Parametric Model Embedding

TL;DR

This paper introduces a method to embed original parametric design parameters into a reduced-dimensionality space, enabling direct use of established parametric models in shape optimization, demonstrated on 2D and 3D design problems.

Contribution

It presents a novel embedding technique that integrates original parametric models into reduced-dimensionality spaces for shape optimization.

Findings

Successful reparameterization of 2D Bezier curves.

Effective application to 3D free-form deformation spaces.

Demonstrated improvements in simulation-driven design optimization.

Abstract

Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space, capable of maintaining a certain degree of the original design variability. Nevertheless, they usually do not allow to use directly the original parameterization method, representing a limitation to their widespread application in the industrial field, where the design parameters often pertain to well-established parametric models, e.g. CAD (computer-aided design) models. This work presents how to embed the parametric-model original parameters in a reduced-dimensionality representation of the design space. The method, which takes advantage from the definition of a newly-introduced generalized feature space, is demonstrated, as a proof of concept, for the reparameterization of 2D Bezier curves and 3D free-form deformation design spaces and the consequent solution of simulation-driven design optimization problems of a subsonic airfoil and a naval destroyer in calm water, respectively.