Abstract: To solve computationally expensive black box problem such as turbomachinery design optimization in an effective way，a meta-model based global design optimization and exploration method named MBOE is proposed by integrating a meta-model based global optimization algorithm named MBGO and data mining techniques. The MBGO algorithm can usually achieve the global optimum with minimum function evaluations. Data mining techniques provide a way to get insights into the interactions among parameters and uncover the mechanism behind performance improvement of the optimal design. Using MBOE，3D design optimization and data mining of Rotor 37 blade are finished. Isentropic efficiency of the optimal design is 1.74% higher than that of the reference design. And the computing time of MBGO is just 1/5 of that by applying a modified differential evolution algorithm as the optimizer. Meanwhile，data mining results indicate that the leading edge and the 3D stacking style have great effect on the blade aerodynamic performance. The performance improvement of the optimal design is benefited from the changes of related parameters. Therefore，the correctness and effectiveness of MBOE method is demonstrated.

Key words: Meta-modeling；Kriging model；Global optimization；Data mining

摘要： 为有效求解大资源黑盒子问题如叶轮机械设计优化等，提出了基于子元模型的全局优化与设计空间知识挖掘方法MBOE。该方法包括全局优化算法MBGO与数据挖掘两部分，其中MBGO算法需要极少的函数估值即可获得全局最优解；数据挖掘技术能有效分析变量间的相关关系，揭示最优设计性能提高的本质原因。利用MBOE，完成NASA Rotor37转子叶栅三维气动设计优化与知识挖掘，最优设计等熵效率相对参考设计提高1.74%。同时，利用MBGO算法所需要的计算量仅为进化算法的1/5。数据挖掘结果表明叶栅前缘及三维积叠参数对叶栅气动性能影响较大，最优设计由于上述叶型参数的改善有效减弱了叶栅进口激波损失，使得最优设计气动性能明显提高。由此，MBOE方法的正确性和有效性得到了验证。

关键词: 子元建模；Kriging模型；全局优化；数据挖掘