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1. Restatement of the problem
1.1 Research Background
The main raw material of glass is quartz sand, and the main chemical composition is silicon dioxide (SiO2). The fluxes added in the calcination process are different, and their main chemical components are 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 my country. The glass of Chu culture is Mainly lead-barium glass. Potassium glass is made by firing substances with high potassium content such as plant ash as a flux. It is mainly popular in Lingnan, Southeast Asia, India and other regions in my country. The relationship between composition analysis and identification of glass products studied in this paper is shown in the figure below
1.2 Asking questions
This article will address the following issues:
Question 1: Analyze the relationship between the surface weathering of these glass cultural relics and its glass type, decoration and color; combine the type of glass, analyze the statistical law of whether there are weathered chemical components on the surface of cultural relic samples, and predict the weathering point according to the detection data of the weathering point. Chemical composition content before weathering.
Question 2: Analyze the classification rules of high-potassium glass and lead-barium glass according to the attached data; select the appropriate chemical composition for each category to 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: Analyze the chemical composition of unknown glass cultural relics in Annex Form 3, identify their type, and analyze the sensitivity of the classification results.
Question 4: For different categories of glass cultural relic samples, analyze the relationship between their chemical components, and compare the differences in the relationship between chemical components of different categories.
2. Analysis of the problem
For the four related issues raised in this paper, we make the following analysis one by one:
Problem 1 thought analysis:
First of all, it is necessary to analyze the differences between the weathering of the glass surface and the glass type, decoration and color, and combine the glass type to analyze the change law of the chemical composition content and predict the chemical composition content before weathering.
The first step of difference analysis: Carry out chi-square test analysis on the categorical variables to determine the relationship between the independent variable and the dependent variable, and bring it into the SPSS software for solution. Analyze whether the significant p value is less than 0.05, and then analyze the difference relationship
The second step is analysis of change law: Discuss the change difference between lead-barium glass and high-potassium glass before and after weathering, conduct descriptive statistical analysis, frequency histogram statistical analysis, normal distribution test, etc., and summarize the changes.
The third step is to predict the chemical composition: according to the data before and after weathering, the change of each chemical composition is summarized, the mapping relationship is found, and the content before weathering is predicted.
Analysis of the second question:
We need to classify and sub-category elevated glass and Qianbei glass, and analyze the rationality and sensitivity of the model.
The first step of analysis: make statistics on the values of different chemical compositions of high-potassium glass and lead-barium glass, and find out the changes of their representative chemical indicators as the basis for classification.
The second step of analysis: divide into subcategories on this basis, observe the changes of chemical components before and after weathering, color changes, texture changes, etc., and give the corresponding classification basis
The third step of analysis: On this basis, the data is disturbed (sensitivity test), and the relevant rationale is given.
Analysis of problem three ideas:
We need to analyze the chemical composition of the unknown glass cultural relics in Form 3, predict their type, and conduct sensitivity analysis.
The first step of analysis: classify and discuss whether there is weathering in the data in Form 3, and combine the questions
Based on the conclusions of the model in Table 2, the different types of glass in Table 3 are classified and judged to analyze the robustness of the model. The second step of analysis: add a disturbance to the content of a certain type of chemical element (-5%, -10%, 10%, 20%)
Bring it into the model of question 2, observe whether the classification situation will change, and give the conclusion of the stability of the model.
Analysis of problem four ideas:
We need to analyze the relationship between chemical components for different types of glass samples.
The first step of analysis: select the chemical composition with a relatively large proportion as the dependent variable (parent sequence) of the analysis, select the remaining suitable variables as independent variables (subsequences), establish a gray relational analysis model, and calculate its gray relational degree.
The second step of analysis: perform variance analysis on the gray correlation coefficients calculated from different types of glasses, and observe the differences between high-potassium glasses and lead-barium glasses by performing significance tests.
3. Model assumptions
In response to the questions raised in this paper, we made the following model assumptions:
(assuming you can design it yourself)
4. Description of symbols
The commonly used symbols in this paper are shown in the table below, and other symbols are explained in the text.
