Improving SWATH Seakeeping Performance using Multi-Fidelity Gaussian Process and Bayesian Optimization
Authors: Bonfiglio Luca , Perdikaris Paris , Vernengo Giuliano , de Medeiros João Seixas , Karniadakis George 
Published: October 2018

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.