The May 1st Mathematical Modeling Problem C question has been updated, get it at the end of the article!
Question C ideas:
Question 1: Now there is a single-story flat-roofed building with a length of 4 meters, a width of 3 meters, and a height of 3 meters. Concrete pouring, the thickness is 30 cm (thermal conductivity 0.2W/㎡·K), the total area of doors and windows is 5 square meters (thermal conductivity 1.6W/㎡·K), and the ground is concrete (thermal conductivity 0.25W/㎡·K). See the table below for the monthly average temperature (unit: Celsius) of the geographical location of the building in a year (calculated on the basis of 365 days).
Question 1: Assume that the temperature in the building needs to be kept at 18-26 degrees all the time. When the temperature is not suitable, the temperature must be adjusted by electricity. The consumption of one degree of electricity is equivalent to 0.28 kilograms of carbon emissions . Please calculate the annual carbon emissions of the building that adjusts the temperature through air conditioning (assuming that the air-conditioning heating performance coefficient COP is 3.5, and the cooling performance coefficient EER is 2.7). (Try to use the conditions given in this question to calculate carbon emissions, without considering other losses)
In order to calculate the annual carbon footprint of a building that is air-conditioned, we need to first calculate the monthly heating and cooling needs. The heat loss or heat gain of a building is related to the thermal conductivity of walls, roofs, doors, windows, and ground, as well as the temperature difference between indoors and outdoors. We can calculate heat loss or heat gain using the following formula:
Heat loss or heat gain = surface area x thermal conductivity x temperature difference
We need to calculate the surface area of the wall, roof, doors, windows and ground first, the surface area of the wall = (4m × 3m × 2 + 3m × 3m × 2), the surface area of the roof = 4m × 3m, the total area of the doors and windows has been given as 5 square meters , the ground surface area = 4m × 3m.
The indoor temperature needs to be kept at 18-26 degrees, and the indoor and outdoor temperature difference can be calculated according to the average temperature of each month. For example, the indoor and outdoor temperature difference in January is: 18 - (-1) = 19 degrees (heating), similar calculations for other months.
Use the formula to calculate the heat loss or gain for each month, then add the heat loss or gain for each section. And according to the COP and EER of the air conditioner, the monthly heat loss or heat gain is converted into electricity demand. For example, the power demand in January is: heat loss/COP, similar calculations for other months. Add the monthly electricity demand to get the annual total electricity demand, and then multiply it by the carbon emission per kWh (0.28 kg/kWh) to get the annual carbon emission.
Question 2 : In the entire life cycle of residential buildings ( construction, operation, demolition ) , there are many factors that affect carbon emissions, such as architectural design standards, climate, production and transportation of building materials, regional differences, energy consumption for construction and demolition, decoration style, usage Energy consumption, building type, etc. Please search and analyze data, establish a mathematical model, and find indicators that are highly correlated with the above factors and are easy to quantify, and based on these indicators, conduct a comprehensive evaluation of the carbon emissions of the entire life cycle of residential buildings.
In order to comprehensively evaluate the carbon emissions of the entire life cycle of residential buildings, we can establish a linear weighted model, which takes into account the correlation of each indicator and its ease of quantification. Firstly, the weight of each indicator needs to be determined, and then the value of each indicator is multiplied by the corresponding weight and summed to obtain a comprehensive evaluation value. Identify indicators that are highly relevant to carbon emissions and easily quantifiable: Based on the factors you provide, we can consider the following indicators:
Building design standards: e.g. building energy ratings
Climate: e.g. mean annual temperature, annual precipitation
Production and transport of construction materials: e.g. carbon emissions per square meter of materials required for construction
Building energy consumption: e.g. heating and cooling energy consumption per square meter per year
Building Type: For example, single-story, multi-storey, or high-rise buildings
The weights are assigned according to the degree of impact of each indicator on carbon emissions and the degree of ease of quantification. For example, building energy consumption may have a higher impact on carbon emissions and may therefore be assigned a larger weight. The weights should sum to 1. The value of each indicator is multiplied by the corresponding weight and summed to obtain the comprehensive evaluation value.
Comprehensive evaluation value = w1 * building design standard + w2 * climate + w3 * production and transportation of building materials + w4 * building energy consumption + w5 * building type
Among them, w1, w2, w3, w4, w5 are the weights of each index respectively.
This linear weighted model is simple and easy to understand, and can provide decision makers with intuitive evaluation results. However, there may be mutual influence among the indicators, which cannot be reflected in the linear weighted model.
Question 3: On the basis of Question 2, consider the carbon emissions of the three stages of the building life cycle, search for relevant information, establish a mathematical model, and conduct a comprehensive evaluation of the carbon emissions of residential buildings in 13 prefecture-level cities in Jiangsu Province in 2021. And the validity of the built evaluation model is verified.
On the basis of Question 2, we can divide the carbon emissions of residential buildings into three stages: construction, operation, and demolition. First, we need to identify relevant and easily quantifiable indicators for each stage. Then, assign weights to the indicators of each stage. Finally, the value of each stage index is multiplied by the corresponding weight and summed to obtain the comprehensive evaluation value.
Identify indicators that are highly relevant and easily quantifiable to carbon emissions:
a. Construction phase:
Architectural design standards, production and transportation of building materials; carbon emissions per square meter of building materials; building types, single-storey, multi-storey or high-rise buildings
b. Run phase:
What are the climates, the annual average temperature and annual precipitation; the annual heating and cooling energy consumption per square meter; the influence of interior design style on energy consumption
c. Demolition phase:
Carbon emissions per square meter of energy required for building demolition; degree of recycling of building materials after demolition
Determine the weight of indicators at each stage: assign weights according to the degree of impact of each indicator on carbon emissions and the degree of ease of quantification. The weights should sum to 1.
Calculate the comprehensive evaluation value: Multiply the value of each stage index by the corresponding weight and sum to obtain the comprehensive evaluation value.
Comprehensive evaluation value = Σ(stage weight * Σ(index weight of each stage * index value))
Validation of the evaluation model: Collect the carbon emission data of residential buildings in 13 prefecture-level cities in Jiangsu Province, and use the established model to predict. Then, the forecast results are compared with the actual data to calculate the forecast error. If the prediction error is within the acceptable range, it indicates that the model has good validity.
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