Tip: DS Mr. C thinks the difficulty: C<B<A, openness: B<A<C .
Problem A: Research on structural optimization control of thermal insulation materials
Question A is a very common physics competition question in digital and analog competitions, and requires a lot of relevant knowledge.
Among them, the first question needs to establish a mathematical model of the relationship between the overall thermal conductivity of the plain weave fabric and the thermal conductivity of a single fiber, and calculate the thermal conductivity of a single A fiber. The second problem is how to select the diameter of a single A fiber and adjust the warp density and weft density bending angle of the fabric so that the overall thermal conductivity of the fabric is the lowest.
For the first two questions, you can use the heat transfer model : based on the theory of fiber heat transfer and gas heat transfer in the gap, establish a relationship model between the overall thermal conductivity of the plain weave fabric and the thermal conductivity of a single fiber. The heat transfer equation and heat conduction model as well as the porous media heat transfer model can be considered. Then perform parameter fitting , that is, use the overall thermal conductivity of the plain weave fabric measured under the experimental sample parameters provided in Annex 2, and use parameter fitting or optimization algorithms to match the experimental data with the theoretical model to obtain a single A Fiber thermal conductivity. Finally, verification and evaluation are carried out , that is, according to the established mathematical model and the calculated thermal conductivity of a single A fiber, the model is verified and evaluated. The fitting degree of the model calculation results and the experimental data can be compared, and the accuracy and reliability of the model can be evaluated.
This question is highly professional, and the follow-up account will conduct specific analysis and modeling when analyzing the specific ideas of this question. The degree of openness is low and the difficulty is moderate. However, this kind of competition questions usually cannot play a good role in practicing hands, so Xiaobai chooses carefully. Mr. DS-C recommends choosing physics, electrical, automation and other related majors.
Problem B: Optimal color scheme design for opaque products
Question B requires the use of many operations research-related algorithms, such as multi-objective optimization, dynamic programming, etc. for visual inspection, and it is recommended to use lingo to solve it.
Here is a simple analysis of the first question, and the follow-up account will conduct specific analysis and modeling when analyzing the specific ideas of this question.
Question 1 needs to calculate the relationship between the KS value and the concentration of the three colorants in Annex 2 at different wavelengths. First, we need to choose an appropriate fitting function. Common choices include polynomial fitting , exponential fitting, logarithmic fitting, etc. Here, we use a polynomial fit to represent KS values versus concentration. The polynomial fitting here, if you want to be simpler, you can use multiple linear regression or quadratic polynomial fitting, it is recommended to use matlab or python for fitting.
The specific steps are as follows:
1 According to the data in Annex 2, denote the wavelength and KS value and concentration as x and y respectively
2 Choose an appropriate polynomial fitting function form
3 Bring the fitting function into the fitting problem to obtain an objective function that minimizes the error
4 Use the least square method or other fitting methods to solve the objective function to obtain the fitting coefficients.
To sum up, through the fitting process, we can get the relationship between the KS value and the concentration of the three colorants of red, yellow and blue at different wavelengths, and fill in the relationship formula and fitting coefficient in the table (Table 1). The specific calculation process needs to be implemented according to the data in Appendix 2 and the selected fitting function.
