Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

Abstract

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes and to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

Enhancing CFD predictions in shape design problems by model and parameter space reduction

“…Active subspaces [10] have been successfully employed in many engineering fields [12,13]. Among other we mention applications in shape optimization [20,38], combustion simulations [29], and in naval engineering [51]. For multifidelity dimension reduction with AS see [32], for multivariate extension of AS we mention [58], while for a coupling with deep neural networks see [52].…”

Projection-based reduced order models for a cut finite element method in parametrized domains

“…[44,45,46,47,48,49,36,29,37] and references therein. Even though such reference domain formulation avoids remeshing when updating the parametric domain, the choice of the transformation map is usually problem-dependent [50,44,47], suitable parameter space dimensionality reduction techniques [51,52,53,54] must be employed to identify the most relevant shape parameters and preserve good quality meshes, and often limited only to small parametric deformations. In contrast, the combination of ROMs with a CutFEM approach results in a novel methodology capable of handling large parametric deformations as well.…”

Synthesizing Designs With Inter-Part Dependencies Using Hierarchical Generative Adversarial Networks

“…Linear dimensionality reduction methods select a set of optimal directions or basis functions where the variance of shape geometry or certain simulation output is maximized. Such methods include the Karhunen-Loève expansion (KLE) [10,11], principal component analysis (PCA) [12], and the active subspaces approach [13].…”