﻿ 基于克隆选择优化的多船转向避碰决策
 舰船科学技术  2018, Vol. 40 Issue (1): 52-56 PDF

Composite evaluation of ship collision risk index based on fuzzy theory
XU Wen, HU Jiang-qiang, YIN Jian-chuan, LI Ke
Navigation College, Dalian Maritime University, Dalian 116026, China
Abstract: In this paper, a calculation method of optimal course alteration for collision avoidance based on the model of ship collision risk index is proposed by clone selection algorithm in multi-ship encounter situation. Membership functions of five main factors such as distance of closest point of approach (DCPA), time to the closest point of approach (TCPA), distance between ships, relative bearing and speed ratio are determined in the consideration of correction to navigational surroundings, visibility and maneuverability etc. The multi-objective function optimization based on the collision risk index and loss of voyage has completely achieved the optimal solution within the feasible region constrained in the International Regulations for Preventing Collisions at sea by means of clone selection algorithm. The results prove the validity and efficiency of composite evaluation.
Key words: clone selection algorithm     multi-ship encounter     course alteration for collision avoidance     fitness function
0 引　言

1 船舶碰撞危险度计算模型

 $u = \{ d,\theta ,K,{t_{{\rm{CPA}}}},{d_{{\rm{CPA}}}}\}{\text{。}}$ (1)

 \left\{ \begin{aligned}& A = {w_d},{w_\theta },{w_k},{w_{{d_{{\rm{CPA}}}}}},{w_{{t_{{\rm{CPA}}}}}},\\& {w_d} > 0,{w_\theta } > 0,{w_k} > 0,{w_{{d_{{\rm{CPA}}}}}} > 0,{w_{{t_{{\rm{CPA}}}}}} > 0,\\& {w_d} + {w_\theta } + {w_k} + {w_{{d_{{\rm{CPA}}}}}} + {w_{{t_{{\rm{CPA}}}}}} = 1{\text{。}}\end{aligned} \right. (2)

 ${B} = \left[ {\begin{array}{*{20}{c}}{{r_d}}\\{{r_\theta }}\\{{r_{{d_{{\rm{CPA}}}}}}}\\{{r_{{t_{{\rm{CPA}}}}}}}\end{array}} \right]{\text{。}}$ (3)

 $u(d) = \left\{ \begin{array}{l}\begin{array}{*{20}{c}}1, & {} & {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{} & {} & {} & {}\end{array}} & {} & {d \leqslant {d_1}},\end{array}}\end{array}\\{[({d_2} - d)/({d_2} - {d_1})]^2}, \;\;\;\;{d_1} < d \leqslant {d_{\rm{2}}}, \\\begin{array}{*{20}{c}}0, & {} & {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{} & {} & {} & {}\end{array}} & {} & {d > {d_2}}{\text{。}}\end{array}}\end{array}\end{array} \right.$ (4)

d1d2的大小取决于航行区域的状况、能见度以及人为因素的影响。动界是以驾驶员开始采取行动以避免紧迫局面时与他船的距离为基础的超级领域。英国学者Davis等通过大量的调查统计得到了动界模型的具体数据，在进行平滑其边界后，得到了一个半径为2.7 n mile的圆的数学模型。令其区域半径为R，可以得到其表达式：

 ${d_1} = {K_1} \cdot {K_2} \cdot {K_3} \cdot {D_{{L}}},$ (5)
 ${d_2} = {K_1} \cdot {K_2} \cdot {K_3} \cdot R,$ (6)
 $R = 1.7\cos (\theta - {19^\circ }) + \sqrt {4.4 + 2.89{{\cos }^2}(\theta - {{19}^\circ })}{\text{。}}$ (7)

 u(\theta ) = \left\{ \begin{aligned}& \frac{1}{{1 + {{(\theta /{\theta _0})}^2}}},\;\;\;\;\;\;\;\;0 \leqslant \theta < {180^\circ }, \\& \frac{1}{{{{(\frac{{{{360}^\circ } - \theta }}{{{\theta _0}}})}^2}}},\;\;\;\;\;\;\;\;{180^\circ } \leqslant \theta < {360^\circ }{\text{。}}\end{aligned} \right. (8)
 ${\theta _0} = \left\{ \begin{array}{l}\begin{array}{*{20}{c}}{{{40}^\circ }}, & {K < 1},\end{array}\\\begin{array}{*{20}{c}}{{{90}^\circ }}, & {K = 1},\end{array}\\\begin{array}{*{20}{c}}{{{180}^\circ }}, & {K > 1}{\text{。}}\end{array}\end{array} \right.$ (9)

 $u(K) = \frac{1}{{1 + \frac{W}{{K\sqrt {{K^2} + 1 + 2K\sin C} }}}}{\text{。}}$ (10)

DCPA小于船舶安全会遇距离时，船舶存在碰撞危险，该值越小，碰撞危险程度越大。任意时刻DCPA的隶属度函数[21]

 $u({d_{{\rm{CPA}}}}) \!=\!\! \left\{\!\!\!\!\!\! {\begin{array}{*{20}{c}}1\\{\displaystyle\frac{1}{2} \!-\! \displaystyle\frac{1}{2}\sin \left[ {\displaystyle\frac{{\rm{\pi }}}{{{d_{{\rm{CP}}{{\rm{A}}_0}}} \!-\! \lambda }}\left( {{d_{{\rm{CPA}}}} \!-\! \displaystyle\frac{{{d_{{\rm{CP}}{{\rm{A}}_0}}} \!+\! \lambda }}{2}} \right)} \right]}{\text{。}}\\ 0 \end{array}} \right.\!\!\!\!$ (11)

 domain{\rm{ = }}\left\{ {\begin{aligned}& {0.85 - \frac{{{\theta _t}}}{{{{180}^\circ }}} \times 0.2},\\& {1.8 - \frac{{{\theta _t}}}{{{{180}^\circ }}} \times 0.73},\\& {1.02 - \frac{{{{360}^\circ } - {\theta _t}}}{{{{180}^\circ }}} \times 0.57},\\& {{\rm{0}}{\rm{.85}} - \frac{{{{360}^\circ } - {\theta _t}}}{{{{180}^\circ }}} \times 0.3},\end{aligned}} \right. (12)
 $FBD = 0.267{D_S}{\text{。}}$ (13)

