基于并行加点kriging模型的拉延筋优化
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摘要
为提高kriging代理模型预测精度,基于最大期望提高加点准则,提出一种改进的自适应加点准则和一种并行加点策略。基于kriging模型的预测响应和预测方差,并行加点方法在建模过程中利用粒子群算法并行求解多个加点准则获取多个新样本点更新代理模型,极大提高建模效率。将该方法应用到低维和高维经典非线性函数中,并与单点加点结果相比较,结果表明该方法在保证全局精度情况下,加点次数减少50%以上,并且建模所需总样本数更少。最后以NUMISHEET2002标准考题翼子板成形为研究对象,将该方法应用到板料成形上,建立等效拉延筋阻力和减薄率之间的kriging代理模型,利用并行加点策略快速获取了拉延筋阻力的最优解,消除了翼子板成形中的拉裂缺陷,提高了板料的成形质量。研究表明,改进的自适应加点准则以及提出的并行加点策略可以有效地提高kriging模型的建模效率和建模精度。
In order to improve the prediction accuracy of a kriging model, an improved adaptive infilling criterion and a parallel infilling strategy are proposed based on the maximum expected improvement criterion. Based on the prediction response and prediction variance provided by a kriging model, multiple new points are obtained to update a kriging model by solving multiple infilling criteria in parallel through the particle swarm optimization algorithm, greatly improving the modeling efficiency. The proposed strategy is applied to low-dimensional and high-dimensional classical nonlinear functions and compared with the single-point infilling method. The results show that the proposed strategy can reduce sampling times by more than 50% at the same global accuracy, and the total number of samples required for a kriging model is less. Finally, the proposed strategy is applied into the sheet metal forming, and the fender in the NUMISHEET2002 is taken as the research object. The kriging model between the equivalent drawbead restraining force and the thinning rate is established to obtain the optimal solution of the drawbead resistance by parallel infilling strategy. So the cracking defect is completely eliminated in the fender forming process and the forming quality of the blank is improved. The research shows that the improved adaptive infilling criterion and the proposed parallel infilling strategy can effectively improve the modeling efficiency and prediction accuracy of the kriging model.
In order to improve the prediction accuracy of a kriging model, an improved adaptive infilling criterion and a parallel infilling strategy are proposed based on the maximum expected improvement criterion. Based on the prediction response and prediction variance provided by a kriging model, multiple new points are obtained to update a kriging model by solving multiple infilling criteria in parallel through the particle swarm optimization algorithm, greatly improving the modeling efficiency. The proposed strategy is applied to low-dimensional and high-dimensional classical nonlinear functions and compared with the single-point infilling method. The results show that the proposed strategy can reduce sampling times by more than 50% at the same global accuracy, and the total number of samples required for a kriging model is less. Finally, the proposed strategy is applied into the sheet metal forming, and the fender in the NUMISHEET2002 is taken as the research object. The kriging model between the equivalent drawbead restraining force and the thinning rate is established to obtain the optimal solution of the drawbead resistance by parallel infilling strategy. So the cracking defect is completely eliminated in the fender forming process and the forming quality of the blank is improved. The research shows that the improved adaptive infilling criterion and the proposed parallel infilling strategy can effectively improve the modeling efficiency and prediction accuracy of the kriging model.
引文
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[19]NADINE H,JOACHIM K.An efficient sequential optimization approach based on the multivariate expected improvement criterion[J].Quality Engineering,2007,19(4):267-280.
[20]TANG B,SUN J,ZHAO Z,et al.Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology[J].International Journal of Advanced Manufacturing Technology,2006,31(3-4):225-234.
[2]韩少强,宋文萍,韩忠华,等.基于梯度增强型Kriging模型的气动反设计方法[J].航空学报,2017,38(7):138-152.HAN Shaoqiang,SONG Wenping,HAN Zhonghua,et al.Aerodynamic inverse design method based on gradient-enhanced kriging model[J].Acta Aeronautica et Astronautica Sinica,2017,38(7):138-152.
