We construct a multi-fidelity framework for statistical learning and global optimization that is capable of effectively synthesizing seakeeping predictions having two different levels of modeling fidelity, namely a strip theory and a boundary element method based on potential flow assumption. The objective of this work is to demonstrate that the multi-fidelity framework can be used efficiently to discover optimal small waterplane area twin hull shapes having superior seakeeping performance using a limited number of expensive high-fidelity simulations combined with a larger number of inexpensive low-fidelity simulations. Specifically, we employ multi-fidelity Gaussian process regression and Bayesian optimization to build probabilistic surrogate models and efficiently explore a 35-dimensional design space to optimize hull shapes that minimize wave-induced motions and accelerations, and satisfy specific requirements in terms of displacement and metacentric height. Our results demonstrate the superior characteristics of this optimization framework in constructing accurate surrogate models and identifying optimal designs with a significant reduction in the computational effort. 1. Introduction: During the past decades, estimating the seaworthiness of a ship in the early design stages has become a primary concern for naval architects. Increased requirements in terms of comfort and ergonomics have steered the research in developing innovative hull forms, with the specific target of decreasing motions in waves. From a safety point of view, extreme accelerations can exert harmful dynamic loads (on the vessel, cargo, or equipment), slamming, or green water effects that can severely damage the structural integrity of the vessel or lead to stability losses. When ship behavior in waves becomes a quantity of interest in the hull-form optimization process, seakeeping performance needs to be predicted with numerical models able to combine high fidelity and high computational efficiency. Nowadays, ship motion predictions mainly rely on three families of numerical models, here sorted by increasing level of fidelity: 2-D strip theories, 3-D boundary element methods (BEM), both developed under the assumption of potential flow, and unsteady fully viscous nonlinear 3-D methods in which ship motions are simulated in six Degrees of Freedom (DOF) for incident regular or irregular waves (see Fig. 5). In this article, we introduce a probabilistic method for constructing surrogate models using multi-fidelity training datasets that allows to increase the accuracy of the model with significant savings in computational resources. For the purpose of demonstration of the multi-fidelity framework, the training datasets used in this article are composed of classical 2-D and 3-D potential flow predictions; for this reason, we will refer to 2-D strip theories as low-fidelity models and a more accurate 3-D BEM as high-fidelity models. In the present study, our goal is to demonstrate the ability of the multi-fidelity framework in efficiently discovering hull forms with superior seakeeping characteristics by using simplified prediction models. Although in the present study, we do not include any viscous effects, the methodology is general and can combine any type of high-fidelity simulations or experimental data with low-fidelity simulations, experimental data, or even empirical correlations.

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.

A proper orthogonal decomposition (POD)-based method is proposed to reduce the dimensions of the design space for the shape optimisation of marine propellers. The effectiveness of the proposed approach is proven in the case of the INSEAN-E779A propeller, which blade shape is modified to maximise efficiency while reducing suction side cavitation. The 23-dimensions design space defined by the conventional shape representation is reduced by the POD method to 5, 12 and 15 dimensions, retaining up to the 98% of the geometric variance of the original space. A multi-objective optimisation algorithm drives the simulation-based design optimisation (SBDO) process in the new design spaces using BEM for the hydrodynamic predictions. Finally, optimal designs are verified using RANSE to assess the correlation between the performance improvements, the dimensionality reduction and the corresponding geometric variance. The effectiveness of the proposed POD-SBDO framework is discussed with respect to a design by optimisation process relying on the conventional parametric representation of the blade geometry.