基于信息矩阵的动态嵌套Kriging模型在船型优化中的应用研究

Information matrix-based dynamically embedded Kriging models in hull form optimization

本文提出一种基于信息矩阵的动态嵌套Kriging模型的构建方法。该方法利用高斯函数信息矩阵,提取加点子空间,利用增量拉丁超立方进行自适应采样,同时为应对采样过程中因样本分布密集而造成的全局近似模型在某些局部空间过拟合的问题,在加点子空间中构建局部近似模型,用于准确地描述局部目标解空间。最后通过数学函数对该方法的有效性与鲁棒性进行验证和分析,并将其应用于S60船型优化中。

Hull form optimization is a typical expensive black-box optimization problem,and Kriging model based optimization algorithms have been recognized as effective solutions to address this problem.In this study,an information matrix-based method was proposed for dynamically embedded local approximate models(IM-DEAM).The method used a Gaussian-function information matrix to extract one or more subspaces for additional sampling and the inherited Latin Hypercube Design(LHD)for adaptive sampling.In addition,to prevent overfitting by global approximate models in some subspaces with a dense sample distribution,local approximate models were embedded in the subspaces identified for additional sampling to enable accurate description of subspaces.The effectiveness and robustness of the method were validated and analyzed by applying the proposed method to optimize mathematical functions and the S60 hull form.