Research on Carbon Emission Pre-Assessment of Residential Buildings in Xi’an City during the Scheme Design Stage

Abstract

The effect of energy saving and carbon reduction in the building industry is closely related to the realization of China’s double carbon goal. In this study, a two-dimensional framework for building life cycle carbon emissions was established, which takes into account the early stages of building design such as the feasibility study stage and scheme design stage. Taking 57 residential buildings in Xi’an City as examples, the life cycle carbon emission characteristics of residential buildings in cold areas were introduced. This study found that the life cycle carbon emission intensity is about 45~55 kgCO₂/(m²·a). The operation and maintenance stage and building materials production stage accounted for the largest proportion of carbon emissions, and the sum of carbon emissions of the two stages accounted for 92.3% of the total carbon emissions. In addition, based on the probability density function, the carbon emission intensity distributions of the building life cycle, building material production stage, building material transportation stage, and operation and maintenance stage were analyzed, and it was found that each distribution fitting graph was generally in line with a lognormal distribution, and their expected value provided a reference index for carbon emission pre-assessment in the feasibility study stage. Based on the analysis and determination of 11 independent variables that affect the total carbon emissions, such as area, floor number, story height, and number of households, a multiple linear regression model for carbon emission pre-assessment in the design stage of building schemes is proposed. The R²_adj of the model is 0.985 and the error is about 10%. The prediction model can provide beneficial guidance for the life cycle carbon emission prediction in the design stage of building projects, so as to reduce carbon emissions by changing building design.

1. Introduction

Since the Industrial Revolution, the catastrophic effects of climate change caused by rising temperatures on the natural environment have become increasingly severe. In March 2023, the IPCC’s Climate Change 2023 [1] clearly pointed out that by 2022, the global average temperature will be 1.13 °C higher than the pre-industrial level, resulting in the deterioration of the climate environment. Catastrophic climate events such as ocean acidification, glacier retreat, local extreme heat, regional droughts, and heavy rainfall are on the rise, and more importantly, rising global temperatures are significantly increasing the risk that the climate system will reach a tipping point [2]. The direct cause of global temperature rise is the increasingly serious greenhouse effect caused by carbon emissions. By 2020, the average concentration of carbon dioxide in the atmosphere will increase from 278.3 ppm in pre-industrial times to 417.9 ppm, which is 149% of the original concentration [3]. The increasingly serious greenhouse effect is bound to cause more serious climate change, and will also have a significant impact on natural ecology and the social economy in the future [4,5]. From the perspective of the carbon emission ratio of major economies in the world, China emits nearly 35 billion tons of carbon dioxide every year, accounting for more than 25% of global carbon emissions, making it the largest economy in the world in terms of carbon emission ratio [6]. In response to climate change caused by carbon emissions, the China government has formulated the strategic goal of “carbon peaking and carbon neutrality”, referred to as the “dual carbon” goal. The construction industry is one of the four major carbon emission industries in China, and it is imperative to promote the rapid development of energy conservation and emission reduction [7].

Pre-assessment of building life cycle carbon emissions in the early stage of construction project design is an effective method for building energy conservation and emission reduction. The existing building carbon emission accounting methods generally focus on the preliminary design stage and construction drawing design stage of the building, at which time there is a considerable progress in drawing output. If the calculation at this time indicates that the carbon emission intensity index of the building exceeds the rated value, then modifying its design is an extremely difficult task, and is sometimes even impossible. Therefore, if the life cycle carbon emission level of the project to be built can be mastered at the early stage of architectural design, such as during the feasibility study stage or the scheme design, the difficulty of design modification can be significantly reduced. Therefore, it is particularly important to put forward a feasible building carbon emission pre-assessment model.

At present, the research on building carbon emission prediction mainly focuses on analyzing the leading factors of carbon emission, and then establishing various forecasting models based on the leading factors, which can be used to predict the carbon emission prospects of individual buildings and analyze the overall carbon emission prospects of urban areas in the future. These models can be divided into two categories: mathematical models and machine learning models [8,9].

