﻿ 浮式钻井天车型升沉补偿系统摇摆装置设计方案优选
 舰船科学技术  2020, Vol. 42 Issue (1): 101-104 PDF

1. 集美大学 轮机工程学院，福建 厦门 361021;
2. 福建省船舶与海洋工程重点实验室，福建 厦门 361021

A optimal selection method of the design projects of swing devices in crown-block heave compensation system for offshore drilling
XIONG Yun-feng1,2, CHEN Zhang-lan1,2, LI Zong-min1,2
1. School of Marine Engineering, Jimei University, Xiamen 361021, China;
2. Fujian Provincial Key Laboratory for Naval Architecture and Ocean Engineering, Xiamen 361021, China
Abstract: In order to solve the optimal selection problem of the design projects of swing devices in crown-block heave compensation system for offshore drilling, the optimal selection method of the design projects of swing devices in crown-block heave compensation system for offshore drilling was studied by integrating analytic hierarchy process, variation coefficient method, grey relational analysis and TOPSIS. The subjective weights of evaluation indexes was figured out by AHP and the objective weights of evaluation indexes was figured out by variation coefficient method. Then the synthetical weights model was established based on relative entropy theory. Furthermore, the optimal selection method of the design projects of swing devices in crown-block heave compensation system for offshore drilling was established based on relative entropy weighted-grey TOPSIS. The method is easy to use and can solve the optimal selection problem of the design projects of swing devices in crown-block heave compensation system for offshore drilling.
Key words: swing devices     crown-block heave compensation system     design scheme optimization     relative entropy weighed     grey TOPSIS
0 引　言

1 优选思路

 图 1 浮式钻井钻柱升沉补偿系统设计方案优选思路 Fig. 1 Optimal process of the design scheme of heave compensation system for floating drilling string
2 优选方法 2.1 建立优选矩阵

 ${ A} = {[{a_{ij}}]_{m \times n}}\text{。}$ (1)

2.2 计算相对熵综合权重

1）层次分析法（AHP）是主观赋权法中的一种代表性方法，故本文运用层次分析法[4]来确定指标的主观权重 $\alpha = {({\alpha _j})_{n \times 1}}$

2）变异系数法是确定客观赋权法中的一种常用方法，故本文应用变异系数法[5-6]来确定指标的客观权重 $\beta = ({\beta _j})$ ${\beta _j}$ 的具体计算公式为：

 ${\beta _j} = \frac{{{\sigma _j}/{\delta _j}}}{{\displaystyle\sum\limits_{j = 1}^n {{\sigma _j}/{\delta _j}} }}\text{，}$ (2)

3）若主客观权重的综合权重向量为 $\omega = ({\omega _j})$ ，则根据相对熵原理，可建立与 $\alpha$ $\beta$ 都尽可能接近的优化模型[7-8]

 $\left\{ \begin{array}{l} \min D =\displaystyle \sum\limits_{j = 1}^n {\left({\omega _j}\ln \dfrac{{{\omega _j}}}{{{\alpha _j}}}\right) + \displaystyle\sum\limits_{j = 1}^n {\left({\omega _j}\ln \dfrac{{{\omega _j}}}{{{\beta _j}}}\right)} }\text{，} \\ \displaystyle\sum\limits_{j = 1}^n {{\omega _j} = 1;{\omega _j} > 0} \text{。} \end{array} \right.$ (3)

 ${\omega _j} = \frac{{\sqrt {{\alpha _j}{\beta _j}} }}{{\displaystyle\sum\limits_{j = 1}^n {\sqrt {{\alpha _j}{\beta _j}} } }}\text{。}$ (4)
2.3 优选矩阵规范化

 ${ B} = {[{b_{ij}}]_{m \times n}}\text{。}$ (5)

2.4 建立加权规范化优选矩阵

 $C = {[{c_{ij}}]_{m \times n}}\text{。}$ (6)

2.5 构建加权灰色TOPSIS综合分析模型

1）确定正理想解和负理想解

 ${D^ + } = \left(\mathop {\max }\limits_{1 \leqslant i \leqslant m,j \in {C^ + }} {c_{ij}},\mathop {\min }\limits_{1 \leqslant i \leqslant m,j \in {C^ - }} {c_{ij}}\right) = (d_j^ + )\text{，}$ (7)
 ${D^ - } = \left(\mathop {\min }\limits_{1 \leqslant i \leqslant m,j \in {C^ + }} {c_{ij}},\mathop {\max }\limits_{1 \leqslant i \leqslant m,j \in {C^ - }} {c_{ij}}\right) = (d_j^ - )\text{，}$ (8)

