基于分区间泛化Kriging近似模型的船舶局部结构形状优化
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摘要
为提高Kriging近似模型在船舶结构性能多维度响应预测方面的适用性,对常规Kriging近似模型进行分区间泛化改进:一是对设计样本点的各个维度(分量)进行划区,并在每一个分区间内采用最优拉丁超立方(OLhd)取样;二是引入比例系数w1组合高斯与指数型相关函数提高模型对数据的泛化能力,从而在每个划分的区间内建立泛化的Kriging近似模型。通过SCH测试函数,验证了构造的分区间泛化Kriging模型有效性。结合参数化建模和改进Kriging近似模型对某过渡肘板和舱口角隅边界进行形状优化,优化第一阶段由改进的近似模型通过多岛遗传算法得到全局初步的最优解,第二阶段在初步解的基础上缩小优化变量范围,由少量的FEM计算即可在小范围内搜寻到精确的最优设计变量。结果表明:分区间泛化Kriging近似模型在预测多维度响应时较常规Kriging模型预测精度更高;分阶段的形状优化流程在保证极小误差和缩小计算成本的情况下能够得到理想的应力分布和重量优化结果,有助于船舶结构的轻量化研究。
Some improvements with regard to partition and generalization have been proposed for Kriging approximation model. The change makes the Kriging approximation model more suitable for the prediction of multi-dimensional responses in ship structure engineering. One of the improvements about partition is to divide each dimension of sampling point's data in the design space into two or four equal parts. The Optimal Latin Hypercube Design sampling is applied in each partition. Then different Kriging approximation models are established among different partitions. The other improvement is combining Gauss and exponential correlation function by introducing of proportional coefficient w1,which increases the type of correlation function and thereby improves the generalization performance of approximation model. The coefficient w1 is defined as the maximum likelihood estimator,which is similar to the definition of parameter in the correlation function. According to the improvement measures,the partition and generalization Kriging approximation model( PGKAM) is established in each interval. With testing the Schaffer function N.1,the partition and generalization Kriging approximation modeling has been proved effective. By integrating with parametric modeling and PGKAM,certain optimization of problems of bracket and hatch corner's boundary shape is carried out. In the process of shape optimization,firstly,the global initial optimal solution is obtained from the improved approximate model with the Multi Island Genetic Algorithm. Then the scope of the optimization variables is trimmed based on the initial solution. With costing few FEM calculations,the exact optimal design variables are able to be found efficiently in a small scale. The results illustrate that the partition and generalization Kriging approximation model has higher prediction accuracy than the conventional Kriging model in the prediction of multi-dimensional responses. Phased shape optimization methodology ensures the ideal stress distribution and weight optimization results to be capable of obtaining when error is minimum and the calculation burden is lessened,which is helpful to the lightweight analysis of ship structure.
Some improvements with regard to partition and generalization have been proposed for Kriging approximation model. The change makes the Kriging approximation model more suitable for the prediction of multi-dimensional responses in ship structure engineering. One of the improvements about partition is to divide each dimension of sampling point's data in the design space into two or four equal parts. The Optimal Latin Hypercube Design sampling is applied in each partition. Then different Kriging approximation models are established among different partitions. The other improvement is combining Gauss and exponential correlation function by introducing of proportional coefficient w1,which increases the type of correlation function and thereby improves the generalization performance of approximation model. The coefficient w1 is defined as the maximum likelihood estimator,which is similar to the definition of parameter in the correlation function. According to the improvement measures,the partition and generalization Kriging approximation model( PGKAM) is established in each interval. With testing the Schaffer function N.1,the partition and generalization Kriging approximation modeling has been proved effective. By integrating with parametric modeling and PGKAM,certain optimization of problems of bracket and hatch corner's boundary shape is carried out. In the process of shape optimization,firstly,the global initial optimal solution is obtained from the improved approximate model with the Multi Island Genetic Algorithm. Then the scope of the optimization variables is trimmed based on the initial solution. With costing few FEM calculations,the exact optimal design variables are able to be found efficiently in a small scale. The results illustrate that the partition and generalization Kriging approximation model has higher prediction accuracy than the conventional Kriging model in the prediction of multi-dimensional responses. Phased shape optimization methodology ensures the ideal stress distribution and weight optimization results to be capable of obtaining when error is minimum and the calculation burden is lessened,which is helpful to the lightweight analysis of ship structure.
引文
[1]胡新明,王德禹.基于迭代均值组合近似模型和序贯优化与可靠性评估法的船舶结构优化设计[J].上海交通大学学报,2017,51(2):150-156.(HU Xinming,WANG Deyu.Optimization of ship structures using ensemble of surrogates with sequential optimization and reliability assessment[J].Journal of Shanghai Jiao Tong University,2017,51(2):150-156.(in Chinese))
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[11]徐昌文,俞铭华.论船舶结构的形状优化[J].中国造船,1989(3):91-100.(XU Cangwen,YU Minghua.On shape optimization of ship structures[J].Shipbuilding of China,1989(3):91-100.(in Chinese))
[2]MYERS D E.Co-Kriging---New developments[M]//Geostatistics for Natural Resources Characterization.Springer Netherlands,1984:295-305.
[3]ROSHAN V,YING H,SUDJIANTO A.Blind kriging:A new method for developing metamodels[J].Journal of Mechanical Design,2008,130(3):350-353.
[4]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.
[5]高月华.基于kriging代理模型的优化设计方法及其在注塑成型中的应用[D].大连:大连理工大学,2009.(GAOYuehua.Optimization methods based on kriging surrogate model and their application in injection molding[D].Dalian:Dalian University of Technology,2009.(in Chinese))
[6]冯国庆,任慧龙,李巧彦,等.舰船典型节点参数化建模及形状优化[J].中国舰船研究,2009,4(4):28-33.(FENGGuoqing,REN Huilong,LI Qiaoyan,et al.Parametric modeling and shape optimization of the typical structural details of ships[J].Chinese Journal of Ship Research,2009,4(4):28-33.(in Chinese))
[7]LINDEMANN T,KAEDING P.An approach to optimization in ship structural design using finite element and optimization techniques[C]//Proceedings of the Twentieth(2010)International Offshore and Polar Engineering Conference.2010:803-808.
[8]LOPHAVEN S N,NIELSEN H B,SNDERGAARD J.Aspects of the matlab toolbox DACE[R].Copenhagen:Informatics&Mathematical Modelling Technical University of Denmark,2002.
[9]MATLAB A,TOOLBOX K,LOPHAVEN S N,et al.DACE-A Matlab Kriging toolbox[R].Copenhagen:Informatics&Mathematical Modelling Technical University of Denmark,2002.
[10]SCHAFFER J D.Multiple objective optimization with vector evaluated genetic algorithms[C]//Proceedings of the International Conference on Genetic Algorithms.1985:93-100.
[11]徐昌文,俞铭华.论船舶结构的形状优化[J].中国造船,1989(3):91-100.(XU Cangwen,YU Minghua.On shape optimization of ship structures[J].Shipbuilding of China,1989(3):91-100.(in Chinese))