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

doi:10.16182/j.issn1004731x.joss.24-0195

摘要/Abstract

摘要：

为了解决扩展卡尔曼滤波(extended Kalman filter，EKF)算法在船舶操纵运动模型参数辨识中存在辨识精度低、稳定性差和泛化能力弱的问题，提出了一种基于均方根容积卡尔曼滤波（square root cubature Kalman filter，SRCKF)的辨识算法。在CKF框架下将方差矩阵的均方根代替原始方差矩阵，使用三角分解对其进行预测和更新以提高辨识的稳定性。将EKF作为对比算法，利用四阶龙格库塔法解算的数值仿真数据，对舵角符合舵机伺服机构变化的船舶二阶非线性响应模型参数进行辨识，并将得到的辨识模型开展泛化能力验证试验。结果表明：SRCKF算法具有比EKF算法更高的辨识精度、稳定性和泛化能力。

关键词: 参数辨识, SRCKF（square root cubature Kalman filter）, 四阶龙格库塔法, 舵机伺服机构, 响应模型

Abstract:

The system identification algorithm, based on the square root cubature Kalman filter (SRCKF)is proposed to address issues such as low accuracy, poor robustness, and weak generalization ability encountered by the extended Kalman filter (EKF) algorithm in parameters identification of ship maneuvering motion models. This algorithm, within the framework of CKF, replaces the original covariance matrix with its root mean square and utilizes triangular decomposition for prediction and update to enhance identification stability. The EKF is used as a comparison algorithm to identify the parameters of the second-order nonlinear response model of a ship with rudder angles that comply with changes in the rudder servo system using the numerical simulation data solved by the fourth-order Lunger Kuta method, and the obtained identification model is subjected to a verification test of the generalisation ability. The results indicate that the SRCKF algorithm has higher identification accuracy, stability, and generalization ability than the EKF algorithm.

Key words: parameters identification, SRCKF(square root cubature Kalman filter), fourth-order Runge-Kutta method, rudder servo system, response model

中图分类号:

TP391.9

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 Qinghao,Ren Junsheng,Hua Yan . 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.

图/表 18

表1

Mariner船模参数

参数	数值	参数	数值
$T 1$	7.875 7	$δ r$	-0.036 993
$T 2$	0.369 4	$α$	247.117 5
$T 3$	0.378 7	$T E$	1
$K$	0.861 3	$h / d$	8.57
$L s h i p$	160.93	$L m o d e l$	3.218 6

表1

图1

图2

图3

图4

表2

船舶操纵性指数解算结果

参数	真实值	EKF		SRCKF
参数	真实值	辨识值	误差/%	辨识值	误差/%
$T 1$	7.875 7	5.840 3	25.844	7.870 4	0.067
$T 2$	0.369 4	0.237 6	35.680	0.344 0	6.876
$T 3$	0.378 7	0.196 3	48.165	0.370 6	2.139
$K$	0.861 3	0.690 6	19.819	0.856 4	0.569
$α$	247.117 5	180.017 6	27.153	245.391 1	0.699
$δ r$	-0.036 993	-0.032 540	12.037	-0.037 611	1.671

表2

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

表3

首向角、位置轨迹的RMSE和CC计算结果(EKF)

泛化试验	首向角/(°)		x位置轨迹/m		y位置轨迹/m
泛化试验	RMSE	CC	RMSE	CC	RMSE	CC
$10 ° / 5 °$ Z 形试验	3.952 2	0.939 4	0.273 9	1.000 0	1.243 8	0.979 9
$10 ° / 10 °$ Z 形试验	3.959 0	0.946 0	0.130 2	1.000 0	0.560 3	0.978 4
$20 ∘ / 10 °$ Z 形试验	1.609 4	0.996 6	0.201 3	1.000 0	0.472 6	0.993 7
$20 ° / 20 °$ Z 形试验	1.557 7	0.996 6	0.076 8	1.000 0	0.171 6	0.996 6
$35 °$ 旋回试验	1.290 7	1.000 0	0.133 9	0.999 8	0.214 5	0.999 7

表3

表4

首向角、位置轨迹的RMSE和CC计算结果(SRCKF)

