﻿ 基于元胞机技术的碎冰模型构建优化方法
 舰船科学技术  2022, Vol. 44 Issue (20): 1-6    DOI: 10.3404/j.issn.1672-7649.2022.20.001 PDF

An optimization method for building a broken ice model based on cellular machine technology
ZHANG Jian, WANG Bei-yi, LI Lan-lan
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: With the exploration of polar resources and the development of Arctic shipping routes, the number of ships sailing in the polar region is increasing day by day. Broken ice should be considered in the study of ship-ice collision as a typical polar ice. However, the methods for constructing broken ice are not complete at present. Now, the theory of cellular automata created location for broken ice. Using the cell points to build a polygonal simulation model of broken ice by Voronoi diagram. The authenticity of the broken ice simulation model can be verified with MCD theory. Then the scale, probability distribution and thickness of the broken ice are optimized separately. What’s more, the optimized value will be optimized after each step of optimization and verified by MCD theory again to make the broken ice model close to the real broken ice condition. It can provide a certain reference meaning for the construction of polar ice crushing model.
Key words: cellular automata     MCD theory     voronoi diagram     crushed ice model
0 引　言

1 元胞自动机理论

1.1 元胞自动机的构成

1）元胞

2）元胞空间

3）邻居

4）演化规则

1.2 元胞自动机的分类

2 基于元胞自动机构建碎冰模型的优化设计 2.1 基于元胞自动机理论构建分布点模型

Grasshopper是一款利用程序算法生成模型的插件，基于蚂蚁规则可以在此环境中构建元胞自动机。蚂蚁规则是指蚂蚁在黑白两色的方形网格上运动，当网格为白色时，向左转90o并将该元胞变为黑色；当网格为黑色时，向右转90o并将该元胞变为白色。

 图 1 VB脚本法创建元胞自动机流程图 Fig. 1 VB script method to create a flow chart of cellular automata

VB脚本运算规则是引入字母ij代表元胞的横纵坐标，引入数字0和1代表元胞的黑白颜色。

 图 2 VB脚本法构建元胞自动机流程图 Fig. 2 Program diagram of a cellular automaton by VB script method

 图 3 VB脚本法生成元胞点模型 Fig. 3 Cellular point model created by VB script method

 图 4 优化后VB脚本法生成元胞点模型 Fig. 4 Cellular point model created by VB script method after optimized
2.2 基于泰森多边形的碎冰分布模型构建

 图 5 二维碎冰构建程序图 Fig. 5 Program chart of 2D crushed ice construction

 图 6 构建二维碎冰分步结果图 Fig. 6 Result chart of creating 2D crushed ice step by step
2.3 利用碎冰MCD理论对碎冰模型构建方法进行优化 2.3.1 碎冰MCD理论

 $D = l/\text{π}。$ (1)

 ${f_{MCD}} = \frac{{ - \beta }}{{{D_{\max }}^{ - \beta } - {D_{\min }}^{ - \beta }}}{D^{ - \beta - 1}},D \in \left[ {{D_{\min }},{D_{\max }}} \right] 。$ (2)

 图 7 不同情况MCD概率分布函数对比图 Fig. 7 Comparison chart of MCD probability distribution function in different situations

 图 8 碎冰模型MCD概率分布函数曲线图 Fig. 8 MCD probability distribution function curve of crushed ice model
2.3.2 碎冰尺度优化

 图 9 尺度优化程序图 Fig. 9 Scale optimization procedure diagram

 图 10 尺度优化前后的二维碎冰模型 Fig. 10 2D crushed ice model before and after scale optimization

 图 11 尺度优化后的碎冰模型MCD概率分布函数曲线图 Fig. 11 Curve of MCD probability distribution function of crushed ice model after scale optimization
2.3.3 碎冰概率分布优化

 图 12 范围分布优化程序图 Fig. 12 Range distribution optimization program diagram

 图 13 概率范围优化前后的二维碎冰模型 Fig. 13 2D ice model before and after optimization of probability range

 图 14 概率范围优化后MCD概率分布函数曲线对比图 Fig. 14 Comparison diagram of MCD probability distribution function curve after probability range optimization
2.3.4 碎冰厚度范围优化

 图 16 厚度优化后碎冰厚度分布图 Fig. 16 Thickness distribution map of crushed ice after thickness optimization

 图 15 厚度范围优化程序图 Fig. 15 Thickness range optimization program diagram
3 结　语

1）碎冰尺度优化。筛选剔除MCD值小于7 m和大于20 m的碎冰，可以发现碎冰模型筛除了过大和过小的碎冰后，使碎冰MCD仿真值概率曲线更加合理，碎冰数量更为集中，受碎冰面积的累计差值影响减小。

2）碎冰概率范围分布优化。将单一缩放因子优化为随机缩放范围，可以使不同的缩放因子作用在各个碎冰块，得到优化后的碎冰分布更具有随机性，碎冰面积尺寸更接近实际碎冰情况。

3）厚度优化。将单一厚度的碎冰优化为一定厚度范围的碎冰，可以使每块碎冰都具有不一样的厚度。该优化可以从三维角度随机赋予每块碎冰不同的厚度，使优化后的碎冰冰厚更接近真实冰区。

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