The mathematical models used for building carbon emission prediction include various regression models and system dynamics models. A regression model is a mathematical model that quantitatively describes statistical relationships and studies the relationship between dependent variables and independent variables. Some extended regression models are mainly used in the actual prediction of building carbon emissions, such as the double regression prediction model, principal component regression model, multiple nonlinear regression model, multiple linear regression model [10], and cubic polynomial model [11]. For example, Luo [12] conducted a quantitative analysis of the implied carbon emissions of 78 office buildings, and proposed a regression formula in which the implied carbon emissions of buildings could be quickly estimated by the amount of steel, concrete, and wall materials, which provided convenience for designers to estimate the implied carbon emissions of buildings at the initial stage of building project construction. When analyzing multi-factor models, the regression model is simple and convenient, and is suitable for preliminary analysis. However, the hypothesis of the regression equation is strict, and it is necessary to know all explanatory variables that cause changes in dependent variables, otherwise it is easy to have the problem of “pseudo-regression”. System dynamics is a method of deepening analysis and problem solving step by step according to “qualitative–quantitative–qualitative–model building” [13]. System dynamics theory has obvious advantages in solving complex and high-order nonlinear practical problems, and is widely used in economic development, environmental protection, and other fields. Li et al. [13] established a prediction model considering the characteristics of the regional energy consumption structure using the theory of system dynamics, and predicted the energy consumption structure of Liaoning Province from 2019 to 2038. The regression model and system dynamics model are the most widely used mathematical models [14]. Neural networks, support vector machines, and other models derived from them are the most widely used machine learning models.

A BP neural network is a multi-layer feedforward neural network model trained according to the error inverse propagation algorithm, and it is a black box model [15]. This model has strong nonlinear mapping ability, can approximate any continuous function, and has adaptive learning, robustness, fault tolerance, and other characteristics, so it is widely used in the field of building carbon emission prediction. However, the BP neural network has slow or even non-convergence and local minimum problems. Therefore, Hao et al. [16] combined the NSGA-II genetic algorithm with a BP neural network to propose a new model with multiple objectives and high convergence speed. Support vector regression (SVR) is often used to study regression equations between independent variables and dependent variables, so it is widely used in predictive analysis, regression estimation, function approximation, and other fields [17]. In contrast to the neural network model, support vector machine overcomes the shortcomings of the former’s overfitting and low generalization ability, and is gradually replacing the neural network model in many application scenarios. Therefore, it is widely used in the carbon emission prediction of the construction industry. For example, Li et al. [18] created a calculation model for carbon emissions in the life cycle of high-rise office buildings, and used support vector machine to carry out fitting analysis on the carbon emissions calculation results and influencing variables, and predicted the carbon emissions of test samples.

Under the premise of training large quantities of sample data, the machine learning model does provide more accurate prediction results for building carbon emissions, but a major feature of the machine learning model is the invisibility of its input and operation, that is, the black box model attribute. In most cases, the training results of machine learning models need to be embedded in special software or platforms before they can be used, which greatly limits the popularity of building carbon emission pre-assessment models.

In recent years, some research has been carried out on the analysis and prediction models of building carbon emission characteristics [19,20]. Aiming at the carbon emissions of residential buildings in Tianjin, Mao [21] established prediction models using four models, namely principal component analysis, random forest, multi-layer perceptron, and support vector machine, and conducted comparative analysis. At the same time, he studied the basic characteristics of carbon emissions of local buildings and found that the carbon emissions of residential buildings in Tianjin ranged from 30 to 60 kgCO₂/(m²·a) during their life cycle. Zhang [22]’s regression of carbon emissions in the demolition stage to a simple one-time function of building area and number of floors is widely used in engineering applications. Li [18] collected and calculated data for 30 high-rise office buildings in Tianjin and found that their life cycle carbon emissions were concentrated in the range of 40~90 kgCO₂/(m²·a). Then, according to the calculation results, the support vector regression method and R language were used to construct a carbon emission prediction model for office buildings. Most of the prediction models of building carbon emissions in existing studies are based on machine learning theory, and the proposal of such models depends on sufficient training samples; however, the collection of building carbon emission samples is not easy, and the application of model transfer is poor. In addition, insufficient attention has been paid to the early stages of construction project implementation, such as the feasibility study stage and the scheme design stage, where the building design parameters are lacking and many complex models cannot be applied. To sum up, this study established a two-dimensional framework for the life cycle carbon emissions of buildings, including the feasibility study and scheme design in the initial stage of project implementation. On this basis, it proposed a convenient and efficient regression model for predicting the life cycle carbon emissions of buildings in the scheme design stage, which can be used by designers at any time.

