改进的Kriging近似方法及其在鱼雷外形优化中应用  

An Improved Kriging Approximation and Its Application to Shape Design Optimization of Torpedo

作　　者：温庆国[1] 宋保维[1] 王鹏[1] 王司令[1] 

机构地区：[1]西北工业大学航海学院,西安710072

出　　处：《上海交通大学学报》2013年第4期613-618,共6页Journal of Shanghai Jiaotong University

基　　金：国家高技术研究发展计划(863)项目(2011AA09A104)

摘　　要：对小样本条件下Kriging拟合精度的研究后发现,由原样本点生成新样本点后,拟合这2组样本点可提高其拟合精度.使用2种方法生成新样本点,一种是基于极大似然估计的生成方法;另一种是基于最小均方误差的生成方法.经分析,第1种方法要求较为苛刻,导致新样本点不能提供有效的样本信息;而第2种方法得到了带有有效附加信息的新样本点.数学算例表明,基于最小均方误差生成新样本点的方法得到的样本点提高了Kriging模型的拟合精度.将该方法应用于鱼雷外形优化中,得到了较为满意的优化结果,表明了改进的Kriging近似方法的有效性.Sample augmentation could improve the accuracy of the Kriging models under small samples. It adds additional data to the original samples, the augmented samples are used to build the Kriging model. There are two methods to create the additional samples. The first one uses maximum likelihood estimation （MLE）, the other uses minimum means squared error （MSE）. The MLE process is too strict to provide enough additional useful information, the augmented samples are exceedingly close to the original samples. The minimum MSE process gets new samples with available information to the original database, the accuracy of the Kriging model under the augmented samples is improved. The minimum MSE process can solve the problem about constructing the high accuracy Kriging models under small samples. Finally, a torpedo shape design optimization was carried out with the technique, and the Kriging model using the minimum MSE process shows its high precision and reliability.

关 键 词：KRIGING插值 极大似然估计 均方误差 优化设计 

分 类 号：TP202.7[自动化与计算机技术—检测技术与自动化装置]