Here is a sample code for quadratic polynomial fitting using Python:
import numpy as np
from scipy.optimize import curve_fit
# 读取附件2中的数据
data = np.loadtxt('附件2.txt', skiprows=1, delimiter='\t')
wavelengths = data[:, 0] # 波长
concentrations = data[:, 1] # 浓度
ks_values = data[:, 2:] # KS值
# 定义二次多项式函数模型
def quadratic_function(x, a, b, c):
return a + b*x + c*x**2
# 对三种着色剂分别进行拟合
fit_params = []
for ks in ks_values.T:
params, _ = curve_fit(quadratic_function, wavelengths, ks)
fit_params.append(params)
# 打印拟合系数
print('拟合系数：')
for i, params in enumerate(fit_params):
print(f'着色剂 {i+1}: a={params[0]}, b={params[1]}, c={params[2]}')
Of course, it is best to plot the fitting results after fitting, as follows:
import numpy as np
import matplotlib.pyplot as plt
# 读取附件2中的数据
data = np.loadtxt('附件2.txt', skiprows=1, delimiter='\t')
wavelengths = data[:, 0] # 波长
concentrations = data[:, 1] # 浓度
ks_values = data[:, 2:] # KS值
# 定义二次多项式函数模型
def quadratic_function(x, a, b, c):
return a + b*x + c*x**2
# 对三种着色剂分别进行拟合
fit_params = []
for ks in ks_values.T:
params, _ = curve_fit(quadratic_function, wavelengths, ks)
fit_params.append(params)
# 绘制拟合结果图
fig, axs = plt.subplots(3, 1, figsize=(10, 15))
colors = ['red', 'yellow', 'blue']
for i, ax in enumerate(axs):
ax.scatter(wavelengths, ks_values[:, i], color='black', label='实际值')
ax.plot(wavelengths, quadratic_function(wavelengths, *fit_params[i]), color=colors[i], label='拟合曲线')
ax.set_xlabel('波长')
ax.set_ylabel('KS值')
ax.set_title(f'着色剂 {i+1}')
ax.legend()
plt.tight_layout()
plt.show()
There is an optimal solution to this question, with a low degree of openness and moderate difficulty. It is best for everyone to choose this question and check the answers online and offline after finishing. It is recommended for students majoring in statistics, mathematics, physics, etc. to choose.
Question C: The influence of the mother's physical and mental health on the growth of the baby
This question is a typical data analysis + modeling question. A certain modeling ability is required, which is similar to the types of questions in other competitions such as national competitions. It is recommended that everyone (all majors can) choose it.
The topic needs to establish a mathematical model, and you can use evaluation algorithms , such as gray comprehensive evaluation method and fuzzy comprehensive evaluation method to establish connections between various indicators.
Before the first question, everyone needs to analyze and numerically process the data, which is EDA (Exploratory Data Analysis) . For numerical data, you can use normalization, removal of outliers, etc. to perform data preprocessing. For quantification of non-numeric data, you can use the following methods:
1 tag encoding
Label encoding is a method of quantizing non-numeric data by converting a set of possible values into integers. For example, in the field of machine learning, for a variable with multiple categories, we can assign a unique integer value to each category, so that it can be converted into numerical data.
2 one-hot encoding onehot
One-hot encoding is a method of converting multiple possible values into a binary array. In one-hot encoding, each possible value corresponds to a binary array whose length is the total number of possible values, in which only one element is 1, and the rest are 0. For example, for a gender variable, one-hot encoding can be used to convert "male" and "female" to [1, 0] and [0, 1] respectively.
3 classification count
Categorical counts are an easy way to convert non-numeric data into numeric data. In categorical counting, we classify data according to some specific attributes (such as education, occupation, etc.), and then count the number or frequency of each category. For example, in a survey questionnaire, we can classify the responses to a question into the categories "yes", "no", and "not sure" and count the number or frequency of each category.
4 principal component analysis
Principal component analysis is a method of converting multidimensional data into a low-dimensional representation. In principal component analysis, we perform dimensionality reduction on raw data by finding the principal components that best explain the variation in the data. This converts non-numeric data to numeric data.
The first question suggests that you use some visualization methods, you can use common EDA visualization methods:
l Histogram and Density Plot: Displays the distribution of numerical variables.
l Scatterplot: Shows the relationship between two continuous variables.
l Boxplot: Shows the distribution and outliers of numerical variables.
l Bar and pie charts: Show the distribution of categorical variables.
l Line chart: shows the trend over time or sequence.
l Heat map: Shows the correlation between different variables.
l Scatter matrix plot: Displays a scatter plot matrix between multiple variables.
l Geographic map: displays geographic location data and spatial distribution information.
For the first question, you can remind Xiaobai first, and we will update the specific ideas for each question later. The first question is that we need to do a correlation analysis to see if the correlation coefficient between those indicators is high. If it is high, it means that the impact is greater, and if it is low, it means that the impact is small. This can be drawn with a heat map to visualize the degree of influence.
Since this article is a suggestion for topic selection, you can see my follow-up articles/videos for detailed ideas. I won't go into details. This question is more open and difficult, and it is the first choice for practice and winning in this competition. Recommended for all major students.
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