﻿ 基于遗传混沌粒子群混合算法的船舶动力定位推力分配研究
 舰船科学技术  2018, Vol. 40 Issue (12): 99-103 PDF

Research on thrust allocation of ship dynamic positioning based on genetic chaos particle swarm optimization algorithm
LI Xin-xiang, WANG Xi-huai, XIAO Jian-mei
Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China
Abstract: To solve the problem of a class of nonlinear constrained thrust distribution in ship dynamic positioning system, a hybrid algorithm based on particle swarm algorithm and crossover and mutation strategy in chaotic theory and genetic algorithm is proposed. To establish the multivariate nonlinear constrained optimization problem, by the minimum propulsion system energy consumption as the goal, including propulsion power consumption, wear and tear, thrust error, avoid singular structure, etc; by the propeller thrust, the azimuth Angle scope of work and change rate as constraint . The simulation results show that the proposed algorithm can solve the optimization problem, and can improve the energy consumption and maneuverability of the ship propulsion system, improve the performance of the ship dynamic positioning system effectively.
Key words: dynamic positioning     thrust distribution     particle swarm optimization     genetic algorithm     singular structure     propulsion system
0 引　言

1 船舶动力定位数学模型

1.1 船舶运动学

 $\dot \eta = {{R}}(\psi ){{v}},$ (1)

 ${{R}}(\psi ) = \left[ \begin{gathered} \cos \psi \quad - \sin \psi \quad {\rm{ 0}} \\ \sin \psi \quad\ \cos\psi \quad\ {\rm{0}} \\ {{ \ 0 \quad\quad\ \ 0 \quad \quad \ 1}} \\ \end{gathered} \right]{\text{。}}$ (2)
1.2 船舶动力学

 ${{M}}\dot v + {{Dv}} = {{\tau }} + {{{R}}^{\rm T}}(\psi ){{b}}{\text{。}}$ (3)

2 推力分配问题

2.1 推力分配数学描述

 图 1 动力定位系统的推力分配原理图 Fig. 1 Schematic diagram of thrust allocation in power system
 ${\bf{\tau }} = {{B}}(\alpha )U{\text{。}}$ (4)

 ${{B}}\left( {\bf{\alpha }} \right) \!\!=\!\! \left[\!\!\! {\begin{array}{*{20}{c}} {\cos \,({\alpha _1})\,\;}& \!\!\!\!\!\!\cdots \!\!\!\!\!\!&{\cos ({\alpha _i})\,} \\ {\sin ({\alpha _1})}& \!\!\!\!\!\!\cdots\!\!\!\!\!\! &{\sin ({\alpha _i})} \\ {lx1\sin ({\alpha _1}) - ly1\cos ({\alpha _1})}& \!\!\!\!\!\!\cdots\!\!\!\!\!\! &{lxi\sin ({\alpha _i}) - lyi\cos ({\alpha _i})} \end{array}} \!\!\!\right],$

2.2 推力分配的目标函数及约束条件

 $\left\{ \begin{gathered} U{\rm min} \leqslant U \leqslant U{\rm max}, \hfill \\ \Delta U{\rm min} \leqslant U - U_0 \leqslant \Delta U{\rm max}, \hfill \\ \alpha {\rm min} \leqslant \alpha \leqslant \alpha {\rm max}, \hfill \\ \Delta \alpha {\rm min} \leqslant \alpha - \alpha_0 \leqslant \Delta \alpha {\rm max}{\text{。}} \hfill \\ \end{gathered} \right.$ (5)

 $\begin{split} \min J(\alpha ,U,s) = P\mathop \Sigma \limits_{i = 1}^m {\left| U \right|^{\tfrac{3}{2}}} + {s^{\rm T}}{ Q}s + \\ {(\alpha - \alpha 0)^{\rm T}}{\varOmega} (\alpha - \alpha 0) + \frac{\delta }{{\varepsilon + \det [B(\alpha ){B^{\rm T}}(\alpha )]}}{\text{。}}\end{split}$ (6)

3 遗传混沌粒子群混合算法 3.1 粒子群优化算法及其缺陷

 $\begin{gathered} {\upsilon _{id}}(t + 1) = \omega {\upsilon _{id}}(t) + {c_1}{r_1}({p_{id}}(t) - {x_{id}}(t))+ \hfill \\ \;\quad \quad \quad \quad {c_2}{r_2}({p_{gd}}(t) - {x_{id}}(t)) , \hfill \\ \end{gathered}$ (7)
 ${x_{id}}(t + 1) = {x_{id}}(t) + {\upsilon _{id}}(t){\text{。}}$ (8)

3.2 混沌优化算子

 ${z_{k + 1}} = \mu {z_k}(1 - {z_k}){\text{。}}$ (9)

3.3 遗传交叉和变异策略

3.3.1 交叉操作

3.3.2 变异操作

 $Pm = \left\{ \begin{gathered} \frac{{k_1({f_{\max }} - f')}}{{{f_{\max }} - {f_{avg}}}},\quad f' \geqslant {f_{avg}}, \hfill \\ k_2, \quad \quad \quad\quad \quad \;f' < favg{\text{。}} \hfill \\ \end{gathered} \right.$ (10)

3.4 遗传混沌粒子群混合算法步骤

1）种群初始化：确定种群数N，随机初始化粒子的位置与速度，并限定粒子的位置与速度范围；计算种群适应度值，并初始化种群的全局最优与个体最优。

2）对全局最优粒子的进行混沌化，利用Logistic映射，生成混沌化后的种群，并更新种群的全局最优与个体最优。

3）利用式（7）和式（8）对粒子进行位置和速度更新。

4）更新个体与全局最优：若当前粒子的适应度值优于个体最优，则用当前粒子位置替换个体最优; 若当前种群粒子的适应度值优于全局最优，则用当前粒子位置替换全局最优。

5）交叉操作：随机产生一个数 $r_1$ ，若 $r_1 < {P_c}$ ，执行交叉操作。得到的子代粒子与父代粒子进行适应值比较,适应值较高的那部分粒子进入下一代。

6）变异操作：随机产生一个数 $r_2$ ，并根据式（10）计算 ${P_m}$ ，若 $r_2 < {P_m}$ ，执行变异操作。

7）计算适应度值并更新个体与全局最优。

8）判断是否满足停止条件：如最大迭代数或者问题所需精度，如果满足则输出最优搜索结果，否则返回步骤3。

4 船舶动力定位推力分配仿真计算

 图 2 船舶动力定位运动响应 Fig. 2 Ship dynamic positioning motion response

 图 3 推进器推力及方位角变化 Fig. 3 Thrust and azimuth curve of propeller

 图 4 控制器推力指令与分配后实际推力指令 Fig. 4 Comparison of resultant force and moment before and after the allocation
5 结　语

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