Active Subspaces for Shape Optimization

Aerodynamic shape optimization plays a fundamental role in aircraft design. However, useful parameterizations of shapes for engineering models often result in high-dimensional design spaces which can create challenges for both local and global optimizers. In this paper, we employ an active subspace method (ASM) to discover and exploit low-dimensional, monotonic trends in the quantity of interest as a function of the design variables. The trend enables us to eciently and eectively nd an optimal design in appropriate areas of the design space. We apply this approach to the ONERA-M6 transonic wing, parameterized with 50 Free-Form Deformation (FFD) design variables. Given an initial set of 300 designs, the ASM discovered a low-dimensional linear subspace of the input space that explained the majority of the variability in the drag and lift coecients. This revealed a global trend that we exploited to nd an optimal design with reduced computational cost.

[1]  Joaquim R. R. A. Martins,et al.  Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration , 2014 .

[2]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[3]  Paul G. Constantine,et al.  Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model , 2015, Comput. Geosci..

[4]  Dimitri J. Mavriplis,et al.  Derivative-Enhanced Variable Fidelity Surrogate Modeling for Aerodynamic Functions , 2013 .

[5]  Juan J. Alonso,et al.  Adjoint-based method for supersonic aircraft design using equivalent area distributions , 2012 .

[6]  Dimitri N. Mavris,et al.  Method to Facilitate High-Dimensional Design Space Exploration Using Computationally Expensive Analyses , 2015 .

[7]  Joaquim R. R. A. Martins,et al.  Multi-point, multi-mission, high-fidelity aerostructural optimization of a long-range aircraft configuration , 2012 .

[8]  Thomas D. Economon,et al.  Stanford University Unstructured (SU 2 ): An open-source integrated computational environment for multi-physics simulation and design , 2013 .

[9]  Dimitri N. Mavris,et al.  Dimensionality Reduction Using Principal Component Analysis Applied to the Gradient , 2015 .

[10]  Francisco M. Capristan,et al.  Active Subspaces Applied to Range Safety Analysis and Optimization , 2015 .

[11]  Zhong-Hua Han,et al.  A New Cokriging Method for Variable-Fidelity Surrogate Modeling of Aerodynamic Data , 2010 .

[12]  Paul G. Constantine,et al.  Discovering an active subspace in a single‐diode solar cell model , 2014, Stat. Anal. Data Min..

[13]  Qiqi Wang,et al.  Erratum: Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces , 2013, SIAM J. Sci. Comput..

[14]  Christian Igel,et al.  A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies , 2006, GECCO.

[15]  I. Jolliffe.  Principal Component Analysis , 2002 .

[16]  Dieter Kraft,et al.  Algorithm 733: TOMP–Fortran modules for optimal control calculations , 1994, TOMS.

[17]  Geoffrey T. Parks,et al.  Accelerating design optimisation via principal components' analysis , 2008 .