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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Y. Sun and D. Jia, “Study on Safety of Up-righting Project for a Capsized Ship Model Based on Cable Tensions, Theoretical Model and Numerical Method Accounting for Dynamic Effect,” Int. J. e-Navigation Marit. Econ., vol. 10, pp. 62–75, 2018.

V. T. Pham, “Using the Vector Autoregression Model to Determine the Relationship Between Some Macroeconomic Targets and The Volume of Goods Transported by Sea in Vietnam,” Int. J. e-Navigation Marit. Econ., vol. 13, pp. 43–49, 2019.

D. H. Anh, “The breakthrough technology solutions for control and treatment oil spill on the sea: A short review,” J. Mech. Eng. Res. Dev., vol. 42, no. 5, pp. 01–05, 2019.

P. H. Hoang, A. T. Hoang, N. H. Chung, L. Q. Dien, X. P. Nguyen, and X. D. Pham, “The efficient lignocellulose-based sorbent for oil spill treatment from polyurethane and agricultural residue of Vietnam,” Energy Sources, Part A Recover. Util. Environ. Eff., vol. 40, no. 3, pp. 312–319, 2018.

V. C. Huynh and G. T. Tran, “Improving the Accuracy of Ship Resistance Prediction Using Computational Fluid Dynamics Tool,” Int. J. Adv. Sci. Eng. Inf. Technol., vol. 10, no. 1, pp. 171–177, 2020.

H. Yasukawa and Y. Yoshimura, “Introduction of MMG standard method for ship maneuvering predictions,” J. Mar. Sci. Technol., 2015.

K. Wang, S. Wang, L. Zhen, and X. Qu, “Ship type decision considering empty container repositioning and foldable containers,” Transp. Res. Part E Logist. Transp. Rev., vol. 108, pp. 97–121, 2017.

S. Luo, N. Ma, and Y. Hirakawa, “Evaluation of resistance increase and speed loss of a ship in wind and waves,” J. Ocean Eng. Sci., 2016.

M. Duan, Z. Liu, D. Yan, W. Peng, and A. Baghban, “Application of LSSVM algorithm for estimating higher heating value of biomass based on ultimate analysis,” Energy Sources, Part A Recover. Util. Environ. Eff., vol. 40, no. 6, pp. 709–715, Mar. 2018.

J. Wang, L. Zou, and D. Wan, “Numerical simulations of zigzag maneuver of free running ship in waves by RANS-Overset grid method,” Ocean Eng., vol. 162, pp. 55–79, 2018.

W. Luo and L. Lan, “Design Optimization of the Lines of the Bulbous Bow of a Hull Based on Parametric Modeling and Computational Fluid Dynamics Calculation,” Math. Comput. Appl., vol. 22, no. 1, p. 4, 2017.

V. V. Pham and A. T. Hoang, “Technological perspective for reducing emissions from marine engines,” Int. J. Adv. Sci. Eng. Inf. Technol., vol. 9, no. 6, pp. 1989–2000, 2019.

T. Khanh Toan, “A Study on ship manoeuvring simulation and ship trajectory optimization based on SQP and BFGS algorithms from sea trials,” Int. J. Eng. Technol., vol. 7, no. 4, pp. 103–111, 2018.

B. Rudloff, F. Ulus, and R. Vanderbei, “A parametric simplex algorithm for linear vector optimization problems,” Math. Program., vol. 163, no. 1–2, pp. 213–242, 2017.

F. Huang, L. Wang, and C. Yang, “A new improved artificial bee colony algorithm for ship hull form optimization,” Eng. Optim., vol. 48, no. 4, pp. 672–686, 2016.

T. K. Toan, D. P, O. A, and S. P, “Simulation of ship manoeuvring in confined waterway using a nonlinear model based on optimization techniques,” Ocean Eng., vol. 142, pp. 194–203, 2017.

X. P. Nguyen and D. K. Pham Nguyen, “Experimental Research on the Impact of Anchor-Cable Tensions in Mooring Ship at Vung Tau Anchorage Area,” Int. J. Adv. Sci. Eng. Inf. Technol., vol. 9, no. 6, pp. 1892–1899, 2019.

F. Tillig and J. W. Ringsberg, “A 4 DOF simulation model developed for fuel consumption prediction of ships at sea,” Ships Offshore Struct., vol. 14, no. sup1, pp. 112–120, 2019.

T. Khanh Toan, “A Study on the Application of Sensitivity Analysis for Ship Hydrodynamic Coefficients,” Int. J. Eng. Technol., vol. 7, no. 4, pp. 953–956, 2018.

T. Tezdogan, Y. K. Demirel, P. Kellett, M. Khorasanchi, A. Incecik, and O. Turan, “Full-scale unsteady RANS CFD simulations of ship behaviour and performance in head seas due to slow steaming,” Ocean Eng., 2015.

T. K. Toan, O. A., N. H., H. F., and A. Pourplanche, “A fast simulation and identification of hydrodynamic parameters for a freely maneuvering ship vessels,” in International Conference on Multiphysics - MULTIPHYSICS 2009, 2009, pp. 09–11.

H. Guo and Z. Zou, “System-based investigation on 4-DOF ship maneuvering with hydrodynamic derivatives determined by RANS simulation of captive model tests,” Appl. Ocean Res., vol. 68, pp. 11–25, 2017.



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