一种用于船舶操纵运动快速建模的混合经验法

doi:10.16182/j.issn1004731x.joss.23-FZ0793

摘要/Abstract

摘要：

仿真测试是验证智能船舶各项功能的重要手段，船舶操纵运动建模与仿真是实现复杂海域下多船智能避碰的关键理论基础。针对现阶段船舶操纵运动建模所需的水动力系数计算复杂且难以获取的问题，提出一种混合经验法，建立了现有回归公式的组合方法，构建了综合性能指标，通过仿真操纵试验对水动力系数组选优，并基于MATLAB研发了快速建模程序代码。结果表明：该方法能够在有限的船型参数下实现高效、便捷、自动化地生成给定船舶的操纵性运动模型，对智能船舶的仿真测试验证具有重要的工程实践意义。

关键词: 智能船舶, 仿真测试, 船舶运动建模, 快速仿真, 混和经验法

Abstract:

Simulation testing is an important means to verify the functions of intelligent ships. Ship maneuvering motion modeling and simulation is the key theoretical basis for the intelligent collision avoidance of multiple vessels in complex sea areas. To address the problem that the calculation of the hydrodynamic coefficients required for ship maneuvering modeling is complex and difficult to obtain, a hybrid empirical method is proposed, a combination method of the existing regression methods is established, the comprehensive performance indicators are constructed, the optimal hydrodynamic coefficients groups are selected by simulated maneuvering experiments, and a rapid modeling program code is developed based on MATLAB. The results show that, under limited ship parameters the proposed method can efficiently, conveniently, and automatically generate the maneuvering motion model of a given ship. The method is of important engineering practical significance for the simulation testing and verification of intelligent ships.

Key words: intelligent ships, simulation testing, ship motion modeling, rapid simulation, hybrid empirical method

中图分类号:

TP391.9

吴鹏,杨宗默,景乾峰等 . 一种用于船舶操纵运动快速建模的混合经验法[J]. 系统仿真学报, 2023, 35(10): 2150-2160.

Wu Peng,Yang Zongmo,Jing Qianfeng,et al . A Hybrid Empirical Method for Fast Modeling of Ship Manoeuvring Motion[J]. Journal of System Simulation, 2023, 35(10): 2150-2160.

图/表 16

图1

表1

船舶基本参数

基础参数	含义	基础参数	含义
$Δ / t$	排水量	$C b$	方型系数
$L P P$ /m	垂线间长	$C p$	菱形系数
$L O A$ $/ m$	全长	$C w$	水线面系数
$B M$ $/ m$	型宽	$D P$ /m	桨直径
$D M$ $/ m$	型深	$H R$ $/ m$	舵高
$d A$ $/ m$	艉吃水	$A R$ /m²	舵叶面积
$d F$ / m	艏吃水

表1

表2

常用系数定义

符号	计算方法
$d M$	$d M = (d A + d F) / 2$
$τ$	$τ = (d A - d F) / d M$
$λ H$	$λ H = 2 d M / L P P$
$l β$	$l β = λ H / 0.5 π λ + 1.4 C b B L P P$
$C p a$	$C p a = ∇ A / (A X L P P / 2)$
$C w a$	$C w a = A W A / (B L P P / 2)$
$e a$	$e a = (L P P / B) (1 - C p a)$
$e a'$	$e a' = e a / 0.25 + 1 / B d M 2$
$σ a$	$σ a = (1 - C w a) / (1 - C p a)$
$k β$	$k β = 1 e a' + 1.5 B L P P - 0.33 0.95 σ a + 0.4$

表2

表3

桨舵水动力系数

系数	文献出处	系数	文献出处
$w P 0$	[8-11]	$a H$	[9, 14, 20]
$κ R$	[12-15]	$l R$	[9, 14-15]
$t P 0$	[5, 8-11]	$z R, z P$	[22]
$x H$	[14, 16-19]	$ε R$	[9, 23-24]
$γ R$	[9, 14, 20-21]	$t R$	[9, 20, 25]

表3

表4

非线性系数(i = 1)

序号	水动力系数模型
1^[26]	$F H, N L 1 = X v v v 2 + X v r v r + X r r r 2 + X v v v v v 4$
2^[27]	同上
3^[9]	$F H, N L 1 = X β r r s i n β$
4^[18]	$F H, N L 1 = X v v v 2 + X v r v r + X r r r 2$
5^[28]	$F H, N L 1 = (a x 2 ⋅ s i n 2 β + a x 4 ⋅ s i n 2 (2 β)) ⋅ c o s β + b x 1 ⋅ r s i n β + b x 2 ⋅ r s i n (2 β) + s i g n (c o s β)$

表4

表5

线性系数(i = 2， 6)

序号	水动力系数模型
1^[29], 2^[9], 3^[30], 4^[17], 5^[15]	$F H, L 2 = Y β β + Y r r F H, L 6 = N β β - N r r$
6^[31], 7^[32], 8^[33], 9^[18], 10^[34]	$F H, L 2 = Y v v + Y r r F H, L 6 = N v v + N r r$

