The 2023 Huashu Cup is a competition with the same frequency as the national competition (questions will be issued at 6:00 on Thursday and papers will be handed in at 8:00 on Sunday), and it is also the only official competition in the summer. This year's registration team has reached more than 6,000 pairs. Based on such a large number of people for team practice before the national competition, and other purposes. In order to make it easier for everyone to choose a better topic, here is a brief analysis of the three topics of the Huashu Cup, and analyze the difficulties that may be encountered in the future stage of the three questions, which may already involve the required mathematical and analog knowledge.
Problem A Research on structural optimization control of thermal insulation materials
Question A is essentially
Physical differential equation topic + optimization problem (single objective) + introduction of new constraints
The topic is set with heat insulation materials as the background. Question 1 requires us to establish a suitable physical differential equation model to solve the thermal conductivity; question 2 establishes an optimization model based on the given data, with the overall thermal conductivity as the objective function, and a single root A The diameter of the fiber and the warp density, weft density, and bending angle of the adjusted fabric are used as constraints to solve it; problem 3 and problem 2 optimize the depth of the model, and introduce new conditions to solve.
The overall difficulty of question A should be the most difficult this time, and the estimated number of people in the original question is also the least. It is recommended that people whose majors and problem backgrounds are extremely suitable, and a team with strong modeling capabilities to try.
Problem B Optimal color scheme design for opaque products
Regression analysis + 0-1 optimization (decision variable + objective function + constraints)
2017C national competition RGB model HVS model
Introduced to the corresponding problem with an opaque colored product background, the main model can be regarded as an optimization model. The background of the question is similar to Question C of the National Competition in 2017, so I will sort out some information of that year for you later for your convenience.
Question 1. Fitting relational expressions. Standard regression analysis questions are not difficult to solve directly. Question 2 involves an optimization model. The goal is to build an optimization model with the closest color difference to the target sample. Constraints There are color difference requirements, etc.; Question 3, based on the optimization model of Question 2, lead to cost control and batch color matching, and continue to solve the objective function ; Excellent color scheme.
This question is a pure optimization type question, so it is a test for everyone's ability to master the optimization model. The overall difficulty is medium, and the model complexity is much lower than that of 2003B open-pit mining.
Question C : The influence of the mother's physical and mental health on the growth of the baby
Multivariate analysis + questionnaire (reliability and validity of questionnaire steps) + regression analysis + optimization model + prediction (construction of index evaluation system) + introduction of new constraints
Based on the background of mother-related indicators and baby sleep, the questions are set. The number of questions is relatively large, but the difficulty of the questions is the lowest in this competition. Therefore, the one with the largest number of selected topics may also be the one with the largest number of people. Therefore how to stand out from the crowd requires a lot of attention to details. The corresponding details will be described in the detailed version of Question C later. Here is only a brief analysis.
Question 1, whether there is such a rule, that is, simply analyze the results, draw a scatter diagram, and conduct a correlation analysis; question 2, the scale questions need to be tested for reliability and validity of the questionnaire, and a y and multiple The relationship model of X, that is, to establish a multiple linear regression model; Question 3, construct an optimization model with the least cost as the objective function, and translate the corresponding constraints according to the title to solve it; Question No, Question 5 can be compared with Question 3 Putting it together to solve, that is, problem five is an extension of problem three, and a new constraint condition of sleep quality rating is introduced to solve it.
Question 4 is divided into two parts: 1. Comprehensive evaluation, and 2. Predict the last 20 sets of data. For question 4, you can choose the appropriate model for the evaluation model, and try to choose an objective evaluation model. For the second half of the forecast, it belongs to multiple independent variables and multiple dependent variables. Therefore, my personal opinion here is to recommend that you use partial least squares regression analysis. As for everyone who has a better idea, you can also try it.
Data preprocessing outliers, missing values
Question 1. Correlation Analysis Multivariate Analysis (Partial Least Squares)
Question 2: Reliability and Validity Analysis of the Questionnaire Multiple Regression Analysis (Partial Least Squares) Using the Model to Predict
Question 3: Optimizing the Model
Question 4.1. Comprehensive evaluation + comprehensive value threshold setting
2. Partial least squares regression analysis
Question 5. Introduction of New Constraints Expansion of Question 3
Estimated number of topic candidates: A:B:C=1:2:4
In the future, due to limited personal energy, this competition will choose question C as the writing topic of semi-finished papers and complete papers. These two papers will also be displayed on August 4th to provide you with a reference answer, which is convenient for everyone to better do the questions.