A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems

Abstract

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry - assuming the topology is inaltered by the deformation -, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

References in corpus (3)

• An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics
• Advances in Reduced Order Methods for Parametric Industrial Problems in Computational Fluid Dynamics
• Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains

Cited by in corpus (5)

• A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces
• Hull shape design optimization with parameter space and model reductions, and self-learning mesh morphing
• On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis
• An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques
• A Dimensionality Reduction Approach for Convolutional Neural Networks