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

Area of Science:

• Naval Architecture
• Computational Fluid Dynamics
• Applied Mathematics

Background:

• Ship design involves complex hydrodynamic simulations to predict total resistance.
• High dimensionality of geometric and physical parameters complicates early-stage design assessments.
• Parameter space reduction is crucial for efficient and accurate ship performance prediction.

Purpose of the Study:

• To apply active subspaces methodology for parameter space reduction in naval architecture.
• To identify dominant parameters influencing ship hull hydrodynamic performance.
• To develop an automated procedure for shape perturbation and flow simulation data collection.

Main Methods:

• Utilized active subspaces properties for parameter space reduction.
• Implemented an automated procedure for generating hull shape perturbations using Free Form Deformation.
• Employed a high-fidelity potential flow solver with nonlinear free surface treatment.
• Integrated tools within SISSA mathLab as open-source components.

Main Results:

• Demonstrated the first application of active subspaces in naval architecture for parameter reduction.
• Successfully identified lower-dimensional structures within the parameter space influencing ship drag.
• Validated the effectiveness of the integrated open-source tools for hydrodynamic analysis.

Conclusions:

• Active subspaces offer a powerful approach for simplifying complex hydrodynamic problems in ship design.
• The developed methodology and tools enable more efficient assessment of hull performance during preliminary design.
• This work provides a foundation for further research in reduced-order modeling for naval applications.