2022亚太建模A题 序列图像的特征提取与建模分析 模具流量的熔融和结晶
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2022年亚太地区数学建模大赛
问题A
序列图像的特征提取与建模分析
模具流量的熔融和结晶
连铸过程中的模具通量对钢半月板进行热绝缘，防止液态钢连铸过程中液态钢再氧
化，控制传热，提供链润滑，吸收非金属夹杂物。模具通量的冶金功能主要由温度
控制曲线下的熔化速率和结晶速率决定。因此，研究模具壁与股壳间隙中模具通量
的相分布具有重要意义。
在模具的顶部加入连铸模具通剂。这些固体矿渣以粉末层的形式堆积在液态钢的表
面，可以防止由于液态钢的温度下降过高而导致的液态钢水平结皮。模具通量的温
度随后逐渐上升到熔点，模具通量被熔化形成烧结层。模具通量的原料通过化学反
应形成低熔点物质，然后形成液渣，模具通量的组成会发生一定程度的变化。这是
熔化过程。
由于模具焊剂完全熔合，将形成液渣层并覆盖在液态钢表面。当液渣从钢液表面的
渣池渗入壳体与铜模壁的间隙时，形成渣膜。由于链表面的高温，对链的矿渣仍然
保持液相。但随着液渣的温度随模具纵向表面的降低，渣膜相对于铜模壁，淬火固
化形成玻璃固体渣膜（渣膜的固化行为），经过模具的强制冷却，而渣膜在一定区
域结晶形成结晶层（渣膜结晶行为），最终形成典型的三层渣膜结构：玻璃层、结
晶层、液渣层。这个过程是结晶。
由于高温、瞬态流体流动、复杂的相变和化学反应以及模具壁的不透明度，很难直
接观察模具通量的相位变化。SHTT II的熔化和结晶温度测试仪
12
目前已广泛应用于观察模具通量的结晶行为。实验结束后，实验人员逐一对图像进
行演示，记录在图像左上角，用肉眼和经验识别关键节点图像（见图1），指导模
具通量设计，满足钢级的凝固要求。这一过程浪费了人力，阻碍了实验过程信息的
开发。发展序列图像的自动特征提取和数学建模技术是当务之急。
附件1有562张模具通量的熔化和结晶的序列图像。这些序列图像是从实验开始时的
第110秒到第671秒之间收集起来的。文件序列号遵循采集时间序列，每隔1秒采集
一次图像。该信息由附件1中的数字图像呈现（见图1）。每幅图像的左上角都标记
有图像对应的时间和No. 1热电偶和No. 2热电偶的温度值。
(a)样本
(b)样品开始融化
在110秒
(c)这个样品是完全的
在141秒熔化
(d)样品可以看到钢
在149秒熔化
(e)结晶开始于
150s
(f)结晶结束于
671s
图1模具通量熔化结晶
为了实现模通量熔化和结晶序列图像的自动特征提取和数学建模，请回答以下三个
问题。
问题1：通过图像分割和识别等技术，请自动提取每个图像左上角的No. 1热电偶和
No. 2热电偶的温度，并自动导入到相应的表中
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附件2（请逐编写技术操作文件），制作温度时间曲线图（
1线温度2线温度时间图
；1线平均温度2线平均温度时间图）。另外，1#线或2#线的测试结果不准确。请把
它指出来并解释一下。
问题2：根据图1中的6个节点图像，应用数字图像处理技术，研究并量化模通量熔
融和结晶过程中相邻序列图像之间的动态差异。在此基础上，请对量化的不同特性
进行时间序列建模，并根据数学模型的仿真结果，讨论模具通量的熔化和结晶过程
曲线。
问题3：鉴于温度和时间的变化，以及问题2的研究结果，请建立数学模型，讨论温
度与时间变化的函数关系以及模具通量的熔融结晶过程，并根据数值模拟结果讨论
模具通量的熔化结晶动力学（温度、熔化速率和结晶速率的关系）。
您的PDF解决方案总共不超过25页，应该包括：
l 一页汇总表。目录。您
l 的完整解决方案。
l
注：APMCM竞赛的页面限制版数为25页。您提交的所有方面都达到了25页的限制（
摘要表，目录，您的完整解决方案）。但是，参考文献列表和附录的页面并不受限
制。
附件：
附件1.zip，请在website：https://share.weiyun.com/ubtXPGz0上下载
附件2.xlsx
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1
Problem A
Feature Extraction of Sequence Images and Modeling Analysis of
Mold Flux Melting and Crystallization
Mold fluxes in continuous casting process thermally insulate the molten steel meniscus,
prevent reoxidation of liquid steel during continuous casting of liquid steels, control heat
transfer, provide lubrication of strand, and absorb nonmetallic inclusions. Metallurgical
functions of mold flux is mainly determined by its melting rate and crystallization rate under
the temperature control curve. It is therefore important to study the phase distribution of mold
fluxes in the gap between mold wall and strand shell.
