﻿ 舰船轴系设计状态评估方法研究
 舰船科学技术  2023, Vol. 45 Issue (1): 141-146    DOI: 10.3404/j.issn.1672-7649.2023.01.025 PDF

Research on evaluation method of marine shaft system design state
FANG Shi-yu, LIU Jin-lin, GU Zheng, ZHANG Rong-guo
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: In order to solve the evaluation standard problem of each scheme in shafting design stage and improve the cost-efficiency ratio of marine shaft system life cycle, based on the analysis of the status quo of state evaluation methods, the construction method of evaluation index system of shafting scheme and the calculation method of index weight were given, and the fuzzy comprehensive evaluation method of shafting design state was put forward. The evaluation index system of shafting design status was established based on two schemes of a shafting. The subjective and objective weights of the indexes were determined by triangular fuzzy analytic hierarchy process and entropy weight method, and the comprehensive weights of each evaluation index were determined by addition integration method. The fuzzy comprehensive evaluation method was used to comprehensively evaluate the two schemes. The excellent and good rates of scheme 1 and Scheme 2 are 0.5150 and 0.7156, and the poor grade rates are 0.0865 and 0.0413. The research results can provide new theoretical support for improving the design quality of marine shaft system.
Key words: ship shafting     design state     triangular fuzzy analytic hierarchy process     entropy method     fuzzy comprehensive evaluation method
0 引　言

1 评价指标体系的构建 1.1 评价指标体系构建方法

 图 1 评价指标体系构建原则图 Fig. 1 The principle diagram of evaluation index system construction
1.2 设计状态下轴系评价指标体系的构建

 图 2 轴系设计状态评价指标体系图 Fig. 2 Shafting design state evaluation index system diagram
2 指标权重计算方法

2.1 主观法——三角模糊层次分析法

1）三角模糊判断矩阵构造

 ${b}_{ij}=\frac{1}{P}\otimes ({b}_{ij}^{1}+{b}_{ij}^{2}+\cdots +{b}_{ij}^{p})\text{，}p=(1,2,\cdots P)。$ (1)

2）评价因子矩阵的构造以及判断矩阵的调整

 \begin{aligned}[b] & {{E = (}}{{\text{e}}_{ij}}) =\\ & \left( {\begin{array}{*{20}{c}} 1&{1 - \dfrac{{{c_{12}} - {a_{12}}}}{{2{b_{12}}}}}& \cdots &{1 - \dfrac{{{c_{1n}} - {a_{1n}}}}{{2{b_{1n}}}}} \\ {1 - \dfrac{{{c_{21}} - {a_{21}}}}{{2{b_{2n}}}}}&1& \cdots &{1 - \dfrac{{{c_{2n}} - {a_{2n}}}}{{2{b_{2n}}}}} \\ \vdots & \vdots & \ddots & \vdots \\ {1 - \dfrac{{{c_{n1}} - {a_{n1}}}}{{2{b_{n1}}}}}&{1 - \dfrac{{{c_{n2}} - {a_{n2}}}}{{2{b_{n2}}}}}& \cdots &1 \end{array}} \right) 。\end{aligned} (2)

 ${\boldsymbol{Q}} = \left( {\begin{array}{*{20}{c}} 1&{{b_{12}}}& \cdots &{{b_{1n}}} \\ {{b_{21}}}&1& \cdots &{{b_{2n}}} \\ \vdots & \vdots & \ddots & \vdots \\ {{b_{n1}}}&{{b_{n2}}}& \cdots &1 \end{array}} \right) \times E 。$ (3)

${\boldsymbol{Q}}$ 矩阵进一步按列调整获得判断矩阵 ${\boldsymbol{P}}$ ，使之满足主对角线元素全为1，且 ${p_{ij}} = \dfrac{1}{{{p_{ji}}}}$

3）判断矩阵的一致化处理

 ${r_{ij}} = \sqrt[n]{{\prod\limits_{k = 1}^n {{p_{ik}} \cdot {p_{kj}}} }}。$ (4)

