﻿ 基于IMONGO算法的船-机-桨参数匹配技术
 舰船科学技术  2023, Vol. 45 Issue (23): 108-114    DOI: 10.3404/j.issn.1672-7649.2023.23.019 PDF

Ship-machine-paddle matching technology based on IMONGO algorithm
ZHANG Zeng-xin, LI Chun-jin, Li Lei, MA Jun, XU Hong-rui
College of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212100, China
Abstract: In view of the fact that the traditional ship-engine-propeller parameter matching still remains in the study of mapping method, which cannot meet the requirements of ship refinement design, a new method of ship-engine-propeller parameter matching is proposed. Firstly, a multi-objective optimization model for ship-engine-propeller parameter matching is constructed based on the dynamic mathematical model of ship-engine-propeller matching; secondly, the objective function of minimizing engine fuel consumption, maximizing propulsion system efficiency and minimizing combustion emissions is adopted; then, the improved multi-objective northern hawk optimization algorithm (IMONGO) is used to calculate the ship-engine-propeller matching parameters; finally, the ranking preference technique (TOPSIS) to rank the performance of the Pareto solution set and select the top ranked matching parameter combination. Through experimental verification, the fuel consumption rate is reduced by 5.97%, the NOx emission volume ratio in engine combustion emissions is reduced by 19.49%, the carbon soot emission mass fraction is reduced by 20.1%, and the ship propulsion system efficiency is improved to 0.59. The optimized ship-machine-propeller matching parameters have great reference value for practical engineering design.
Key words: ship-machine-paddle matching     MONGO     multi-objective optimization
0 引　言

1 船-机-桨实时匹配的动态数学模型
 图 1 船-机-桨实时匹配数学模型 Fig. 1 Real-time ship-machine-paddle matching mathematical model

 ${V}_{P}={V}_{S}(1-W)，$ (1)
 $J=\frac{{V}_{P}}{\sqrt{{{V}_{P}}^{2}+{n}^{2}{D}^{2}}}。$ (2)

 ${K}_{T}=\sum _{n=1}^{39}{{C}_{n}\left(J\right)}^{{S}_{n}}{\left(\frac{P}{D}\right)}^{{t}_{n}}{\left(\frac{{A}_{E}}{{A}_{O}}\right)}^{{u}_{n}}{\left(Z\right)}^{{V}_{n}} ，$ (3)
 ${K}_{Q}=\sum _{n=1}^{47}{{C}_{n}\left(J\right)}^{{S}_{n}}{\left(\frac{P}{D}\right)}^{{t}_{n}}{\left(\frac{{A}_{E}}{{A}_{O}}\right)}^{{u}_{n}}{\left(Z\right)}^{{V}_{n}}。$ (4)

 ${T}_{P}={K}_{T}\rho {n}^{2}{D}^{4}，$ (5)
 ${M}_{P}={K}_{Q}\rho {n}^{2}{D}^{5}。$ (6)

 $\begin{split} \left(m+\Delta m\right)\frac{{\rm{d}}{V}_{S}}{{\rm{d}}t}=& {T}_{e}-{R}_{m}={T}_{e}-({R}_{V}+{R}_{W}+{R}_{B}+\\ & {R}_{tr}+{R}_{A}+{R}_{app})。\end{split}$ (7)

2 多目标北方苍鹰优化算法改进 2.1 北方苍鹰优化算法

1)识别猎物及攻击猎物（全局搜索）

 ${X}_{ij}^{new,P1}=\left\{\begin{array}{c}{X}_{ij}+r\left({P}_{ij}-I{X}_{i,j}\right),{F}_{{P}_{i}} < {F}_{i}，\\ {X}_{ij}+r\left({X}_{i,j}-{P}_{ij}\right),{F}_{{P}_{i}}\geqslant {F}_{i}。\end{array}\right.$
 ${X}_{i}=\left\{\begin{array}{c}{X}_{ij}^{new,P1},{F}_{i}^{new,P1} < {F}_{i}，\\ {X}_{i},{F}_{i}^{new,P1}\geqslant {F}_{i}。\end{array}\right.$ (8)