泛化试验	首向角/(°)		x位置轨迹/m		y位置轨迹/m
泛化试验	RMSE	CC	RMSE	CC	RMSE	CC
$10 ° / 5 °$ Z 形试验	0.310 9	0.999 7	0.009 0	1.000 0	0.098 9	0.999 9
$10 ° / 10 °$ Z形试验	0.950 3	0.997 0	0.015 5	1.000 0	0.090 1	0.998 8
$20 ° / 10 °$ Z形试验	0.323 5	0.999 9	0.027 9	1.000 0	0.049 0	0.999 8
$20 ° / 20 °$ Z形试验	0.747 3	0.999 2	0.035 8	1.000 0	0.127 0	0.998 7
$35 °$ 旋回试验	0.222 7	1.000 0	0.025 7	1.000 0	0.029 1	1.000 0

表4

参考文献 15

1	张秀凤, 王晓雪, 孟耀, 等. 船舶运动建模与仿真研究进展及未来发展趋势[J]. 大连海事大学学报, 2021, 47(1): 1-8.
	Zhang Xiufeng, Wang Xiaoxue, Meng Yao, et al. Research Progress and Future Development Trend of Ship Motion Modeling and Simulation[J]. Journal of Dalian Maritime University, 2021, 47(1): 1-8.
2	Fossen T I. Guidance and Control of Ocean Vehicles[M]. New York: Wiley, 1994.
3	褚式新. 基于RLS方法的无人艇操纵性参数辨识研究[D]. 武汉: 武汉理工大学, 2020.
	Chu Shixin. Research on Parameter Identification of Unmanned Surface Vehicle Maneuverability Based on RLS Method[D]. Wuhan: Wuhan University of Technology, 2020.
4	方磊, 陈勇, 赵理, 等. 基于模糊控制的扩展卡尔曼滤波SOC估计研究[J]. 系统仿真学报, 2018, 30(1): 325-331.
	Fang Lei, Chen Yong, Zhao Li, et al. SOC Estimation with Extended Kalman Filter Based on Fuzzy Control[J]. Journal of System Simulation, 2018, 30(1): 325-331.
5	赵大明, 施朝健, 彭静. 应用扩展卡尔曼滤波算法的船舶运动模型参数辨识[J]. 上海海事大学学报, 2008, 29(3): 5-9.
	Zhao Daming, Shi Chaojian, Peng Jing. Parameter Identification to Motion Model of Ship by Extended Kalman Filter[J]. Journal of Shanghai Maritime University, 2008, 29(3): 5-9.
6	Perera Lokukaluge P, Oliveira P, Guedes Soares C. System Identification of Nonlinear Vessel Steering[J]. Journal of Offshore Mechanics and Arctic Engineering, 2015, 137(3): 031302.
7	Guan Wei, Peng Haowen, Zhang Xianku, et al. Ship Steering Adaptive CGS Control Based on EKF Identification Method[J]. Journal of Marine Science and Engineering, 2022, 10(2): 294.
8	Dong Zaopeng, Yang Xin, Zheng Mao, et al. Parameter Identification of Unmanned Marine Vehicle Manoeuvring Model Based on Extended Kalman Filter and Support Vector Machine[J]. International Journal of Advanced Robotic Systems, 2019, 16(1): 1729881418825095.
9	Zheng Jian, Yan Ming, Li Yun, et al. An Online Identification Approach for a Nonlinear Ship Motion Model Based on a Receding Horizon[J]. Transactions of the Institute of Measurement and Control, 2021, 43(13): 3000-3012.
10	Zeng Daohui, Xia Guihua, Cai Chengtao. Parameter Identification of Hydrodynamic Model of Ship Using EKF[C]//2021 China Automation Congress (CAC). Piscataway: IEEE, 2021: 1427-1432.
11	Wang Tongtong, Li Guoyuan, Wu Baiheng, et al. Parameter Identification of Ship Manoeuvring Model Under Disturbance Using Support Vector Machine Method[J]. Ships and Offshore Structures, 2021, 16(S1): 13-21.
12	Luo Weilin, Guedes Soares C, Zou Zaojian. Parameter Identification of Ship Maneuvering Model Based on Support Vector Machines and Particle Swarm Optimization[J]. Journal of Offshore Mechanics and Arctic Engineering, 2016, 138(3): 031101.
13	Wang Ning, Meng Joo Er, Han Min. Large Tanker Motion Model Identification Using Generalized Ellipsoidal Basis Function-based Fuzzy Neural Networks[J]. IEEE Transactions on Cybernetics, 2015, 45(12): 2732-2743.
14	任俊生. 船舶运动与控制[M]. 大连: 大连海事大学出版社, 2021.
15	Wang Sisi, Wang Lijun, Im Namkyun, et al. Real-time Parameter Identification of Ship Maneuvering Response Model Based on Nonlinear Gaussian Filter[J]. Ocean Engineering, 2022, 247: 110471.

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