Calculation of ship floating state by quasi-Newton iteration method for onboard loading computer

Abstract

ABSTRACT Calculating the floating state of a ship is the basic function of onboard loading computer, which is crucial for ship safety. Aiming at the deficiencies in the existing algorithms, we used the quasi-Newton iteration method to calculate the floating state of a ship. Firstly, the section model database of ship's hull was established by cutting the stereolithographic (STL) 3D model which is created by ship design software. Then, Sutherland–Hodgma polygon clipping algorithm and Shoelace Formula were used to calculate the Jacobian matrix. Finally, We selected a 108,000 DWT bulk carrier, ADMIRAL SCHMIDT, as an example to verify the correctness of the algorithm. We performed 100,000 random loading numerical tests, the average number of iterations was 2–3, and the number of convergence failures was zero. We calculated 24 typical standard loading conditions. We found the maximum average absolute error of the draught and trim were 0.0081 and −0.0283 m, respectively. The calculation error was far less than the requirements of the classification society. The results showed that the Quasi-Newton iteration method is simple to implement and easy to program, and has high robustness and accuracy and appropriate convergence. The method is suitable for the real-time calculation of a ship's floating state and has considerable engineering application value.