﻿ 粗糙集与包络分析下舰船运行数据聚类算法
 舰船科学技术  2022, Vol. 44 Issue (20): 149-152    DOI: 10.3404/j.issn.1672-7649.2022.20.030 PDF

1. 华北电力大学，北京 102206;
2. 鄂尔多斯应用技术学院，内蒙古 鄂尔多斯 017000;
3. 湖南工程学院，湖南 湘潭 411101

Clustering algorithm of ship operation data based on rough set and envelope analysis
LI Yue-jie1,2, LI Shi-jun3
1. North China Electric Power University, Beijing 102206, China;
2. Ordos Institute of Technology, Inner Mongolia, Ordos 017000, China;
3. Hunan Institute of Engineering, Xiangtan 411101, China
Abstract: The working status and performance parameters of the main engine, generator, auxiliary engine and other equipment of the power system in the engine room of the ship are constantly changing during the operation process. In order to improve the reliability of ship operation and enable the engine management personnel to monitor the operating status of key equipment in the engine room in real time in the centralized control room, it is necessary to configure a reasonable engine room operation data acquisition system and improve the data processing capacity of the engine room data acquisition system. Rough set theory and envelope analysis theory are two commonly used data analysis theories. This paper introduces the principles of rough set theory and envelope analysis in detail, and performs cluster analysis on the data of the ship engine room operation data acquisition system to improve the efficiency of data processing.
Key words: rough set     envelope analysis     clustering     engine room     data analysis
0 引　言

1 粗糙集理论

1）知识表达系统

2）决策表

 $S{\text{ = }}\left( {U,V,f} \right),U = C \cap D \text{，}$

 图 1 粗糙集理论的决策表原理图 Fig. 1 Schematic diagram of decision table of rough set theory

3）分辨矩阵和分辨函数

 ${m_{ij}} = \left\{ {\begin{array}{*{20}{l}} {{a_i} \in C,\quad {a_i}\left( {{x_i}} \right) \ne {a_k}\left( {{x_j}} \right)}，\\ {\phi ,\quad U\left( {{x_i}} \right) = U\left( {{x_j}} \right)\quad i,j = 1,2, \ldots ,n} 。\end{array}} \right.$

4）粗糙集的约简

 $core\left( C \right) = \left( {{a_i} \in D:mij = \left( {{a_k}} \right),1 \leqslant j \leqslant i \leqslant n} \right) 。$

5）粗糙集理论的流程

 图 2 粗糙集理论进行数据预处理的流程图 Fig. 2 Flow chart of data preprocessing based on rough set theory
2 数据包络分析理论

 $\left\{ {\begin{array}{*{20}{l}} {{X_j} = \left( {{x_1},{x_{2j}}, \cdots ,{x_{mj}}} \right)} ，\\ {{Y_j} = \left( {{y_{1j}},{y_{2j,}}, \cdots ,{y_{kj}}} \right)}，\\ {j = 1,2, \cdots ,n} 。\end{array}} \right. \text{}$

$\left( {{X_i},{Y_i}} \right)$ 集合的包络分析表示为：

 $T = \left\{ {(X,Y)\mid \sum\limits_{j = 1}^n {{x_j}} ,\sum\limits_{j = 1}^n {{y_j}} ,j = 1, \cdots ,n} \right\} \text{。}$

${C^2}R$ 模型是数据包络分析的基础模型，构建 ${C^2}R$ 模型：

 $\left( {{C^2}R} \right) = \left\{ {\begin{array}{*{20}{l}} {\min \theta } \\ {\displaystyle\sum\limits_{j = 1}^m {{X_j}} {\lambda _j} \leqslant \theta {X_{jn}},} \\ {\displaystyle\sum\limits_{j = 1}^j {{Y_j}} {\lambda _j} \geqslant {Y_{jn}},} \\ {{\lambda _j} \geqslant 0,j = 1, \cdots ,n} \end{array}} \right. \text{，}$

 图 3 数据包络性 ${C^2}R$ 模型示意图 Fig. 3 Schematic diagram of data envelopment ${C^2}R$ model
3 基于粗糙集与包络分析的舰船机舱运行数据聚类分析 3.1 舰船机舱运行数据采集系统

 图 4 船舶机舱数据采集系统原理图 Fig. 4 Principle diagram of data acquisition system for ship energy consumption

1）传感器

2）CAN总线

3）RS232接口

RS-232C标准协议是一种数据终端设备和通讯设备之间的二进制接口标准，最早由美国电子工业协会联合开发，RS-232C标准协议规定了0~20 kb/s传输速率的通信信号。在RS232接口中，电平介于−3~3 V时信号无效，当传输电平的绝对值大于3 V时可以视为有效电平。

4）机舱主控终端：机舱主控终端使用C#编写程序，接收传感器采集的数据并将数据进行分析，在分析后对数据进行显示，并绘制相关曲线。

3.2 基于粗糙集与包络分析的舰船机舱运行数据聚类分析

1）获取数采系统的振动信号为：

 ${X_0} = \left( {{x_0}\left( 1 \right),{x_0}\left( 2 \right),...,{x_0}\left( n \right)} \right) \text{，}$

 ${X_i} = \left( {{x_i}\left( 1 \right),{x_i}\left( 2 \right),...,{x_i}\left( n \right)} \right)\;\;i = 1,2,...,n 。$

2）进行数据的无量纲处理分别得到：

 ${X_0}* = \left( {{x_0}\left( 1 \right)*,{x_0}\left( 2 \right)*,...,{x_0}\left( n \right)*} \right) \text{，}$
 ${X_i}* = \left( {{x_i}\left( 1 \right)*,{x_i}\left( 2 \right)*,...,{x_i}\left( n \right)*} \right)\;\;i = 1,2,...,n \text{。}$

3）建立振动信号数据的粗糙集分辨函数如下：

 $\gamma \left( {X_0^*(k),X_i^*(k)} \right) = \frac{{m + \rho M}}{{{\Delta _i}(k) + \rho M}} \text{。}$

 ${\Delta _i}(k) = X_0^*(k) - X_i^*(k) 。$

4）结合分辨函数建立振动信号的包络性 ${C^2}R$ 模型： $\gamma \left( {{C^2}R} \right) = \left\{ \begin{array}{l} \min \theta ，\\ \displaystyle \frac{1}{n}\sum\limits_{i = 1}^n {} \gamma \left( {X_0^*(k),X_i^*(k)} \right) \\\end{array} \right.$

5）结合包络模型，得到舰船振动信号的数据聚类分析结果。

 图 5 发电机输出端不动信号的聚类分析结果 Fig. 5 Results of cluster analysis of stationary signal at generator output
4 结　语

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