1 Question C: Composition analysis and identification of ancient glass products
The Silk Road was a channel for cultural exchanges between China and the West in ancient times, and glass was a valuable evidence of early trade exchanges. Early glass
was often made into bead-shaped ornaments in West Asia and Egypt and introduced to China. After absorbing its technology, ancient glass in China was made from
local materials similar in appearance to foreign glass products, but its chemical composition is different. .
The main raw material of glass is quartz sand, and the main chemical composition is silicon dioxide (SiO2). Due to the high melting point of pure quartz sand,
in order to lower the melting temperature, it is necessary to add flux during refining. Commonly used fluxes in ancient times include plant ash, natural natron, saltpeter
and lead ore, etc., and limestone was added as a stabilizer, and the limestone was converted into calcium oxide (CaO) after calcination. The added flux
is different, and its main chemical composition is also different. For example, lead-barium glass is added with lead ore as a flux during the firing process, and its
content of lead oxide (PbO) and barium oxide (BaO) is relatively high. It is generally considered to be a glass variety invented by China. The
glass of Chu culture It is mainly lead-barium glass. Potassium glass is fired from substances with high potassium content such as plant ash as a flux, and is mainly
popular in Lingnan, Southeast Asia, India and other regions in China.
Ancient glass is extremely susceptible to weathering due to the environment in which it was buried. During the weathering process, internal elements undergo a large exchange with environmental elements
, resulting in changes in their composition ratios, which affect the correct judgment of their categories. As shown in Figure 1, the cultural relics are marked as having no weathering on the surface
, and the color and decoration of the cultural relics can be clearly seen on the surface, but it does not rule out local light weathering
. The layer is the obvious weathered area, and the purple part is the general weathered surface. In partially
weathered artifacts, there are also unweathered areas on the surface.
There are a batch of data related to ancient glass products in China. Archaeologists have classified these cultural relics
into two types: high-potassium glass and lead-barium glass according to their chemical composition and other detection methods. Attached Form 1 gives the classification information of these cultural relics, and
Attached Form 2 gives the proportion of the corresponding main components (the blank space indicates that the component was not detected). The characteristic of these data
is compositional, that is, the cumulative sum of the proportions of each component should be 100%, but the cumulative sum of the proportions of the components may not be
100% due to detection methods and other reasons. In this question, the cumulative sum of the component ratios and the data between 85% and 105% are considered valid data.
Ask your team to conduct analysis and modeling based on the relevant data in the attachment to solve the following problems:
Question 1 analyzes the relationship between the surface weathering of these glass cultural relics and their glass type, decoration and color; combined with the
type of glass, analyze the statistical law of whether there is weathering on the surface of the cultural relic samples, and
predict Its chemical composition content before weathering.
Question 2 Analyze the classification rules of high-potassium glass and lead-barium glass based on the attached data; select the appropriate
chemical divide it into subcategories, give the specific division method and division results, and evaluate the reasonableness of the classification results and sensitivity
analysis.
Question 3 is to analyze the chemical composition of unknown glass cultural relics in Annex Form 3, identify its type, and
analyze the sensitivity of the classification results.
Question 4 analyzes the relationship between the chemical composition of different types of glass cultural relic samples, and compares
the differences of the chemical composition relationship between different categories.
appendix
Form 1 Basic information of glass cultural relics
Form 2 The chemical composition ratio of classified glass cultural relics, where
(1) The cultural relic sampling point is a random sampling of a certain part of the surface of the numbered cultural relic, and its weathering properties are
consistent with the corresponding cultural relics in the attached form 1.
(2) Part 1 and Part 2 are two parts with different shapes of cultural relics, and their composition and content may be different.
(3) Unweathered points are points within the unweathered area on the surface of weathered cultural relics.
(4) Severely weathered points are taken from regolith.