4）指标权重的计算

 ${w_i} = \frac{{{c_i}}}{{\displaystyle\sum\limits_{k = 1}^n {{c_k}} }}(i = 1,2, \cdots n) 。$ (5)

2.2 客观法——熵权法

1） 针对评价体系中的 $m$ 个方案， $n$ 个评价指标，构建原始矩阵

 ${\boldsymbol{X}} = {\left( {\begin{array}{*{20}{c}} {{x_{11}}}&{{x_{12}}}& \cdots &{{x_{1n}}} \\ {{x_{21}}}&{{x_{22}}}& \cdots &{{x_{2n}}} \\ \vdots & \vdots & \vdots & \vdots \\ {{x_{m1}}}&{{x_{m2}}}& \cdots &{{x_{mn}}} \end{array}} \right)_{m \times n}} 。$ (6)

2） 计算各指标下每个方案的比重

 ${t}_{ij}=\frac{{x}_{ij}}{{\displaystyle \sum _{i=1}^{m}{x}_{ij}}}（i=1,2\cdots ,mj=1,2,\cdots ,n）。$ (7)

3） 计算各指标的信息熵

 ${s_j} = - k \cdot \sum\limits_{i = 1}^m {{t_{ij}} \cdot \ln {t_{ij}}}，$ (8)

4） 确定各指标的熵权

 ${w_j} = \frac{{1 - {s_j}}}{{\displaystyle\sum\limits_{j = 1}^n {(1 - {s_j})} }} 。$ (9)
2.3 综合权重法

1）“乘法”集成法

 ${w_i} = {a_i}{b_i}/\sum\limits_{i = 1}^n {{a_i}{b_i}}。$ (10)

2）“加法”集成法

 ${w_i} = \alpha {a_i} + (1 - \alpha ){b_i}。$ (11)
3 模糊综合评价法

1）根据所构建的评价体系确定评价对象的评价指标因素集

 $U = \left\{ {\begin{array}{*{20}{c}} {{u_1}}&{{u_2}}& \cdots &{{u_m}} \end{array}} \right\}，$ (12)

2）划分指标评价等级，构建评语集

 $V = \left\{ {\begin{array}{*{20}{c}} {{v_1}}&{{v_2}}& \cdots &{{v_l}} \end{array}} \right\} 。$ (13)

3）确定各指标因素对评语集的隶属度，建立模糊评价矩阵

 ${\boldsymbol{R}} = \left( {\begin{array}{*{20}{c}} {{r_{11}}}&{{r_{12}}}& \cdots &{{r_{1l}}} \\ {{r_{21}}}&{{r_{22}}}& \cdots &{{r_{2l}}} \\ \vdots & \vdots & \ddots & \vdots \\ {{r_{m1}}}&{{r_{m2}}}& \cdots &{{r_{ml}}} \end{array}} \right)。$ (14)

4）确定各评价因素的权重，构建权重集

 ${\boldsymbol{W }}= \left\{ {\begin{array}{*{20}{c}} {{w_1}}&{{w_2}}& \cdots &{{w_m}} \end{array}} \right\}。$ (15)

5）构建模糊综合评价模型

 \begin{aligned} & {\boldsymbol{B}}={\boldsymbol{W}}·{\boldsymbol{R}}=\left(\begin{array}{cccc}{w}_{1}& {w}_{2}& \cdots & {w}_{m}\end{array}\right)\times \\ & \left(\begin{array}{cccc}{r}_{11}& {r}_{12}& \cdots & {r}_{1l}\\ {r}_{21}& {r}_{22}& \cdots & {r}_{2l}\\ ⋮& ⋮& \ddots & ⋮\\ {r}_{m1}& {r}_{m2}& \cdots & {r}_{ml}\end{array}\right)=\left(\begin{array}{cccc}{b}_{1}& {b}_{2}& \cdots & {b}_{l}\end{array}\right)。\end{aligned} (16)
4 算　例

 图 3 轴系方案设计简图 Fig. 3 Shafting scheme design diagram
4.1 主观权重的确定

 \begin{aligned} {W}_{主观}=& \Big[0.0126 \;\; 0.2046 \;\; 0.0293 \;\; 0.1095\;\; 0.0577\;\; \\ & 0.0965\;\; 0.1633 \;\; 0.1497 \;\; 0.1769\Big]。\end{aligned}
4.2 客观权重的确定 4.2.1 模糊指标的定量分析

