A framework for efficient simulation-based multidisciplinary robust design optimization with application to a keel fin of a racing sailboat

A framework is presented for efficient simulation-based Multidisciplinary Robust Design Optimization (MRDO) of steady fluid-structure interaction problems, affected by uncertainty. The focus is on a racing-sailboat keel fin, subject to stochastic operating conditions. The elastic deformation of the fin, induced by hydrodynamic loads, cannot be neglected while evaluating the hydrodynamic performances, thus a fully coupled hydroelastic problem is considered, including fluid mechanics (CFD) and structural analysis (FEM). The multidisciplinary analysis (MDA) identifies the steady multidisciplinary state by numerical iterations. Stochastic operating conditions are given in terms of probability density function of the yaw angle. The objective function is the expected value of the fin efficiency over the stochastic operating conditions, whereas the design variables pertain to the fin geometry. Distributions of the relevant outputs are evaluated using uncertainty quantification methods (UQ), requiring a large number of multidisciplinary analyses (MDA). Solving the MRDO problem represents a challenge from the algorithmic and computational viewpoints, requiring: (1) a minimization algorithm, (2) a UQ tool and (3) simulation-based MDAs. Herein, the MDA is solved with a variable level of coupling between the disciplines involved; the UQ is carried out using the Monte Carlo method with a variable level of accuracy; the design optimization is solved using subsequent design of experiments (DoE), thin-plate spline metamodels, and particle swarm optimizations (PSO). Results are compared to benchmark solutions, given by fully coupled MDA, fully convergent UQ and optimization without metamodels, showing a close agreement and requiring the 50% of the benchmark computational cost.