Hull shape design optimization with parameter space and model reductions, and self-learning mesh morphing

TL;DR

This paper introduces a data-driven shape optimization framework that combines model reduction, mesh morphing, and active subspace techniques to efficiently optimize complex geometries like ships.

Contribution

It presents a novel integration of POD, ASGA, and mesh morphing with RBF interpolation for efficient shape optimization in PDE problems.

Findings

Significant reduction in computational resources for shape optimization.

Effective preservation of mesh quality during shape deformation.

Successful validation on a ship benchmark demonstrating framework effectiveness.

Abstract

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.