4.2.2 定量指标的计算

1）重量指标

2）校中特性指标

 $Y=\delta {X}_{后尾}+(1-\delta ){X}_{差值}$ (17)

 图 4 轴系总体垂向图 Fig. 4 Overall vertical deformation of shafting system

3）振动特性指标

 $x={\delta }_{1}{x}_{后}+{\delta }_{2}{x}_{前}+{\delta }_{3}{x}_{推}。$ (18)

2种方案的一阶纵向模态如图5所示。

 图 5 轴系一阶纵向模态图 Fig. 5 First order longitudinal modal diagram of shafting system

 \begin{aligned}[b] {W}_{客观}= & \Big[0.0882 \;\; 0.0496 \;\; 0.1272 \;\; 0.0650 \;\; 0.0882 \;\; \\ & 0.1272 \;\; 0.1272 \;\; 0.2624 \;\; 0.0650 \Big]。\end{aligned}
4.3 综合权重的确定

 ${W}_{综合}=\alpha {W}_{主观}+(1-\alpha ){W}_{客观}，$
 \begin{aligned}[b] {W}_{综合}= & \Big[ 0.03528 \;\; 0.1581 \;\; 0.05867 \;\; 0.09615 \;\; 0.06685 \;\; \\ & 0.10571 \;\; 0.15247 \;\; 0.18351 \;\; 0.14326\Big]。\end{aligned}
4.4 综合评价

 ${{\boldsymbol{R}}_1} = \left( {\begin{array}{*{20}{c}} {0.2}&{0.3}&{0.4}&{0.1} \\ {0.3}&{0.2}&{0.4}&{0.1} \\ {0.2}&{0.3}&{0.5}&0 \\ {0.3}&{0.3}&{0.3}&{0.1} \\ {0.1}&{0.2}&{0.5}&{0.2} \\ {0.1}&{0.2}&{0.6}&{0.1} \\ {0.2}&{0.4}&{0.3}&{0.1} \\ {0.1}&{0.3}&{0.5}&{0.1} \\ {0.5}&{0.3}&{0.2}&0 \end{array}} \right) ，{{\boldsymbol{R}}_2} = \left( {\begin{array}{*{20}{c}} {0.1}&{0.3}&{0.6}&0 \\ {0.6}&{0.4}&0&0 \\ {0.1}&{0.4}&{0.4}&{0.1} \\ {0.2}&{0.4}&{0.3}&{0.1} \\ {0.2}&{0.5}&{0.3}&0 \\ {0.1}&{0.3}&{0.5}&{0.1} \\ {0.1}&{0.5}&{0.3}&{0.1} \\ {0.3}&{0.5}&{0.2}&0 \\ {0.5}&{0.4}&{0.1}&0 \end{array}} \right)。$

 ${B_1} = \left[ {\begin{array}{*{20}{c}} {0.2328}&{0.2822}&{0.3985}&{0.0865} \end{array}} \right]，$
 ${B_2} = \left[ {\begin{array}{*{20}{c}} {0.2894}&{0.4262}&{0.2432}&{0.0413} \end{array}} \right]。$

5 结　语

1）本文分析船舶及动力装置状态评估国内外研究现状，研究舰船轴系设计状态评价指标体系构建原则及方法，建立了轴系在方案设计阶段的评价指标体系；

2）结合轴系设计的特点，提出基于综合权重法的轴系设计指标评价方法，研究三角模糊层次分析法和熵权法的算法实现，以计算轴系设计评价指标的主客观权重，在基础上研究采用“加法”集成法计算指标的综合权重；

3）以某轴系2种设计方案为实例，采用上述方法进行设计方案综合评价，通过计算得到：方案1的优良率为0.5150，差等级率为0.0865；方案2的优良率为0.7156，差等级率为0.0413；方案2优于方案1，为该轴系设计方案评估提供理论依据。

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