Journal article
Design-space dimensionality reduction in shape optimization by Karhunen–Loève expansion
Computer methods in applied mechanics and engineering, Vol.283, pp.1525-1544
01/01/2015
DOI: 10.1016/j.cma.2014.10.042
Abstract
The paper presents a methodology to reduce the dimension of design spaces in shape optimization problems, while retaining a desired level of geometric variance. The method is based on a generalized Karhunen–Loève expansion (KLE). Arbitrary shape modification spaces are assessed in terms of Karhunen–Loève modes (eigenvectors) and associated geometric variance (eigenvalues). The former are used as a basis in order to build a reduced-dimensionality representation of the shape modification. The method is demonstrated for the shape optimization of a high-speed catamaran, based on CFD simulations and aimed at the reduction of the wave component of calm-water resistance. KLE is applied to three design spaces with large dimensionality (≥20), based on a free form deformation technique. The space with the largest geometric variance is selected for dimensionality reduction and design optimization. N-dimensional design spaces are used, with N=1, 2, 3, and 4, retaining up to the 95% of the geometric variance associated to the original space. The correlation between the objective reduction achieved, the dimension N and the geometric variance of the reduced-dimensionality space is shown and found significant.
•A derivation for dimensionality reduction in shape optimization is proposed.•The design space is assessed before simulation-based optimization is performed.•A continuum formulation for shape-design variability is given.•The design space is reduced in dimensionality by KLE, based on confidence levels.•Optimization example based on CFD is provided, showing effectiveness of the method.
Details
- Title: Subtitle
- Design-space dimensionality reduction in shape optimization by Karhunen–Loève expansion
- Creators
- Matteo Diez - University of IowaEmilio F Campana - CNR–INSEAN, Natl. Research Council–Marine Technology Research Inst., Rome, ItalyFrederick Stern - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Computer methods in applied mechanics and engineering, Vol.283, pp.1525-1544
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.cma.2014.10.042
- ISSN
- 0045-7825
- eISSN
- 1879-2138
- Grant note
- name: US Navy Office of Naval Research, award: N00014-11-1-0237; DOI: 10.13039/100007297, name: Office of Naval Research Global, award: N62909-11-1-7011
- Language
- English
- Date published
- 01/01/2015
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984196619902771
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