Accelerations and added-resistance predictions using machine learning for planing hulls

While vertical motions and added resistance in displacement ships can generally be predicted following a linear pattern based on the sea spectrum using the RAO method, high-speed vessels operating in irregular waves exhibit nonlinear seakeeping that requires alternative semi-empirical predictive approaches at early design phases. These nonlinearities stem from vessel geometry, speed, and wave spectrum characteristics. This study performs the prediction of vertical acceleration and added resistance statistics in planing hulls using five machine learning methods, including neural networks. The dataset includes experimental series in irregular waves conducted by Fridsma, extended cases from Brown, and further expansions by Zarnick and Turner. These data-driven models outperform traditional empirical methods, such as those by Savitsky and Brown, particularly under high-speed conditions where nonlinear effects dominate. Machine learning emerges as a robust tool for preliminary design assessments, offering enhanced prediction capability without requiring explicit L/B input, thereby increasing model generalizability. INTRODUCTION Seakeeping analysis is a fundamental aspect throughout all stages of ship design. For displacement vessels operating at relatively low speeds, wave-induced motions can typically be approximated as linear, allowing the application of Response Amplitude Operators (RAO) to predict ship behavior under different sea conditions. This method assumes that ship motions are directly proportional to wave amplitudes, a reasonable approximation due to the moderate dynamic responses observed in conventional hull forms. Using either experimental testing or numerical simulations, it becomes feasible to generalize a vessel's seakeeping performance across a range of sea states based on its RAO characteristics (Lewis, 1989). Predicting vessel motions is crucial not only for operational safety but also for ensuring passenger comfort, as studies on motion sickness incidence (MSI) have highlighted the effects of vertical accelerations on human tolerance limits (O'Hanlon & McCauley, 1974). However, when the vessel type transitions to a planing hull, the effects of speed introduce strong nonlinearities (Fridsma, 1971), rendering traditional linear superposition methods like RAO invalid for predicting motions. In planing conditions, seakeeping behavior cannot be generalized through simple transfer functions; instead, it becomes highly dependent on the specific sea state and operational parameters. At high speeds, vessels experience significantly larger motions due to increased wave impacts and dynamic pressures. This phenomenon directly impacts structural design, as accelerations are critical inputs for calculating hydrodynamic pressures and structural loads, according to classification society guidelines such as DNV's Rules for Ships (2025) and ABS High-Speed Craft Rules (2024).