﻿ 基于模糊层次分析的海上发射船性能优化
 舰船科学技术  2023, Vol. 45 Issue (12): 20-26    DOI: 10.3404/j.issn.1672-7619.2023.12.004 PDF

1. 烟台哈尔滨工程大学研究院，山东 烟台 264000;
2. 中集海洋工程研究院有限公司，山东 烟台 264670;
3. 山东海洋集团有限公司，山东 济南250102

Performance optimization of offshore launch ship based on fuzzy analytic hierarchy process
YANG Xiao-jie1, WANG Bao-lai1, LIU Da-hui2, ZHANG Chi1, SHI Lai-qiang3
1. Yantai Research Institute of Harbin Engineering University, Yantai 264000, China;
2. CIMC Offshore Engineering Research Institute, Yantai 264670, China;
3. Shandong Marine Group Ltd, Jinan 250102, China
Abstract: Aiming at the imperfection of the performance optimization system of offshore launch ship, the bending moment model of rocket erection is established. Taking the square coefficient, Captain and ship width as the optimization variables, the performance optimization model of offshore launch ship based on fuzzy analytic hierarchy process is designed.Firstly, starting from the factors affecting the performance of launch ship, the evaluation indexes of rocket bearing bending moment, launch ship stability, resistance and cost are proposed. Then, the weight of each performance index is determined through the judgment matrix, and each index is analyzed and calculated separately. Finally, the comprehensive scores of the mother ship and 96 sample points are calculated. Compared with the mother ship, the bending moment of the optimized ship is increased by 19.87%, the stability is improved by 2.99%, the resistance is increased by 23.19%, and the cost is reduced by 8.35%. The research of this subject plays an important guiding role in the optimization of the performance of offshore launch ship.
Key words: sea launch     moment model     fuzzy analytic hierarchy process     performance optimization
0 引　言

1 性能优化基本原理 1.1 模糊数学基础理论

1.1.1 隶属函数的定义

 ${{{V}}}\left({{{u}}}\right)\to {{U}} \to \left[\mathrm{0,1}\right]，$ (1)

1.1.2 隶属函数的确定

1）模糊统计法

2）德尔菲法

3）对比排序法

1.2 模糊层次分析法 1.2.1 层次分析法概述

1）衡量两两重要程度的判断矩阵以1~9为衡量标度可能过于精准，不符合人为判断的模糊性，因此计算结果可能不够精准。

2）对于非一致判断矩阵的修正较为复杂，并且有可能违背了实际情况。

1.2.2 模糊层次分析法

1）构建层次结构

 图 1 递阶结构示意图 Fig. 1 Schematic diagram of hierarchical structure

2）构建两两模糊判断矩阵

3）判断矩阵的一致性检验

 $a_{ij}=\frac{a_{ik}}{a_{jk}}\quad i,j={1,2},{3,4}\cdots {{{n}}}。$ (2)

 $CI=\frac{{{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}-n}{n-1} 。$ (3)

$RI$ $RI$ 比较得到一致性比率 $CR$ ，当 $CR＜$ 0.1时，则判断矩阵的一致性标准可以接受，如不满足，需要对判断矩阵进行调整，直到满足一致性标准。

4）依据判断矩阵计算各因素的权重

 ${\boldsymbol{A}}=\left(\begin{array}{cccc}{\mathit{a}}_{11}& {\mathit{a}}_{12}& \cdots & {\mathit{a}}_{1\mathit{n}}\\ {\mathit{a}}_{21}& {\mathit{a}}_{22}& \cdots & {\mathit{a}}_{2\mathit{n}}\\ \cdots & \cdots & \ddots & \cdots \\ {\mathit{a}}_{\mathit{n}1}& {\mathit{a}}_{\mathit{n}2}& \cdots & {\mathit{a}}_{\mathit{n}\mathit{n}}\end{array}\right)，$ (4)

 ${\boldsymbol{A}}M={\lambda }_{{\rm{max}}}{\boldsymbol{A}} 。$ (5)
2 基于模糊层次分析的海上发射船性能优化 2.1 评价体系建立

