Applying Simplex Algorithm for Ship’s Motion Simulation Optimization by Using Maneuvering Tests Data

Manh Cuong Nguyen, Khanh Toan Tran


This article demonstrates an effective method to find OHCs (optimal hydrodynamic coefficients) by applying the Simplex algorithm to reduce the errors of the ship’s motion simulation. The solution is to determine OHCs, which are also the coefficients of the ship’s motion equations. A ship’s motion simulation model was programed by contributing the mathematical model of the ship’s motion, applying the numerical method and MATLAB. In the optimization procedure, the form of Objective Function was contributed corresponding to the type of maneuvering test. The Sensitivity Analysis technique and Simplex algorithm are applied to filter and optimize the most sensitive hydrodynamic coefficients. The numerical model was validated by experimental maneuvering test data, including Turning Circle and Zigzag tests of Esso Bernicia 193000DWT Tanker. A good optimization solution was obtained: for Turning Circle test, after optimization, the ship’s simulation trajectory is close to the experimental trajectory with a RMSD of 5.8m, which reduced from an original value of 69m. In the Zigzag test, the RMSD between the ship’s simulation yaw angle and experimental data was reduced 17.3deg to 5.9deg. The other optimization results, such as the convergence of Objective Function, the number of iteration of Optimization Variables, calculated time, etc. are accepted. Therefore, the Simplex algorithm can be applied quite effectively to optimize ship movement (ship’s trajectory, the ship’s yaw angle, etc.). By defining a common set of values by merging the optimal value of the most sensitive coefficients of two tests, which may be used for the other ship’s motion simulation applications.


ship’s motion simulation; optimization technique; Simplex algorithm; hydrodynamic; experimental maneuvering.

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