表5

表6

非线性系数（i = 2， 6）

序号	水动力系数模型
1^[35], 2^[36], 3^[18]	$F H, N L 2 = Y v v v 2 + Y v r v r + Y r r r 2 F H, N L 6 = N r r r 2 + N v r r v r 2 + N v v r v 2 r$
4^[7], 5^[9], 6^[30], 7^[17]	$F H, N L 2 = Y β β \| β \| β + Y β r \| β \| r + Y r r \| r \| r F H, N L 6 = N r r r r + N β r r β r 2 + N β β r β 2 r$
8^[28]	$F H, N L 2 = (a y 1 + c y 1 ⋅ r 2) s i n β + a y 3 × s i n 3 β + a y 5 × s i n 5 β + (d y 1 × r + e y 1 × r 3) c o s β F H, N L 6 = (a n 2 + c n 2 × r 2) s i n 2 β + a n 4 × s i n 4 β + d n 0 × r + e n 0 × r 3 + d n 2 ⋅ r ⋅ c o s 2 β$

表6

表7

常用操纵性指标

操纵性指标	指标含义
$A D (± δ, n)$	左/右旋回进距
$T R (± δ, n)$	左/右旋回横距
$T D (± δ, n)$	左/右旋回初径
$O S A 1 s t (± δ / δ, n)$	第一超越角
$O S A 2 n d (± δ / δ, n)$	第二超越角
$v (n)$	船舶设计航速

表7

表8

散货船基本参数

基础参数	数值	基础参数	数值
$Δ / t$	34 757	$C b$	0.790 6
$L P P$ /m	160.4	$C p$	0.798 7
$L O A$ $/ m$	169.37	$C w$	0.884 7
$B M$ $/ m$	27.2	$D P$ /m	5.25
$D M$ $/ m$	13.6	$H R$ $/ m$	7.29
$d A$ $/ m$	10.5	$A R$ /m²	26.4
$d F$ / m	9.82

表8

表9

水动力系数组

组号	$F H, N L 1$	$F H, L 2,6, F H, L 6$	$F H, N L 2,6, F H, N L 6$
1	No.5		No.8
2	No.1	No.10	No.4
3	No.1	No.5	No.1
4	No.1	No.8	No.2
5	No.1	No.1	No.5
6	No.1	No.6	No.7
7	No.1	No.3	No.6

表9

图2

图3

图4

图5

图6

表10

水动力系数组误差

指标	e₁	e₂	e₃	e₄	e₅	e₆	e₇	实船
$E R M S, i$	28.658	15.569	27.612	22.083	Nan	11.926	3.234	\
A_D(+35°, 122)	0.235	0.175	0.185	0.113	0.541	0.078	0.078	468 m
T_R(+35°, 122)	0.520	0.196	0.790	0.669	0.737	0.206	0.206	244 m
T_D(+35°, 122)	0.373	0.071	0.492	0.336	1.053	0.083	0.083	536 m
A_D(-35°, 122)	0.284	0.134	0.230	0.158	0.525	0.136	0.102	483 m
T_R(-35°, 122)	0.583	0.261	0.832	0.723	0.629	0.295	0.008	253 m
T_D (-35°, 122)	0.489	0.049	0.551	0.418	Nan	0.233	0.096	590 m
A_D(+35°, 90)	0.187	0.056	0.131	0.056	0.607	0.014	0.100	458 m
T_R(+35°, 90)	0.516	0.410	0.784	0.660	0.783	0.173	0.296	244 m
T_D(+35°, 90)	0.351	0.010	0.471	0.305	1.150	0.028	0.260	517 m
$A D - 35 °, 90$ A_D (–35°, 90)	0.219	0.033	0.161	0.085	0.597	0.052	0.034	465 m
T_R( $-$ 35°, 90)	0.580	0.479	0.821	0.710	0.623	0.271	0.112	262 m
T_D( $-$ 35°, 90)	0.349	0.083	0.432	0.255	Nan	0.003	0.255	472 m
OSA_1st(+20°/20°)	2.124	1.272	2.078	1.668	0.076	0.869	0.166	8.2°
OSA_2nd(+20°/20°)	1.406	0.904	2.350	1.661	0.146	0.856	0.087	7.7°
OSA_1st( $-$ 20°/20°)	2.153	1.486	2.442	1.956	0.016	1.061	0.066	7.8°
OSA_2nd( $-$ 20°/20°)	1.023	0.870	2.389	1.614	0.198	0.650	0.218	8.4°
OSA_1st(+10°/10°)	5.508	2.396	2.743	2.552	0.903	2.206	0.028	2.7°
OSA_2nd(+10°/10°)	4.268	2.706	4.154	3.405	0.277	1.773	0.351	4.3°
OSA_1st(-10°/10°)	3.000	1.589	1.887	1.727	0.394	1.408	0.273	3.9°
OSA_2nd(-10°/10°)	4.489	2.390	3.689	3.013	0.182	1.528	0.417	4.4°

表10

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