Table 3 Chemical composition ratio of unclassified glass cultural relics
2 Problem-solving ideas
Overall
Question A Wave Energy Maximum Output Power Design
This question belongs to the traditional physics class and requires excellent professional skills and computing power. The ability to simulate is required. This question is recommended for students of related majors to choose. Since all indicators are clearly given, there is an optimal solution (possibly a range value). It is recommended to check the answers at the end. Whether the answers are correct or not will have a greater impact on the final score. Recommended majors such as physics, electrical engineering, mathematics, etc. Higher difficulty, lower openness.
Azimuth-only passive positioning of unmanned aerial vehicles in formation flight of problem B
The question types are relatively common. In the past digital-analog competitions, there have been many questions about the scheduling of drones. This time it is about positioning. The core of the problem is how to achieve effective positioning of drones with fewer signal sources (signals emitted by drones). It is recommended to use simulation to increase signal sources one by one and calculate their positioning. In this question, since each UAV is in continuous motion, a pre-judgment optimization model should be designed to minimize the target value. This question is suitable for students majoring in mathematics and statistics. The difficulty is moderate. Since the numerical values have been given, the degree of openness is relatively low, and there is an optimal solution (possibly a range value). It is recommended to check the answers at the end. Whether the answers are correct or not will have a greater impact on the final score.
C. Composition analysis and identification of ancient glass products
This question is the type of question that many students often do during training, and it belongs to big data and data analysis questions. It is necessary to analyze the composition of glass products, which involves the establishment of some evaluation models, commonly used machine learning algorithms such as factor analysis and principal component analysis, and some visual diagrams for support. There will be a detailed analysis of the idea of question C updated later. This topic is recommended for all major students to choose, the threshold is low and the degree of openness is relatively high.
Question C is the easiest
The first question can be answered by association analysis algorithm
The second question is to do principal component analysis and cluster the data
The third question is classified according to the cluster analysis of the second question to calculate the center distance
The fourth question Mr. A thinks that the core is difference, so you have to find a feature extraction algorithm with obvious effect
The details will be updated in the thinking
The four questions have been updated
preprocessing
1. First, perform data preprocessing. According to the requirements of the topic: consider the data with the cumulative sum of component ratios between 85% and 105% as valid data. According to the analysis, the total components of No. 15 and No. 17 are less than 85%, so in the following No. 15 and No. 17 two sets of error data are not considered in the calculation, and they are eliminated.
2. In the data in the color column in the attached form 1, we found four null values. By observing the changes in the data, we found that the depth of the color and the degree of weathering showed a positive correlation. Therefore, we filled the four null values and filled them. for "black".
3. Attachment Form 2 gives the proportion of the corresponding main components. The blank space indicates that the component is not detected, not a missing value. Therefore, we will fill the undetected data with "0" to facilitate the next calculation. .
Chi-square test for surface weathering
First, use the VLOOKUP function in Excel to combine the data in Form 1 and Form 2 to facilitate subsequent statistics. By observing the data, it is found that decoration, type, color, and surface weathering are all definite variables. We used chi-square test to analyze the difference between the two groups.
The chi-square test is mainly to compare the difference analysis between the categorical variables and the categorical variables. By counting the degree of deviation between the actual observed value of the sample and the theoretically inferred value, the degree of deviation between the actual observed value and the theoretically inferred value determines the size of the chi-square value. If the chi-square value is larger, the degree of deviation between the two is greater ; Conversely, the smaller the deviation between the two; if the two values are completely equal, the chi-square value is 0, indicating that the theoretical value is completely consistent.
Variable X: surface weathering; variable Y: ornamentation, type, color, using SPSS software for interactive analysis, the following table is obtained
Statistical analysis of weathering on the surface of different glass types
Next, we screened out the comparative analysis of the frequency distribution histograms of relatively important chemical components in lead-barium glass and high-potassium glass before and after weathering, and used Matlab programming to solve the problem. The results are shown in the figure below
From the frequency distribution histogram, it can be seen intuitively that the content of main chemical components of high-potassium glass shows a downward trend after weathering; the content of main chemical components of lead-barium glass shows an upward trend after weathering.