Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 403–419 | Cite as

Surrogate-based aerodynamic shape optimization with the active subspace method

  • Jichao LiEmail author
  • Jinsheng Cai
  • Kun Qu
Research Paper


Surrogate-based optimization is criticized in high-dimensional cases because it cannot scale well with the input dimension. In order to overcome this issue, we adopt a snapshot active subspace method to reduce the input dimension. A smoothing operation of samples is used to reduce the demand for snapshots in the construction of active subspaces. This operation significantly reduces the computational cost on the one hand, and on the other hand, it leads to more feasible subspaces. We use a 90∼95% energy coverage criterion to define the dimension of the subspace. With this criterion, the surrogate-based airfoil optimization in the active subspace is both efficient and effective. We also validate this optimization approach in an ONERA M6 wing optimization case with 220 shape variables. Compared with original surrogate-based optimization, the new approach reduces the computational time by 70% and obtains a more practical design with a smaller drag.


Active subspace method Surrogate-based optimization High-dimensional optimization 



The first author would like to thank the MDO Lab at the University of Michigan for the valuable inspirations and suggestions in this work. The authors are thankful for the constructive feedback and suggestions provided by the reviewers.

Funding information

This work was supported by the 111 Project of China (B17037).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Key Laboratory of Aerodynamic Design and Research, School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

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