[3]李铁柱,李光耀,陈涛,等.基于Kriging近似模型的汽车乘员约束系统稳健性设计[J].机械工程学报,2010,46(22):123-129.LI Tiezhu,LI Guangyao,CHEN Tao,et al.Robustness design of occupant restraint system based on kriging model[J].Journal of Mechanical Engineering,2010,46(22):123-129.
[4]谢延敏.基于动态Kriging模型的板料成形工艺稳健设计[J].西南交通大学学报,2014,49(1):160-164.XIE Yanmin.Robust design of sheet forming process based on dynamic kriging model[J].Journal of Southwest Jiaotong University,2014,49(1):160-164.
[5]汪怡平,王涛,黎帅.基于自由变形技术的汽车气动减阻优化[J].机械工程学报,2017,53(9):135-143.WANG Yiping,WANG Tao,LI Shuai.Aerodynamic drag reduction of vehicle based on free form deformation[J].Journal of Mechanical Engineering,2017,53(9):135-143.
[6]JONES D R,SCHONLAU M,WELCH W J.Efficient global optimization of expensive black-box functions[J].Journal of Global Optimization,1998,13(4):455-492.
[7]FORRESTER A I J,KEANE A J.Recent advances in surrogate-based optimization[J].Progress in Aerospace Sciences,2009,45(1-3):50-79.
[8]LAURENCEAU J,MEAUX M,MONTAGNAC M,et al.Comparison of gradient-based and gradient-enhanced response-surface-based optimizers[J].Aiaa Journal,2010,48(5):981-994.
[9]曾锋,周金柱.集成最小化置信下限和信赖域的动态代理模型优化策略[J].机械工程学报,2017,53(13):170-178.ZENG Feng,ZHOU Jinzhu.Optimization strategy for dynamic metamodel integrating minimize lower confidence bound and trust region[J].Journal of Mechanical Engineering,2017,53(13):170-178.
[10]HUANG D.Global optimization of stochastic black-box systems via sequential kriging meta-models[J].Journal of Global Optimization,2012,54(2):431-431.
[11]KLEIJNEN J P C.Expected improvement in efficient global optimization through bootstrapped kriging[J].Journal of Global Optimization,2012,54(1):59-73.
[12]GINSBOURGER D,RICHE R L,CARRARO L.Kriging is well-suited to parallelize optimization[M]//Computational Intelligence in Expensive Optimization Problems.Springer Berlin Heidelberg,2010,131-162.
[13]FENG Z,ZHANG Q,ZHANG Q,et al.A multiobjective optimization based framework to balance the global exploration and local exploitation in expensive optimization[J].Journal of Global Optimization,2015,61(4):677-694.
[14]CHAUDHURI A,HAFTKA R T,IFJU P,et al.Experimental flapping wing optimization and uncertainty quantification using limited samples[J].Structural&Multidisciplinary Optimization,2015,51(4):1-14.
[15]LI Z,RUAN S,GU J,et al.Investigation on parallel algorithms in efficient global optimization based on multiple points infill criterion and domain decomposition[J].Structural&Multidisciplinary Optimization,2016,54(4):747-773.
[16]LIU J,SONG W P,HAN Z H,et al.Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models[J].Structural&Multidisciplinary Optimization,2017,55(3):925-943.
[17]高月华,王希诚.基于Kriging代理模型的多点加点序列优化方法[J].工程力学,2012,29(4):90-95.GAO Yuehua,WANG Xicheng.A sequential optimization method with multi-point samoling criterion based on kriging surrogate model[J].Engineering Mechanics,2012,29(4):90-95.
[18]陈霞,李磊,岳珠峰,等.Kriging代理模型下基于垂距的多点取样算法[J].机械工程学报,2015,51(9):153-158.CHEN Xia,LI Lei,YUE Zhufeng,et al.Sampling method with multi-point sampling algorithm based on vertical distance in kriging model[J].Journal of Mechanical Engineering,2015,51(9):153-158.
[19]NADINE H,JOACHIM K.An efficient sequential optimization approach based on the multivariate expected improvement criterion[J].Quality Engineering,2007,19(4):267-280.
[20]TANG B,SUN J,ZHAO Z,et al.Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology[J].International Journal of Advanced Manufacturing Technology,2006,31(3-4):225-234.