A Hybrid Empirical Method for Fast Modeling of Ship Manoeuvring Motion

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

Abstract

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

CLC Number:

TP391.9

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

Figures/Tables 16

Fig. 1

Table 1

Basic ship parameters

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

Table 1

Table 2

Commonly used coefficients definitions

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

Table 2

Table 3

Coefficients of propeller and rudder

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]

Table 3

Table 4

Nonlinear coefficients (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]	$F H, N L 1 = (a x 2 ⋅ s i n 2 β + a x 4 ⋅ s i n 2 (2 β)) ⋅ c o s β + b x 1 ⋅ r s i n β + b x 2 ⋅ r s i n (2 β) + s i g n (c o s β)$

Table 4

Table 5

Linear coefficients (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]	$F H, L 2 = Y v v + Y r r F H, L 6 = N v v + N r r$

Table 5

Table 6

Nonlinear coefficients (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]	$F H, N L 2 = (a y 1 + c y 1 ⋅ r 2) s i n β + a y 3 × s i n 3 β + a y 5 × s i n 5 β + (d y 1 × r + e y 1 × r 3) c o s β F H, N L 6 = (a n 2 + c n 2 × r 2) s i n 2 β + a n 4 × s i n 4 β + d n 0 × r + e n 0 × r 3 + d n 2 ⋅ r ⋅ c o s 2 β$

Table 6

Table 7

Commonly used maneuverability indices

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

Table 7

Table 8

Basic parameters of bulk carrier

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

Table 8

Table 9

Hydrodynamic coefficients groups

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

Table 9

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Table 10

Hydrodynamic coefficients groups

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°

Table 10

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