A Hybrid Gaussian Process Framework for Rapid Prediction of Umbilical Cable Mechanics in Deep-Sea Mining

The umbilical cable is an important component of the deep-sea mining system, serving as the sole connection between the surface support vessel and the seabed mining system. The harsh marine environment poses significant challenges to umbilical cable safety. Methods based on traditional time-domain simulation are time-consuming and it is hard for them to meet the needs of real-time prediction. In this paper, a novel forecasting method is proposed, PFLM-PSML, which integrates the theory of potential flow (PF), the lumped mass method (LM), and a parameterised supervised machine learning method (PSML) to forecast the safety of umbilical cables. Six environmental and system parameters—wave height, wave direction, current velocity, current direction, cable length, and the relative position between vehicle and vessel—are used as model inputs, while outputs include cable top tension, curvature, and mining vehicle overturning moments. The model employs Latin hypercube sampling and an active learning approach with hybrid kernel functions to efficiently map input–output relationships. Validation through numerical simulations and a 6000 m deep-sea trial confirms that the proposed method achieves high accuracy and a computational speed thousands of times faster than traditional approaches, enabling real-time mechanical state prediction. Parametric analyses reveal that increases in wave height, current velocity, and water depth lead to higher cable tension and vehicle overturning moments. The PFLM-PSML framework demonstrates strong potential for real-time safety assessment and control of deep-sea mining systems under complex ocean conditions.