Parameter identification of Norrbin model for ship maneuvering based on three-parameter simplex method&nbsp;

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Journal of Dalian Maritime University ›› 2026, Vol. 52 ›› Issue (1) : 1-11.

Parameter identification of Norrbin model for ship maneuvering based on three-parameter simplex method

SUN Qingjie^1a,1b，REN Junsheng^*1a,1b，LI Qinghao²

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Abstract

To effectively estimate the parameters of ship maneuvering motion models, this paper proposes a nonlinear identification method based on the threeparameter simplex algorithm (SA). A precision indicator function is constructed based on experimental data to establish a discrepancy criterion between model outputs and experimental data. It performs geometric operations such as reflection, expansion, and contraction in a threedimensional parameter space to achieve iterative optimization of parameters. The algorithm undergoes continuous iteration until it meets the convergence criterion, ultimately obtaining the globally optimal parameter combination that minimizes the indicator function. The proposed SA algorithm is applied to identify the parameters of the Norrbin model for the Mariner ship, and support vector machine (SVM) and extended Kalman filter (EKF) algorithms are used as comparison methods to systematically analyze identification performance. It can be seen from the calculation of the relative errors of the parameters obtained by each method that the identification accuracy of the SA algorithm is significantly superior to that of the other two methods: the relative error of its parameters is 0.022% for all cases, with the maximum error not exceeding 0.041%; the relative error of the EKF algorithm ranges from 8.150% to 32.068%, while the relative error of the SVM algorithm is 11.2% for all parameters, and the error of some parameters even exceeds 20%. The results show that the model identified by the SA algorithm is more consistent with the actual maneuvering performance of the ship. Furthermore, in terms of algorithm structure, the SA method is more concise than the SVM and EKF algorithms, requires fewer preset parameters, and therefore exhibits better practicality and engineering applicability.

Key words

ship maneuverability / Norrbin model；parameter identification； simplex algorithm（SA）

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SUN Qingjie, REN Junsheng, LI Qinghao. Parameter identification of Norrbin model for ship maneuvering based on three-parameter simplex method [J]. Journal of Dalian Maritime University. 2026, 52(1): 1-11

References

［1］张炜灵,蔡烽,霍龙.船舶操纵响应模型参数辨识的发展趋势分析［J］.舰船电子工程,2019,39(11):4-5.
ZHANG W L, CAI F, HUO L. Development trend of parameter identification of ship maneuvering response equation［J］. Ship Electronic Engineering, 2019,39(11):4-5. (in Chinese)
［2］朱曼,文元桥,孙吴强,等.船舶运动模型参数辨识研究综述［J］.交通信息与安全,2022,40(5):1-11.
ZHU M, WEN Y Q, SUN W Q, et al. A review of parameter identification methods for ship dynamic models［J］. Journal of Transport Information and Safety, 2022,40(5):1-11. (in Chinese)
［3］郑文龙,肖昌润.船舶操纵非线性KT方程参数的辨识［J］.舰船科学技术,2017,39(17):129-132.
ZHENG W L, XIAO C R. The parameter identification of KT equations on ship maneuverability［J］. Ship Science and Technology, 2017,39(17):129-132. (in Chinese)[ZK)]
［4］王雪刚,邹早建.基于果蝇优化算法的船舶操纵响应模型的辨识［J］.大连海事大学学报,2012,38(3):1-4.
WANG X G, ZOU Z J. Identification of ship manoeuvring response model based on fruit fly optimization algorithm［J］. Journal of Dalian Maritime University, 2012,38(3):1-4. (in Chinese)
［5］TOMERA M. Swarm intelligence applied to identification of nonlinear ship steering model［C］//2015 IEEE 2nd International Conference on Cybernetics (CYBCONF). Gdynia:IEEE, 2015: 133-139.
［6］张心光,邹早建.基于支持向量回归机的船舶操纵响应模型辨识［J］.上海交通大学学报,2011,45(4):501-504.
ZHANG X G, ZOU Z J. Identification of response models of ship manoeuvring motion using support vector regression［J］. Journal of Shanghai Jiao Tong University, 2011,45(4):501504. (in Chinese)
［7］LUO W L, ZOU Z J. Parametric identification of ship maneuvering models by using support vector machine［J］. Journal of Ship Research. 2009, 53: 19-30.
［8］宋利飞,王毓清,彭伟,等.基于SVR的船舶简化分离型模型水动力系数辨识研究［J］.中国舰船研究,2025,20(1):65-75.
SONG L F,WANG Y Q,PENG W, et al. Hydrodynamic coefficients identification of ship simplified modular model based on support vector regression［J］. Chinese Journal of Ship Research, 2025,20(1):6575. (in Chinese).
［9］祝添权,初秀民,田国昊,等.基于LSSVM的船舶操纵响应模型参数辨识及应用［J］.武汉理工大学学报,2021,43(12):28-36.
ZHU T Q, CHU X M, TIAN G H, et al. Parameter identification and application of ship maneuvering response model based on LS-SVM［J］. Journal of Wuhan University of Technology, 2021,43(12):2836. (in Chinese)
［10］褚式新,俞剑,姜文,等.基于遗传算法的水面无人艇操纵响应模型参数辨识仿真研究［J］.中国电子科学研究院学报,2023,18(10):930-935.
CHU S X, YU J, JIANG W, et al. Simulation research of parameter identification of maneuvering response model of unmanned surface vessel based on genetic algorithms［J］. Journal of China Academy of Electronics and Information Technology, 2023,18(10):930935. (in Chinese)
［11］谢朔,陈德山,初秀民,等.改进多新息卡尔曼滤波法辨识船舶响应模型［J］.哈尔滨工程大学学报,2018, 39(2):282-289.
XIE S, CHEN D S, CHU X M, et al. Identification of ship response model based on improved multiinnovation extended Kalman filter［J］. Journal of Harbin Engineering University, 2018,39(2):282289. (in Chinese)
［12］李晴昊,任俊生,华焱.基于均方根容积卡尔曼滤波的船舶操纵运动响应模型参数辨识［J］.系统仿真学报,2024,36(8):1790-1799.
LI Q H, REN J S, HUA Y. Parametric identification of ship maneuvering motion response model based on square root cubature Kalman filtering［J］. Journal of System Simulation, 2024, 36(8): 17901799. (in Chinese)
［13］MENG Y, ZHANG X K, ZHANG X F, et al. Maneuverability indices estimation of nonlinear response model based on full-scale trial data and square root unscented Kalman filter［J］. Ocean Engineering, 2023, 286:115699.
［14］MENG Y, ZHANG X F, ZHU J X. Parameter identification of ship motion mathematical model based on fullscale trial data［J］. International Journal of Naval Architecture and Ocean Engineering, 2022, 14:100437.
［15］黄小斌,杨盐生.船舶操纵运动数学模型预报精度的研究［J］.大连海事大学学报,1997,23(2):27-31.
HUANG X B, YANG Y S. Improvement on precise prediction of ship manoeuvring mathematical model［J］. Journal of Dalian Maritime University, 1997,23(2):27-31. (in Chinese)
［16］任俊生.船舶运动与控制［M］.大连:大连海事大学出版社,2021.
REN J S. Ship motion and control［M］.Dalian：Dalian Maritime University Press, 2021. (in Chinese)
［17］Fossen T I. Handbook of marine craft hydrodynamics and motion control［M］. John Wiley & Sons, 2011.