Kriging model[J].Computer Integrated Manufacturing Systems,2010,16(5):905-911(in Chinese).[黄章俊,王成恩.基于Kriging模型的涡轮盘优化设计方法[J].计算机集成制造系统,2010,16(5):905-911.]
[22]ALEXANDROV N M,DENNIS J E,LEWIS R M,et al.Atrust-region framework for managing the use of approximation models in optimization[J].Structural and Multidisciplinary Optimization,1998,15(1):16-23.
[23]MARTIN J D,SIMPSON T W.Use of kriging models to approximate deterministic computer models[J].AIAA Journal,2005,43(4):853-863.
[24]KURSAWE F.A variant of evolution strategies for vector optimization[C]//Proceedings of the International Conference on Parallel Problem Solving from Nature.Berlin,Germany:Springer-Verlag,1990:193-197.
[25]DENNIS J,JOHN E.,ROBERT B,et al.Numerical methods for unconstrained optimization and nonlinear equations[M].Philadelphia,Pa.,USA:Society for Industrial and Applied Mathematics,1996.
[26]ZANG Mingjun,ZHANG Shuyou,JIA Weiqiang,et al.Multi-objective particle swarm optimization based on territorial behavior and its application in optimum design of plate-fin heat exchanger[J].Computer Integrated Manufacturing Systems,2015,21(1):76-87(in Chinese).[藏明君,张树有,郏维强,等.基于领地行为的多目标粒子群算法及在板翅换热器设计中的应用[J].计算机集成制造系统,2015,21(1):76-87.]