98年建模a题论⽂_2019年第九届APMCM亚太地区⼤学⽣数学
建模竞赛A题（中英版）...
中⽂赛题：基于图像分析的⼆氧化硅熔融表征模型
冷眼旁观
铁尾矿的主要成分是⼆氧化硅，⽽⼆氧化硅是铁尾矿组分中最难熔化的部分。因此，铁尾矿的熔融⾏为可以由⼆氧化硅的熔化⾏为来表⽰。但⾼温熔池温度超过 1,500
统。在⾮接触⽅式下，该组获得了⾼温熔池中⼆氧化硅的动态视觉数据（时序图像），并通过视频分析观察到了⼆氧化硅的实时熔化速率，为渣棉制备过程中尾矿添加和热补偿提供了指导，从⽽间接改善了⾼炉渣直接成纤维技术。
附件给出了熔融过程中⾼温熔池中⼆氧化硅的时序图像（共114幅图像；⽂档名称的序列号为时间序列，每隔 1s 收集⼀个图像）。采⽤的实验设备情况见下图：
图 1. 具有放⼤效应的 CCD 设备⽰意图
图 2. 实物设备⽰意图
为了揭⽰铁尾矿在⾼炉渣中的溶解⾏为，采⽤铁尾矿中的主要成分
（见图4）：
图 3. 分析⽤纯⼆氧化硅颗粒
图 4. 直径 8 mm 刚⽟坩埚
附件的数字图像中显⽰的信息包括：
坩埚在图像中的固定位置；
未熔融的⼆氧化硅颗粒的位置随时间顺序⽽变化。
需要对附件中的图像进⾏以下分析
1. ⼆氧化硅颗粒在熔融过程中在⾼温熔池中的位置不断变化，分析⼆氧化硅熔化⾏为的第⼀步是跟踪⽬标。建⽴了⼆氧化硅颗粒在熔化
过程中质⼼位置的数学模型，并给出了⼆氧化硅质⼼的运动轨迹。
2. 建⽴了⼆氧化硅熔融过程中⼆氧化硅（如形状、周长、⾯积、⼴义半径等）的边缘轮廓特征的指标；参与者可以⾃⾏选择，只要它们
能代表⼆氧化硅的熔化过程。
3. 附件中给出的图像是 2 维的，⽽表⽰⼆氧化硅熔化速率的关键参数是质量，质量与三维体积成正⽐，根据第 2 题中⼆氧化硅的边缘轮
廓特征指数来估计⼆氧化硅的实际熔化速率。
英⽂赛题：Melting Reprentation Model of Silicon Dioxide Analyzed Bad on Image
The main component of iron tailings is silicon dioxide, while the silicon dioxide is the hardest part to melt among the iron tailing components. Therefore, the melting behavior of iron tailing can be reprented by the melting behavior of silicon dioxide. However, the temperature of high-temperature molten tank is over 1,500
relevant rearch group firstly adopted a kind of rifted CCD video shooting system with amplification effect for the first time at home and abroad. In the non-contact way, the group has obtained the dynamic visual data of silicon dioxide in the high-temperature molten pool (quence image under time quence), and has obrved the real-time melting rate of silicon dioxide in the time quence through video analysis, which provided guidance for the tailing addition and heat compensation in the process of slag cotton preparation, thus indirectly improved the direct fiber forming technology of blast furnace slag. Time quential image of silicon dioxide in high-temperature molten pool during the melting process (e Attachment, 114 images in total; the rial number of document name is the time quence, collecting one image every other 1s). See the figure below for the situation of adopted experimental equipment:
Figure 1. Drawing of Refitted CCD Equipment with Amplification Effect
Figure 2. Diagram of Physical Equipment Object
To reveal the dissolution behavior of iron tailings in blast furnace slag, the main component
pure
Figure 3. Pure SiO2 Particles for Analysis
Figure 4. Corundum Crucible with Diameter of 8 mm
The information shown in the digital image of Attachment includes:
下雨用英语怎么说The fixed position of crucible in the image;
The position of
It is required to conduct the following analysis on the image in the Attachment
1. The position of silicon dioxide particles in the high-temperature molten pool during the melting process is changing
constantly, and the first step to analyze the melting behavior of silicon dioxide is to track the target. Plea establish a mathematical model to track the centroid position of silicon dioxide particles during the melting process, and prent the motion trail of centroid of silicon dioxide.接待
2. Establish indexes which reprent the edge outline characteristics of silicon dioxide during the melting process of
silicon dioxide (such as shape, perimeter, area, generalized radius, etc.); the participants can lect by themlves, as long as they can reprent the melting process of silicon dioxide.
竹子画法3. For the image given in the attachment is 2D, while the key parameter which reprents the melting rate of silicon
二年级科学小实验dioxide is mass, and the mass is in direct proportion to the 3D volume, estimate the actual melting rate of silicon dioxide bad on edge outline characteristic indexes of silicon dioxide in the No. 2 question.
下个星期去英国>甜言蜜语短句转载请注明出处：知乎地址或微信“数学模型”公众号（微信号：MATHmodels）
>粉色水晶