2)追逐及逃生（局部搜索）

 ${X}_{ij}^{new,P2}={X}_{i,j}+R(2r-1){X}_{i,j}，$
 $R=0.02\left(1-\frac{t}{T}\right),$
 ${X}_{i}=\left\{\begin{array}{c}{X}_{ij}^{new,P2},{F}_{i}^{new,P2} < {F}_{i}，\\ {X}_{i},{F}_{i}^{new,P2}\geqslant {F}_{i}。\end{array}\right.$ (9)

2.2 改进的北方苍鹰算法 2.2.1 种群初始化策略改进

NGO采用随机方式生成初始种群，生成的种群分布不均，不能保证初始种群覆盖问题的决策空间，易陷入局部最优[1-4]。因此，引入Sine混沌映射和精英反向学习策略对种群初始化方式进行改进。Sine混沌映射的公式如下：

 ${s}_{i+1}=\mu \cdot \mathrm{sin}\left(\text{π} {s}_{i}\right),i=\mathrm{1,2},\cdots ,n。$ (10)

 $X=lb+rand\cdot (ub-lb)，$ (11)
 ${X}_{s}=lb+S\cdot (ub-lb)，$ (12)
 ${X}_{t}=rand\cdot \left(ub-lb\right)-X。$ (13)

2.2.2 动态自适应因子调整策略

 $\omega ={-e}^{\frac{-t}{T}}+1。$ (14)

 \begin{aligned} & {X}_{ij}^{new,P1}=\left\{\begin{array}{c}{\omega \cdot X}_{ij}+r\left({P}_{ij}-I{X}_{i,j}\right),{F}_{{P}_{i}} < {F}_{i}，\\ \omega \cdot {X}_{ij}+r\left({X}_{i,j}-{P}_{ij}\right),{F}_{{P}_{i}}\geqslant {F}_{i}。\end{array}\right.\\ & {X}_{i}=\left\{\begin{array}{c}{X}_{ij}^{new,P1},{F}_{i}^{new,P1} < {F}_{i}，\\ {X}_{i},{F}_{i}^{new,P1}\geqslant {F}_{i}。\end{array}\right. \end{aligned} (15)
2.3 算法性能验证

3 基于改进多目标北方苍鹰优化算法的优化问题建模
 图 2 改进的多目标北方苍鹰优化算法流程图 Fig. 2 Flowchart of the improved multi-objective northern eagle optimization algorithm
3.1 设计变量

 $X=\left[Z,\frac{P}{D},\frac{{A}_{E}}{{A}_{O}},n,D,{V}_{S},\frac{{P}_{xq}}{{P}_{S}}\right] 。$ (16)
3.2 目标函数 3.2.1 推进系统效率

 $\eta ={\eta }_{a}\cdot {\eta }_{s}\cdot {\eta }_{d}\cdot {\eta }_{f}。$ (17)

 ${\eta }_{f}=\frac{1-t}{1-W} 。$ (18)

 ${\eta }_{d}=\frac{{K}_{T}\cdot J}{{K}_{Q}\cdot 2\text{π} }。$ (19)

3.2.2 经济性和排放性指标

 $\begin{split} {\rm{min}}f\left(1\right)=& -16.6{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{4}+36.3\left(\frac{{P}_{xq}}{{P}_{S}}\right)+66.4{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{2}-\\ & 144\frac{{P}_{xq}}{{P}_{S}}+264^{3}。\\[-10pt] \end{split}$ (20)

 $\begin{split} {\rm{min}}f\left(2\right)=& -2.46{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{4}+4.45\left(\frac{{P}_{xq}}{{P}_{S}}\right)+\\ & 0.739{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{2}+0.033\frac{{P}_{xq}}{{P}_{S}}+0.426^{3}。\end{split}$ (21)

