Shape-supervised Dimension Reduction: Extracting Geometry and Physics Associated Features with Geometric Moments
Khan S. Kaklis P. Serani A. Diez M. Kostas K.
September 2022Elsevier Ltd
CAD Computer Aided Design
2022#150
In shape optimisation problems, subspaces generated with conventional dimension reduction approaches often fail to extract the intrinsic geometric features of the shape that would allow the exploration of diverse but valid candidate solutions. More importantly, they also lack incorporation of any notion of physics against which shape is optimised. This work proposes a shape-supervised dimension reduction approach. To simultaneously tackle these deficiencies, it uses higher-level information about the shape in terms of its geometric integral properties, such as geometric moments and their invariants. Their usage is based on the fact that moments of a shape are intrinsic features of its geometry, and they provide a unifying medium between geometry and physics. To enrich the subspace with latent features associated with shapes geometrical features and physics, we also evaluate a set of composite geometric moments, using the divergence theorem, for appropriate shape decomposition. These moments are combined with the shape modification function to form a Shape Signature Vector (SSV) uniquely representing a shape. Afterwards, the generalised Karhunen–Loève expansion is applied to SSV, embedded in a generalised (disjoint) Hilbert space, which results in a basis of the shape-supervised subspace retaining the highest geometric and physical variance. Validation experiments are performed for a three-dimensional wing and a ship hull model. Our results demonstrate a significant reduction of the original design spaces dimensionality for both test cases while maintaining a high representation capacity and a large percentage of valid geometries that facilitate fast convergence to the optimal solution. The code developed to implement this approach is available at https://github.com/shahrozkhan66/SSDR.git.
Computer-aided design , Design space , Dimensionality reduction , Geometric moment invariants , Shape optimisation , Subspace
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Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, United Kingdom
National Research Council-Institute of Marine Engineering, Italy
School of Engineering and Digital Sciences, Nazabayev University, Kazakhstan
Department of Naval Architecture
National Research Council-Institute of Marine Engineering
School of Engineering and Digital Sciences
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