Risk-adaptive set-based design and applications to shaping a hydrofoil

The paper presents a framework for set-based design under uncertainty and demonstrates its viability through designing a super-cavitating hydrofoil of an ultrahigh speed vessel. The framework achieves designs that safely meet the requirements as quantified precisely by superquantile measures of risk (s-risk) and reduces the complexity of design under uncertainty. S-risk ensures comprehensive and decision-theoretically sound assessment of risk and permits a decoupling of parametric uncertainty and surrogate (model) uncertainty. The framework is compatible with any surrogate building technique, but we illustrate it by developing for the first time risk-adaptive surrogates that are especially tailored to s-risk. The numerical results demonstrate the framework in a complex design case requiring multifidelity simulation.