 $\begin{split} {\rm{min}}{f\left(2\right)}^{*}=& -1.7{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{5}+5{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{4}-5.1{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{3}+\\ & 2.4{\left(\frac{{P}_{xq}}{{P}_{S}}\right)}^{2}+0.37\frac{{P}_{xq}}{{P}_{S}}+0.0.37。\end{split}$ (22)
3.3 约束条件

 $\begin{split} \left(m+\Delta m\right)\frac{{\rm{d}}{V}_{S}}{{\rm{d}}t}=& {T}_{e}-{R}_{m}={T}_{e}-\left({R}_{V}+{R}_{W}+{R}_{B}+\right.\\ & \left.{R}_{tr}+{R}_{A}+{R}_{app}\right) ，\end{split}$ (23)
 $2\text{π} n{M}_{P}=P\cdot {\eta }_{a}\cdot {\eta }_{s}，$ (24)
 $\frac{{A}_{E}}{{A}_{O}}\geqslant \frac{\left(1.3+0.3Z\right)T}{{P}_{O}-{P}_{V}}+K。$ (25)

 ${T}_{e}={(1-t)K}_{T}\rho {n}^{2}{D}^{4} ，$ (26)
 ${M}_{P}={K}_{Q}\rho {n}^{2}{D}^{5} 。$ (27)
3.4 基于IMONGO算法的船-机-桨实时匹配多目标优化模型

 ${\rm{min}}f\left(x\right)=\left[f\left(1\right),f\left(2\right),-\eta \right]。$ (28)
 ${\rm{s.t}}.\left\{\begin{array}{c}0.1\leqslant P/D\leqslant 1.2，\\ 0.1\leqslant {A}_{E}/{A}_{O}\leqslant 1，\\ {n}_{\rm min}\leqslant n\leqslant {n}_{\rm max}，\\ {D}_{\rm min}\leqslant D\leqslant {D}_{\rm max}，\\ {Z}_{\rm min}\leqslant Z\leqslant {Z}_{\rm max}，\\ 0\leqslant V\leqslant {V}_{\rm max}，\\ 0\leqslant {P}_{xq}/{P}_{S}\leqslant 1.2，\\ 0.10\leqslant t\leqslant 0.22，\\ 0.08\leqslant w\leqslant 0.20。\end{array}\right.$ (29)
3.5 基于TOPSIS的船-机-桨匹配参数决策

TOPSIS即“逼近于理想值的排序方法”，是一种高效先进的MCDM(多准则决策)方法[10-13]。在实际优化设计过程中，参数匹配往往只需要某几组匹配参数，因此为获得直观清晰的船-机-桨匹配参数解，以建立的燃油消耗率、燃烧物排放及系统推进效率为目标，以(minf1，minf2，max $\eta$ )作为匹配参数解性能评价指标，利用TOPSIS对IMONGO计算得到的匹配参数解集合进行多属性决策过程。

 图 3 船-机-桨匹配参数性能排名流程图 Fig. 3 Ship-engine-paddle matching parameters performance ranking flow chart
4 算例分析

 图 4 船-机-桨参数匹配优化结果Pareto图 Fig. 4 Pareto diagram of the optimization result of ship-engine-paddle parameter matching

 图 6 航速仿真结果图 Fig. 6 Speed simulation results

 图 7 发动机功率仿真结果图 Fig. 7 T Engine power simulation results graph

 图 8 螺旋桨推力仿真结果图 Fig. 8 Propeller thrust simulation results

 图 9 船舶航行阻力仿真结果图 Fig. 9 Ship sailing resistance simulation results

 图 10 氮氧化物体积比仿真结果图 Fig. 10 Nitrogen oxide volume ratio simulation results graph

 图 11 soot质量分数仿真结果图 Fig. 11 Soot mass fraction simulation results graph

5 结　语

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