1）火箭的弯矩

2）发射船稳性

3）发射船阻力

4）发射船造价

2.2 评价指标计算

 图 2 母型船模型 Fig. 2 Mother ship model

1）火箭弯矩的计算

 图 3 火箭模型图 Fig. 3 Rocket model

 图 4 火箭微元受力分析图 Fig. 4 Force analysis diagram of micro element of rocket
 $S = {\theta z\sin\lambda t} ，$ (6)
 $a = \ddot S = {{\theta z}}{{\text{λ }}^{\text{2}}}\sin {\text{λ t}} ,$ (7)
 $f(x,t) = m(z)a = m(z)\ddot S = m(z){\theta z}{{\text{λ }}^{\text{2}}}\sin {\lambda t} 。$ (8)

 $N + \dot Ndz - N + m\ddot ydz - Fdz + c\dot y = 0 ，$ (9)

 $\dot N{\rm{d}}z + m\ddot ydz - F{\rm{d}}z + c\dot y = 0 ,$ (10)

 ${\varepsilon } = {{y}} \cdot {\ddot y},$ (11)
 ${\text{σ }} = {{E\varepsilon }} + {{\text{c}}_{\text{s}}}{{\dot \varepsilon }},$ (12)

 $M = \int\limits_A {\sigma y{\rm{d}}A},$ (13)

 $\begin{split} {My_\theta } =& {\lambda ^2}\theta \sin \lambda t\int_0^{L} m (z) \cdot {z^2}{\rm{d}}z + \\ & \dfrac{\eta }{{{{m}_\eta }}}\int_0^L f (z) \cdot m(z){\rm{d}}z\int_0^L f (z) \cdot {z^2} \cdot m(z){\rm{d}}z ，\end{split}$ (14)
 $M{y_L} = (g + \ddot z)\sin \alpha \int_0^{{L}} {\rm{m}} ({\rm{z}}) \cdot {{\rm{z}}^2}{\rm{d}}z,$ (15)
 $M = M{y_\theta } + M{y_L},$ (16)
 $\sin \alpha = \frac{{\theta \int_0^L f (z) \cdot z \cdot m(z){\rm{d}}z}}{{{L}}} \cdot \frac{\eta }{{{{\rm{m}}_\eta }}},$ (17)
 $\eta = \dfrac{{{{\left( {\dfrac{\lambda }{{\rm{p}}}} \right)}^2}}}{{\sqrt {{{\left( {1 - \dfrac{{{\lambda ^2}}}{{{{\rm{p}}^2}}}} \right)}^2} + 4\varphi {{\left( {\dfrac{\lambda }{{\rm{p}}}} \right)}^2 }} }} ，$ (18)
 ${m_{\text{η }}} = \int_0^L {{f^2}(z)} \cdot m(z){{{\rm{d}}}}z 。$ (19)

 $M = 2278322.838 \cdot {\theta_{}} + 103495.6558 \cdot {\theta_{}} \cdot \ddot {{z}}。$ (20)

2）稳性的计算

3）阻力的计算

Maxsurf的Hullspeed模块计算粘性阻力时采用ITTC-57计算，航速取为12 kn，粘性阻力计算公式如下：

 ${R}_{v}={C}_{F}\left(1+k\right)\frac{1}{2}\rho {v}^{2}S。$ (21)

4）造价的估算

2.3 计算结果归一化

 $x_{ij}^{*}=\left|\frac{{x}_{ij}-\mathrm{min}x}{\mathrm{max}x-\mathrm{min}x}\right|，$ (22)

 ${x}_{ij}^* = \frac{{x}_{ij}}{{\mathop{{\rm {max}}x}\nolimits }}{或}x_{ij}^* = \frac{{{\mathop{{\rm {min}}x}\nolimits} }}{{\rm{{\rm{x}}}}_{ij}}。$ (23)

2.4 建立判断矩阵

 ${\boldsymbol{A}}=\left[\begin{array}{cccc}1& 3/2& 2& 3\\ 2/3& 1& 6/5& 4/3\\ 1/ 2& 5/6& 1& 11/10\\ 1/3& 3/4& 10/11& 1\end{array}\right]。$
2.5 计算各样本点综合评分

3 结　语

1）相比于母型船，火箭承受弯矩的评分提高了19.87%，稳性评分提高了2.99%，阻力评分提高了23.19%，造价评分降低了8.35%。造价提高9.13%，验证了该模型在火箭发射船性能优化方面的适用性，为海上发射船性能优化提供了一种研究思路。

2）计算结果表明，为了保证火箭发射的安全，应采用较大的方形系数以减少火箭承受的弯矩。长细比对阻力影响很大，应采用较大的长细比以减少航行阻力。

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