Continuous casting mold fluxes are added to the top of liquid steel in the mold. These solid
slags, accumulating on the surface of liquid steel as a powder layer, can prevent liquid steel
level crusting due to excessive temperature drop of liquid steel. The temperature of mold fluxes
then gradually rise to the melting point, and mold fluxes are melted to form a sintered layer.
Raw materials of mold fluxes form low-melting-point substances and then liquid slag through
chemical reactions, and the composition of mold fluxes will change to a certain extent. It is
melting process.
As mold fluxes are completely fused, a liquid slag layer will be formed and covering on
the surface of liquid steel. The slag film will be formed when the liquid slag infiltrates from the
slag pool at the steel liquid surface into the gap between the shell and the copper mold wall.
The slag against the strand still maintains liquid phase, because of the high temperature of the
strand surface. However, as the temperature of liquid slag decreases with that of the strand
surface in the longitudinal direction of the mold, the slag film, against the copper mold wall, is
quenched and solidified to form a glassy solid slag film (solidification behavior of slag film),
with mold’s forced cooling, while slag film will crystallize at certain areas and form a
crystalline layer (crystallization behavior of slag film) under suitable conditions, finally
creating a typical three-layer slag film structure: glassy layer, crystalline layer and liquid slag
layer. This process is crystallization.
Because of the high temperature, transient fluid flow, complex phase transitions and
chemical reactions as well as the opacity of mold wall, it is difficult to observe the phase
changes of mold fluxes directly. The SHTT II tester of melting and crystallization temperature
2022 Asia and Pacific Mathematical Contest in Modeling2
is now widely applied to observe the crystallization behaviors of mold fluxes. After the
experiment is finished, experimenters demonstrate the images one by one, record the
information in the upper left corner of the images, and identify the key node images with naked
eyes and experience (see Figure 1), so as to guide the design of mold fluxes to meet the
solidification requirements of steel grades. This process wastes manpower and hinders the
development of experimental process information. It is urgent to develop automatic feature
extraction and mathematical modeling technology of sequence images.
Attachment 1 has 562 sequence images of mold fluxes’ melting and crystallization. These
sequence images are collected from the 110th to 671st seconds when the experiment starts. The
file serial numbers follow the collection time sequence, and images are collected every 1s. The
information is presented by digital images in Attachment 1 (see Figure 1). The upper left corner
of each image is marked with the corresponding time of the image and the temperature values
of No.1 thermocouple and No.2 thermocouple.
(a) The sample
(b) The sample begins to melt
at 110s
(c) The sample is completely
melted at 141s
(d) The sample sees steels
melting at 149s
(e) Crystallization begins at
150s
(f) Crystallization ends at
671s
Fig. 1 Melting and crystallization of mold fluxes
To realize automatic feature extraction and mathematical modeling of sequence images of
mold fluxes melting and crystallization, please answer the following three questions.
Question 1: With image segmentation and recognition or other technologies, please
automatically extract temperatures of No.1 thermocouple and No.2 thermocouple in the upper
left corner of each image and import them automatically into the corresponding table in 3
Attachment 2 (please write a step-by-step technical operation document), and please make a
temperature-time curve diagram (1#wire temperature-2#wire temperature-time diagram;
1#wire average temperature-2#wire average temperature-time diagram). In addition, the test
result of 1#wire or 2 #wire is inaccurate. Please point it out and explain.
Question 2: According to the six node images in Fig.1, please study and quantify the
dynamic differences between adjacent sequence images in the process of mold fluxes melting
and crystallization by applying digital image processing technology. On this basis, please make
a time series modeling of the quantified different characteristics, and discuss the melting and
crystallization process curve of mold fluxes based on the simulation results of mathematical
model.
Question 3: Given the changes of temperature and time, as well as the research results of
Question 2, please make a mathematical model to discuss the functional relationship between
the changes of temperature and time as well as the melting and crystallization process of mold
fluxes, and discuss the kinetics of melting and crystallization of mold fluxes (the relationship
between temperature, melting rate and crystallizing rate) based on numerical simulation results.
Your PDF solution of no more than 25 total pages should include:
l One-page Summary Sheet.
l Table of Contents.
l Your complete solution.
Note: The APMCM Contest has a 25-page limit. All aspects of your submission count toward
the 25-page limit (Summary Sheet, Table of Contents, your complete solution). However, the
pages of Reference List and Appendices are not limited.
Attachment:
Attachment 1.zip, download on the website: https://share.weiyun.com/ubtXPGz0
Attachment 2.xlsx
