A Force-Correcting Machine Learning Method for Nonlinear Marine Dynamics

Abstract

Wave-induced motion has a significant effect on the efficiency, economy, safety, and operability of a ship, so predicting the motion of a ship in waves is a subject of considerable interest. However, the ship motion problem is fraught with difficulties: stochasticity in the wave environment, nonlinearity in the hydrodynamic forces, and a large number, or cardinality, of environmental, operational, or design conditions which need to be analyzed. The cost of high-fidelity computational or experimental methods makes a direct assessment using high-fidelity methods intractable. To keep the seakeeping problem tractable necessitates simplifying assumptions in the modeling of the hydrodynamic forces. This has led to widespread use of low-fidelity methods, such as linear potential flow, which still comprise a majority of industrial seakeeping evaluations. However, nonlinearity in the hydrodynamic forces is necessary to predict large amplitude responses, global structural loads, and important nonlinear phenomena such as capsize, parametric roll, and slamming. As a result, there exists a strong compromise between accuracy and computational cost in the present state-of-the-art. In recent years, data-driven methods have been explored in pursuit of low-cost models. However, most data-driven models require large training datasets to generalize, and therefore do not adequately address the cardinality of seakeeping evaluations. Furthermore, literature on data-driven methods suffers from a crisis of reproducibility, inconsistency in the metrics that are used to evaluate performance, and limited industrial adoption. In this dissertation, a question is posed: Can a data-driven approach reduce the computational cost associated with the hydrodynamic forces acting on a ship in waves and reduce the challenge of the cardinality of a seakeeping evaluation? To address this question, five attributes are proposed to guide development of a data-driven method, considering accuracy, inference cost, training cost, generalizability, and interpretability. Following this, a new method, which takes a data-driven approach to the decomposition of the hydrodynamic forces in a governing equation of motion, is proposed. The method is developed mathematically and numerically, and the configuration is explored using two data sources: a nonlinear differential equation and a higher-order nonlinear potential flow boundary element method. The proposed method is then applied in two case studies: predicting the roll responses of a tumblehome hull using computational fluid dynamics training data, and to predict the heave and pitch responses of a fast displacement ship in a region of the North Atlantic. The first case study demonstrates an accuracy improvement over low-fidelity industry tools and shows that the proposed method can be used as a new lumped-moment roll damping model. The second case study demonstrates a new workflow for seakeeping evaluations, where the proposed method is used as a data-leveraging tool to predict responses over a wave scatter diagram using a small initial high-fidelity dataset. It is found that the proposed method offers low inference cost and an order-of-magnitude reduction in training data compared to other published methods. The method also collapses the wave frequency-amplitude space in the seakeeping problem, thereby reducing the burden of cardinality in evaluations by at least a factor of ten.