A spatial deformation reconstruction method of deep-sea mining riser from sparse inclination measurements

Mining risers, as critical components of deep-sea mining systems, are susceptible to excessive bending and displacement due to environmental loads, vessel motion, and mining vehicle operations. Accurate monitoring of their spatial deformation is essential for operational safety and efficiency. This paper proposes a novel method for reconstructing the 3D spatial deformation of mining risers using sparse inclination measurements. In this method, the 3D configuration of the riser is projected onto two orthogonal planes, followed by discretization of the structure through dual-axis inclinometer nodes and modeling of each segment using second-order interpolation functions. By integrating spatial curve length equations and correlating the 2D projections through shared coordinates, the 3D shape of the riser is efficiently reconstructed. A numerical simulation on a kilometer-scale deep-sea riser demonstrates the method's feasibility and effectiveness. Inversion accuracy exceeds 92.9 % with a sensor spacing ratio of 1/9, while correlation coefficients remain above 84.3 % and 83.4 % under varying levels of sensor and shipboard GPS noise, respectively. These results confirm that the proposed approach provides both high accuracy and robust performance for real-time spatial deformation reconstruction of mining risers under dynamic conditions.