1）当能见度不良时， ${d_{{\rm{CP}}{{\rm{A}}_0}}}$ 应该增大来扩大危险预报范围；在复杂水域航行时，航行水域受限， ${d_{{\rm{CP}}{{\rm{A}}_0}}}$ 应该减小。这里取为：

 ${d_{{\rm{CP}}{{\rm{A}}_0}}}{\rm{ = }}\left\{ {\begin{array}{*{20}{c}}{{K_1} \cdot {K_2} \cdot {K_3} \cdot \left( {{D_S}{\rm{ - }}FBD} \right)},\\{{K_1} \cdot {K_2} \cdot {K_3} \cdot \left( {1{\rm{ - }}0.276} \right){D_S}}{\text{。}}\end{array}} \right.$ (14)

2） $\lambda = {K_4} \cdot {d_{{\rm{CP}}{{\rm{A}}_0}}}$ ，其中系数K4由船舶状态的不稳定性、避碰不协调性和设备的误差决定，一般情况下K4=2， $\lambda = 2{d_{{\rm{CP}}{{\rm{A}}_0}}}$

TCPA值大小与碰撞危险度的关系与DCPA类似，任意时刻TCPA的隶属度函数：

 u({t_{{\rm{CPA}}}}) = \left\{ {\begin{aligned}& 1, & {} & {{t_{{\rm{CPA}}}} < {t_1}},\\& {\frac{{{t_2} - {t_{{\rm{CPA}}}}}}{{{t_2} - {t_1}}}}, & {} & {{t_1} < {t_{{\rm{CPA}}}} \leqslant {t_2}}, \\& 0, & {} & {{t_{{\rm{CPA}}}} > {t_2}}{\text{。}}\end{aligned}} \right. (15)
 ${t_1} = \frac{{\sqrt {\left( {d_1^2 - {\lambda ^2}} \right)} }}{{{v_s}}},\;{t_2} = \frac{{\sqrt {\left( {d_{\rm{m}}^2 - d_{{\rm{CP}}{{\rm{A}}_0}}^2} \right)} }}{{{v_s}}}{\text{。}}$ (16)

 \begin{aligned}& CRI = {A} \cdot {B} = \\& \left[ {\begin{array}{*{20}{c}}{{w_d}}\!\!\!\!\! & \!\!\!\!\!\!\!{\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{{w_\theta }} \! & \! {{w_k}}\end{array}} \!\!\! & \!\!\! {{w_{{d_{{\rm{CPA}}}}}}}\end{array}} \!\!\! & \!\!\! {{w_{{t_{{\rm{CPA}}}}}}}\end{array}}\end{array}} \right] \left[ {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{{r_d}}\\{{r_\theta }}\end{array}}\\{{r_k}}\end{array}}\\{{r_{{d_{{\rm{CPA}}}}}}}\end{array}}\\{{r_{{t_{{\rm{CPA}}}}}}}\end{array}} \right]{\text{。}} \end{aligned} (17)

 $CRI \!=\! {w_d}{u_d} \!+\! {w_\theta }{u_\theta } \!+\! {w_k}{u_k} \!+\! {w_{{d_{{\rm{CPA}}}}}}{u_{{d_{{\rm{CPA}}}}}} \!+\! {w_{{t_{{\rm{CPA}}}}}}{u_{{t_{{\rm{CPA}}}}}}{\text{。}}$ (18)

2 转向避碰多目标函数模型

2.1 碰撞危险度目标函数

 ${f_1}({x_i}) = \mathop {\max }\limits_{i = 1}^N {f_i}({u_{{d_i}}},{u_{{\theta _i}}},{u_{{K_i}}},{u_{{d_{CP{A_i}}}}},{u_{{t_{CP{A_i}}}}}){\text{。}}$ (19)

2.2 航程损失目标函数

 ${f_2}({x_i}) = \frac{1}{{60}} \times ({x_i} - 30)(90 - {x_i}){\text{。}}$ (20)

 $f = \sum\limits_{i = 1}^N {\left\{ {1{\rm{ - }}\left[ {0.8{f_1}({x_i}){\rm{ + 0}}{\rm{.2}}{f_2}({x_i})} \right]} \right\}}{\text{。}}$ (21)
3 基于分级变异动态克隆选择优化的船舶转向避碰决策 3.1 克隆选择算法基本原理

3.2 分级变异动态克隆选择算法

$\forall ab \in A{b_{\left\{ m \right\}}}(g)$ $\forall ab \in a{b_{\left\{ m \right\}}}(g)$ 的变异概率分别为 ${P_{m1}}$ ${P_{m2}}$ ，尺度变换因子分别为η1η2，分级变异操作的思想是让高亲和度抗体有较小的搜索空间，搜索局部最优解，而低亲和度抗体有较大的搜索空间，进行全局最优解的粗搜索和避免陷入局部最优。当平均适应值变化很小时，种群也可能时陷入了局部最优需要调整变异参数。

4 转向避碰幅度仿真和结果分析 4.1 仿真实例

4.2 结果分析

 图 1 最优解迭代变化 Fig. 1 Optimal evolution for iteration

5 结　语

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