2023 Huawei Cup Postgraduate Mathematical Modeling Question D Idea Code Analysis

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Question 1: Analysis of the current situation of regional carbon emissions, economy, population, and energy consumption

(1) Establish indicators and indicator systems

Requirement 1: The indicator can describe the economy, population, energy consumption and carbon emissions of a certain region;

Requirement 2: The indicator can describe the carbon emission status of each department (energy supply department, industrial consumption department, construction consumption department, transportation consumption department, residential consumption department, agriculture and forestry consumption department);

Requirement 3: The indicator system can describe the interrelationship between the main indicators;

Requirement 4. Changes in some indicators (year-on-year or month-on-month) can become the basis for carbon emission predictions.

We can consider the following for indicator selection :

Economic indicators: GDP growth rate is selected as the main indicator to measure regional economic conditions. It can comprehensively reflect the level of economic development and the activity of economic activities in a region.

Population indicators: Total population and population growth rate are important indicators for evaluating population status. They can reflect the size and growth rate of regional population and have a direct impact on energy consumption and carbon emissions.

Energy consumption indicators: Total energy consumption and energy consumption structure (the ratio of fossil energy to non-fossil energy) are key indicators to measure energy consumption. They directly affect the size and structure of carbon emissions.

Carbon emission indicators: Total carbon emissions, carbon emissions per unit of GDP and carbon emissions of each department are the main indicators to evaluate the carbon emission status. They can comprehensively describe the carbon emission level and structure of a region.

Sector division: The entire region is divided into the energy supply sector, industrial consumption sector, construction consumption sector, transportation consumption sector, residential consumption and agriculture and forestry consumption sectors, and the energy consumption and carbon emissions of each sector are independently analyzed.

After selecting indicators, it is necessary to establish a relationship model between these indicators. A multiple linear regression model can be used here, using carbon emissions as the dependent variable and the remaining indicators as independent variables to establish the mathematical relationship between them. For example, you can explore the impact of GDP growth rate, population growth rate and energy consumption structure on carbon emissions, and analyze the sensitivity and elasticity between them. For selected indicators, their year-on-year and month-on-month changes are calculated, and these changes can serve as the basis for carbon emission forecasts. If energy consumption increases significantly in a given year, carbon emissions are likely to increase that year as well. By analyzing these changes, we can better understand the impact of each indicator on carbon emissions.

(2) Analyze the current status of regional carbon emissions, economy, population, and energy consumption

Requirement 1: Using 2010 as the base period, analyze the 12th Five-Year Plan (2011-2015) and the 13th Five-Year Plan for a certain region

Carbon emission status (such as total amount, change trend, etc.) during the period (2016-2020);

Requirement 2: Analyze the factors that affect carbon emissions in the region and their contributions;

Requirement 3: Analyze and determine the main challenges that the region needs to face to achieve carbon peaking and carbon neutrality, and provide a basis for differentiated path selection in the region’s dual-carbon (carbon peaking and carbon neutrality) path planning.

Using existing historical data, we can analyze the changing trends and conditions of regional carbon emissions, economic growth, population growth and energy consumption from 2010 to 2020. Through methods such as graphing and calculating growth rates, we can clearly see the development trajectory of these indicators, thereby gaining a preliminary understanding of the current carbon emissions in this region. Then we analyze the impact of changes in various indicators on carbon emissions and find out the main driving factors for the growth of carbon emissions.

For models, statistical methods such as correlation analysis and regression analysis can be used to quantify the contribution of each factor to carbon emissions. We can analyze the contribution of economic growth to carbon emissions and determine whether economic development is the main reason for the growth of carbon emissions.

Of course, there are other external factors, such as government policies, technological progress, etc., which will also affect changes in carbon emissions. Based on the analysis of the current situation and understanding of the influencing factors, we can predict the main challenges in achieving carbon peak and carbon neutrality in this region. Including difficulties in energy structure adjustment, restrictions on the development of non-fossil energy, conflicts between economic development and carbon emission reduction , etc.

(3) Regional carbon emissions, economic, population, energy consumption indicators and their correlation models

Requirement 1: Analyze changes in relevant indicators (month-on-month and year-on-year);

Requirement 2: Establish a relationship model between various indicators;

Requirement 3: Based on changes in relevant indicators, combined with multiple effects such as dual-carbon policy and technological progress, determine the values ​​of carbon emission prediction model parameters (such as energy utilization efficiency improvement and the proportion of non-fossil energy consumption, etc.).

After analyzing the current status and influencing factors of each indicator, we need to establish a correlation model between each indicator. Here, methods such as multiple linear regression and principal component analysis can be used to fit the mathematical relationship between various indicators based on historical data.

We use carbon emissions as the dependent variable, GDP, population, energy consumption, etc. as independent variables, and establish linear and nonlinear models between them through regression analysis. It can help us understand the interaction between various indicators. After establishing the correlation model, we need to determine the parameters in the model. These parameters include energy utilization efficiency, proportion of non-fossil energy consumption, etc. They are the core components of the model and directly affect the prediction effect of the model.

Question 2: Forecasting model of regional carbon emissions, economy, population, and energy consumption 

(1) Energy consumption forecast model based on demographic and economic changes

Requirement 1: Using 2020 as the base period and combining the two time nodes of Chinese-style modernization (2035 and 2050), predict the population, Changes in the economy (GDP) and energy consumption.

Requirement 2: Energy consumption is linked to population projections.

Requirement 3: Energy consumption is linked to economic (GDP) forecasts;

The Huang Futao model can be chosen to predict future population size. The model takes into account the effects of factors such as birth rate and death rate.

Pt+1 = Pt + Bt - Dt + It - Et

We can also use population prediction models such as logarithmic linear models or logistic models, combined with regional historical population data, to predict future population change trends. Of course, we need to consider factors that may have an impact, such as fertility rate, mortality rate, and migration rate . During the prediction process, model parameters must be continuously adjusted to ensure the accuracy of the prediction results.

Economic (GDP) forecasting can use time series analysis, multiple regression analysis and other methods, combined with national macroeconomic policies, global economic situation, etc., to predict the future economic development trend of the region.

G(t) = G0 / [1 + ae^(-bt)]

Energy consumption forecasting needs to be combined with predicted population and economic data, and methods such as cointegration analysis and causal models should be used to predict future energy consumption.

E(t) = c1P(t) + c2G(t) - c3*E'(t)

(2) Regional carbon emissions prediction model

Requirement 1: Carbon emissions are related to population, GDP and energy consumption forecasts;

Requirement 2: Carbon emissions and various energy consumption sectors (industrial consumption sector, construction consumption sector, transportation

consumption sector, residential consumption, agriculture and forestry consumption sector) and the energy supply sector (such as reflecting the impact of energy efficiency improvements on the distribution of total energy consumption in the above energy consumption sectors);

Requirement 3: Carbon emissions and energy consumption types (primary energy) in each energy consumption sector (same as above)

Fossil energy consumption is related to non-fossil energy consumption and secondary energy (electricity or heat) consumption) and the types of energy consumption in the energy supply sector (fossil energy power generation and non-fossil energy power generation) (such as reflecting the impact of the increase in the proportion of non-fossil energy consumption on each The impact of sectoral energy consumption types or carbon emission factors).

We need to first establish a relationship model between carbon emissions and population, GDP and energy consumption. Here you can consider using multiple regression analysis, using carbon emissions as the dependent variable and population, GDP and energy consumption as independent variables to fit the relationship between them. We can then quantify the impact of population, economy and energy consumption on carbon emissions to predict future changes in carbon emissions.

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