Augmented Design-Space Exploration by Nonlinear Dimensionality Reduction Methods

Abstract

The paper presents the application of nonlinear dimensionality reduction methods to shape and physical data in the context of hull-form design. These methods provide a reduced-dimensionality representation of the shape modification vector and associated physical parameters, allowing for an efficient and effective augmented design-space exploration. The data set is formed by shape coordinates and hydrodynamic performance (based on potential flow simulations) obtained by Monte Carlo sampling of a 27-dimensional design space. Nonlinear extensions of the principal component analysis (PCA) are applied, namely kernel PCA, local PCA and a deep autoencoder. The application presented is a naval destroyer sailing in calm water. The reduced-dimensionality representation of shape and physical parameters is set to provide a normalized mean square error smaller than 5%. Nonlinear methods outperform the standard PCA, indicating significant nonlinear interactions in the data structure. The present work is an extension of the authors’ research [1] where only shape data were considered.