2）计算正关联度和负关联度

$i$ 个评价方案的正负理想解的灰色关联度（简称为正关联度 $f_i^ +$ 和负关联度 $f_i^ -$ [9-11]计算式如下：

 $f_i^ + = \frac{1}{n}\sum\limits_{j = 1}^n {e_{ij}^ + }\text{，}$ (9)
 $f_i^ - = \frac{1}{n}\sum\limits_{j = 1}^n {e_{ij}^ - }\text{。}$ (10)

3）计算正距离和负距离

$i$ 个评价对象分别与正理想解和负理想解的欧氏距离（简称为正距离 $g_i^ +$ 和负距离 $g_i^ -$ [911]计算式如下：

 $g_i^ + = \sqrt {\sum\limits_{j = 1}^n {{{[{c_{ij}} - d_j^ + ]}^2}} }\text{，}$ (11)
 $g_i^ - = \sqrt {\sum\limits_{j = 1}^n {{{[{c_{ij}} - d_j^ - ]}^2}} }\text{。}$ (12)

4）计算相对贴近度

 ${z_i} = \frac{{[\lambda x_i^ + + (1 - \lambda )y_i^ - ]}}{{[\lambda x_i^ + + (1 - \lambda )y_i^ - ] + [\lambda x_i^ - + (1 - \lambda )y_i^ + ]}}\text{。}$ (13)

2.6 优选结论

3 案例分析 3.1 建立优选矩阵

 $A = {[{a_{ij}}]_{4 \times 6}} = \left[\!\! {\begin{array}{*{20}{c}} {4.95}&{1.32}&{5.15}&{1.94}&{1.04}&{4.50} \\ {2.50}&{1.08}&{2.90}&{1.82}&{1.19}&{3.39} \\ {2.80}&{1.12}&{3.18}&{1.78}&{1.16}&{4.52} \\ {3.25}&{1.28}&{2.77}&{1.98}&{1.17}&{3.28} \end{array}}\!\! \right]\text{。}$
3.2 计算综合权重

 $\begin{split} & \alpha = (0.094\;2,0.526,0.094\;2,0.052\;6,0.555\;9,0.150\;5)\text{，}\\ & \beta = (0.316\;7,0.095\;8,0.310\;6,0.049\;5,0.058\;1,0.169\;3)\text{，}\\ & \omega = (0.214\;5,0.088\;2,0.212\;5,0.063\;4,0.223\;2,0.198\;3)\text{。} \end{split}$
3.3 建立加权规范化优选矩阵

 $\begin{split} & B = \!{[{b_{ij}}]_{4 \times 6}} \\ & =\! \left[ \!\!\! \!\! {\begin{array}{*{20}{c}} {0.2145} \!\!&\!\! {0.088\;2}\!\!&\!\!{0.212\;5}\!\!&\!\!{0.050\;7}\!\!&\!\!{0.000\;0}\!\!&\!\!{0.195\;1} \\ {0.000\;0}\!\!&\!\!{0.000\;0}\!\!&\!\!{0.011\;6}\!\!&\!\!{0.012\;7}\!\!&\!\!{0.223\;2}\!\!&\!\!{0.017\;6} \\ {0.026\;3}\!\!&\!\!{0.014\;7}\!\!&\!\!{0.036\;6}\!\!&\!\!{0.000\;0}\!\!&\!\!{0.178\;6}\!\!&\!\!{0.198\;3} \\ {0.065\;7}\!\!&\!\!{0.075\;3}\!\!&\!\!{0.000\;0}\!\!&\!\!{0.063\;4}\!\!&\!\!{0.193\;5}\!\!&\!\!{0.000\;0} \end{array}} \!\! \!\! \right]{\text{。}} \end{split}$
3.4 计算相对贴近度及优选结果

1）由于6个评价指标均为成本性指标，因此，根据式（7）和式（8），正负理想解分别为 ${D^ + } = (0,0,0,0,0,0)$ ${D^ - } = (0.214\;5,0.088\;2,0.212\;5,0.063\;4,0.223\;2,0.198\;3)$

2）按式（9）～式（13）可求得正负关联度、正负距离及相对贴近度，计算结果如表1所示。

3）根据表1的数据，4个浮式钻井钻柱天车型升沉补偿系统摇摆装置设计方案的优劣排序为：方案2>方案4>方案2>方案1，即方案2为最优方案。

4 结　语

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