5. Modeling and solution
5.1 Modeling and solution of problem 1
First of all, it is necessary to analyze the weathering of the glass surface and the differences in glass type, decoration and color, and combine the glass type to analyze the change law of chemical composition content and predict the chemical composition content before weathering. Three small problems need to be solved. A modeling analysis flow chart is shown in Figure 5.1 below
Figure 5.1 Question 1 Analysis Flowchart
5.1.1 Data 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. After processing, there are 67 valid data left in the table.
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". (This can also be removed as invalid data)
3. Attachment Form 2 gives the proportion of the corresponding main components. The blank space indicates that the component was not detected, not a missing value. Therefore, we will fill the undetected data with "0" to facilitate the next calculation. .
5.1.1 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. Through 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, use SPSS software for interactive analysis, and get the chi-square test table shown in Table 5.2 below:
Table 5.2 Chi-square test table for surface weathering
From the results of the chi-square test analysis in the above table, it can be concluded that: surface weathering and decoration, the significant P value is 0.071*, the null hypothesis is accepted, so there is no significant difference; surface weathering and type, the significant P value is 0.01 ** *, reject the null hypothesis, there is a significant difference; surface weathering and color, the significance P value is 0.067*, accept the null hypothesis, there is no significant difference.
On this basis, effect quantitative analysis is carried out, including phi, Crammer's V, contingency coefficient, and lambda, which are used to analyze the degree of correlation between surface weathering and the other three indicators. The quantitative analysis indicators are explained as follows:
1) phi coefficient: The size of the phi correlation coefficient indicates the degree of correlation between two samples. When the phi coefficient is less than 0.3, it means that the correlation is weak; when the phi coefficient is greater than 0.6, it means that the correlation is strong
2) Cramer's V: It is similar to the phi coefficient, but the Cramer's V coefficient has a wider range of action.
3) Contingency coefficient: C coefficient for short.
4) lambda: It is used to reflect the predictive effect of the independent variable on the dependent variable. Use SPSS to operate, and the results are shown in Table 5.3 below:
Table 5.3 Quantitative analysis of surface weathering effect
From the results of the effect quantitative analysis in Table 5.3 above, it can be concluded that: the Cramer's V value of the decoration is 0.326, so the difference between the decoration and the surface weathering is a medium degree difference; similarly, the Cramer's V value of the glass type is 0.316, which is a medium degree difference; The color has a Cramer's V value of 0.341, which is moderately different.
From the analysis of the PHI value, it can be concluded that the PHI value of the ornamentation, color, and glass type is less than 0.3, indicating that the correlation with surface weathering is weak; the PHI value of the color and glass type is between 0.3 and 0.6, indicating that its The degree of correlation is moderate.
5.1.1 Statistical analysis of weathering on the surface of different glass types
Firstly, SPSS software was used to conduct a statistical analysis of the chemical composition content of the descriptive lead-barium glass before and after weathering, and the results are shown in Table 5.4 below:
(Too many tables will not be displayed temporarily)
Next, we screened out the comparative analysis of the frequency distribution histograms of the relatively important chemical components of lead-barium glass and high-potassium glass before and after weathering, and used Matlab programming to solve the problem. The results are shown in Figure 5.2 below:
Figure 5.2 Histogram of the frequency distribution of different chemical compositions of different glass types before and after weathering
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.
5.1.1 Weighted average proportion prediction model
Further analysis, due to the different chemical composition content of each type of glass, some chemical content may not be detected, so there are more "0" values in the data as a whole, we carry out weighted average processing on the data, in the weight calculation Partially use the normal distribution curve function for weight distribution, the calculation process is as follows:
Let me update the code for Question 1 and 2.
Question 1 (2) code, for reference only, do not use directly
clc
clear
close all
fName = ["GKN.xlsx","GKF.xlsx","KBN.xlsx","KBF.xlsx"];
average = zeros(4,16);
for t=1:4
A = xlsread(fName(t));
[n,m] = size(A);
for i = 1:m
temp = sort(A(:,i));
ave = 0;
sum = 0;
for j=1:n
alpha = normpdf((j/n-0.5)*3);
ave = ave + temp(j)*alpha;
sum = sum + alpha;
end
ave = ave / sum;
average(t,i)=ave;
end
end
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