﻿ 多种群综合学习粒子群算法在动力定位能力分析中的应用
 舰船科学技术  2018, Vol. 40 Issue (6): 61-66 PDF

Application of multi-swarm comprehensive learning particle swarm optimizer in dynamic positioning capability analysis
ZHANG Lian-wei, CHEN Hong-wei
School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: The calculation of ship dynamic positioning (DP) capability is a process of solving nonlinear multi-modal problems, and the comprehensive learning particle swarm optimization (CLPSO) is a suitable algorithm for this kind problems. The paper presents the multi-swarm comprehensive learning particle swarm optimization (MCLPSO) for convergence of the original CLPSO is relatively slow at the late stage of evolution. Then the proposed optimization is used to calculate the DP capability for one DP system case. The results calculated by MCLPSO meet well with Kongsberg’s report, and are much better than the results calculated by CLPSO.
Key words: DP capability     nonlinear optimization     multi-swarm     CLPSO
0 引　言

1 环境载荷的计算

 $\left\{ \begin{array}{l} {F_{wdx}}(\alpha ) = {C_{wdx}}(\alpha )V_{wd}^2, \\[5pt] {F_{wdy}}(\alpha ) = {C_{wdy}}(\alpha )V_{wd}^2, \\[5pt] {M_{wd}}(\alpha ) = {C_{wdM}}(\alpha )V_{wd}^2{\text{。}} \end{array} \right.$ (1)

 $\left\{ \begin{array}{l} {F_{cx}}(\alpha ) = {C_{cx}}(\alpha )V_c^2, \\[5pt] {F_{cy}}(\alpha ) = {C_{cy}}(\alpha )V_c^2, \\[5pt] {M_c}(\alpha ) = {C_{cM}}(\alpha )V_c^2{\text{。}} \end{array} \right.$ (2)

 $\left\{ \begin{array}{l} {F_{wvx}}(\alpha ) = \int_0^\infty {S(\omega ){C_{wvx}}(\omega ){\rm d}\omega }, \\[5pt] {F_{wvy}}(\alpha ) = \int_0^\infty {S(\omega ){C_{wvy}}(\omega ){\rm d}\omega }, \\[5pt] {M_{wv}}(\alpha ) = \int_0^\infty {S(\omega ){C_{wvM}}(\omega ){\rm d}\omega } {\text{。}}\end{array} \right.$ (3)

2 动力定位系统定位能力

 $\left\{ {\begin{array}{*{20}{l}} {\min g(T) = \sum\limits_{i = 1}^{num} {{T_i}} }, \\ {s.t. } \\ {\sum\limits_{i = 1}^{num} {{T_i}} \cos ({\theta _i}) = {F_{wdx}} + {F_{cx}} + {F_{wvx}} }, \\ {\sum\limits_{i = 1}^{num} {{T_i}} \sin ({\theta _i}) = {F_{wdy}} + {F_{cy}} + {F_{wvy}}}, \\ {\sum\limits_{i = 1}^{num} {{T_i}} ({x_i}\sin ({\theta _i}) - {y_i}\cos ({\theta _i})) = {M_{wd}} + {M_c} + {M_{wv}}} {\text{。}}\end{array}} \right.$ (4)

 $\begin{split} &\min {\text{ G}}(T) = \sum\limits_{i = 1}^{num} {{T_i}} {\text{ + }} \\& {\lambda _1}(\sum\limits_{i = 1}^{num} {{T_i}} \cos ({\theta _i}) - {F_{wdx}} - {F_{cx}} - {F_{wvx}})+ \\ &{\lambda _2}(\sum\limits_{i = 1}^{num} {{T_i}} \sin ({\theta _i}) - {F_{wdy}} - {F_{cy}} - {F_{wvy}}) + \\& {\lambda _3}(\sum\limits_{i = 1}^{num} {{T_i}} ({x_i}\sin ({\theta _i}) - {y_i}\cos ({\theta _i})) - {M_{wd}} - {M_c} - {M_{wv}})\text{。} \end{split}$ (5)

 图 1 动力定位能力计算流程图 Fig. 1 Flow chart of DP capability calculation
3 多种群综合学习粒子群算法 3.1 综合学习粒子群算法

 $\left\{ \begin{array}{l} V_{jd}^{t + 1} = \omega V_{jd}^t + cr_{jd}^t(pb_{{f_j}(d)}^t - X_{jd}^t), \\ V_{jd}^{t + 1}{\text{ = }}\min ({V_{jd\max }},\max ({V_{jd\min }},V_{jd}^{t + 1})), \\ X_{jd}^{t + 1} = X_{jd}^t + V_{jd}^{t + 1}, \\ X_{jd}^{t + 1}{\text{ = }}\min ({X_{jd\max }},\max ({X_{jd\min }},X_{jd}^{t + 1})){\text{。}} \\ \end{array} \right.$ (6)

${f_j}(d)$ 的确定方法：对于粒子j的每一维，都生成一个随机概率，若这个随机概率大于学习概率 $P{c_j}$ ，则该粒子的这一维向其自身个体最优值的对应维学习；反之，则从群体中随机选出2个粒子，学习它们中较好的那个个体最优值。为了保证种群的多态性，CLPSO还设置了一个更新间隔代数m，即当粒子j的个体最优值 $p{b_j}$ 连续m代未得到更新，则重新生成 ${f_j}(d)$

3.2 多种群综合学习粒子群算法

 图 2 多种群综合学习粒子群算法计算结构 Fig. 2 MCLPSO computing framework

MCLPSO算法主要步骤如下：

 $\left\{\!\!\!\! \begin{array}{l} V_{jd}^{t + 1} = \omega V_{jd}^t + {c_1}r_{1jd}^t(pb_{{f_j}(d)}^t - X_{id}^t) + {c_2}r_{2jd}^t(pg_d^t - X_{jd}^t), \\ V_{id}^{t + 1}{\text{ = }}\min ({V_{id\max }},\max ({V_{id\min }},V_{id}^{t + 1})), \\ X_{jd}^{t + 1} = X_{jd}^t + V_{jd}^{t + 1}, \\ X_{jd}^{t + 1}{\text{ = }}\min ({X_{jd\max }},\max ({X_{jd\min }},X_{jd}^{t + 1})) {\text{。}}\end{array} \right.$ (7)

 $X_{jd}^t = X_{jd}^t + randn({X_{jd\max }} - {X_{jd\min }})(G - g)/G\text{。}$ (8)

 图 3 多种群综合学习粒子群算法流程 Fig. 3 MCLPSO flow chart
4 实例仿真与分析

4.1 船舶相关参数

 图 4 坐标系及推进器布置 Fig. 4 Coordinate system and thrusters’ configuration

4.2 定位能力计算及结果分析

 图 5 模式1—所有推进器正常 Fig. 5 Case 1 - All thrusters normal

 图 6 模式2—推进器2失效 Fig. 6 Case 2 – Thruster 2 failure

 图 7 模式3—推进器4失效 Fig. 7 Case 3 – Thruster 4 failure
5 结　语

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