2. Methodology

2.1. A Two-Dimensional Framework for Building Life Cycle Carbon Emissions

Life Cycle Assessment (LCA)is a general tool used to analyze the resource consumption and environmental impact involved in the life cycle process of a product from raw material mining, production and processing, transportation, and use to waste, and is a method of environmental impact assessment [23,24]. Generally, the life cycle is divided into three stages: “cradle–gate–grave”; “cradle to gate” includes raw material mining and acquisition, processing and preparation, and delivery, and “gate to grave” includes product transportation, use, and maintenance until disposal. Applying this theory to the field of building carbon emission analysis is “building life cycle carbon emission”. The “Building Carbon Emission Calculation Standard” GB/T 51366-2019 [25] divides the building life cycle into five stages: building materials production and transportation, construction, demolition and recycling, and operation and maintenance, that is, accounting for the whole process of carbon emissions from the “cradle” stage to the “grave” stage of building materials production. Each building life cycle stage can be further classified according to the process it has gone through. For example, building demolition and recycling can be further divided into three sub-parts: “building demolition”, “waste transportation”, and “recycling of building materials”. A detailed and complete stage division clarifies the boundaries and accounting lists of the research on carbon emissions in the building life cycle [26], as shown in Figure 1.

There are two perspectives for examining the carbon emissions of a building. One is to examine the whole life cycle of a building from the point of view of the building itself, from the production of building materials to the recycling of building materials, as described in the code. The other is from the perspective of engineering project investigation, design, and implementation; construction projects go through the life cycle stage from decision design to construction landing, which is successively “feasibility study–scheme design–preliminary design–construction drawing design–completion operation”, i.e., five stages. In this study, the carbon emission stages from the above two perspectives are called the “building life cycle stage” and the “construction project implementation stage”, respectively. The design data available at the implementation stage of different construction projects are very different. For example, the carbon emission calculation method recommended by the code requires a detailed building materials list, bill of quantities, building thermal parameters, and other information as support, but such data can only be obtained comprehensively in the preliminary design or even the construction drawing design stage. However, the decision-making and design work of construction projects largely determine the carbon emissions of the building life cycle. Carbon emission estimation in the early stage of construction projects can help designers understand the composition and intensity of carbon emissions, guide the selection of design schemes, and provide data support for the formulation of carbon reduction schemes. Therefore, this study proposes to combine the life cycle stage of a building with the implementation stage of a construction project to form a two-dimensional framework of carbon emissions in the life cycle of a building, as shown in Figure 2.

The feasibility study stage of a building project is the stage where the data of building design are most scarce, so the carbon emission index method is generally used to estimate the life cycle carbon emission in this stage. Drawings have been produced in the scheme design stage, and the design data have been refined but still not enough to support detailed carbon emission accounting, so the regression formula method is generally used to estimate carbon emissions. In the preliminary design stage and construction drawing design stage, there is a detailed list of building materials, bill of quantities, and other data, and detailed carbon emission inventory accounting can be carried out according to the method described in the code. The actual consumption value of building materials and energy is already available in the building operation stage, and it is easy to obtain the actual occurrence value of carbon emissions. With the gradual advancement of the project implementation stage, the design data are gradually improved, the accounting methods are gradually more complicated and refined, and the carbon emission accounting value gradually approaches the actual value.

2.2. Building Carbon Emissions Accounting

2.2.1. Building Carbon Emission Factor

Generally, there are three methods for carbon emission accounting: the carbon emission factor method, the material balance method, and the measured method [27]. Considering the production mode and the characteristics of the input–output flow inventory of the construction industry, the carbon emission factor method can only be used for the life cycle carbon emission accounting of a single building. The carbon emission factor is a coefficient that characterizes the carbon dioxide emissions of energy or a product, which is multiplied by the consumption of the energy or product to obtain the carbon emissions of the emission source. The principle of the carbon emission factor method is easy to understand, widely used, and easy to calculate. The accuracy of the result depends on the accuracy of the carbon emission factor. In order to facilitate the calculation of carbon emissions in the stages of building materials transportation and building maintenance, this paper also clarified the quality conversion coefficient, recovery rate, renewal rate, and other parameter information of each building material when collecting and sorting out the carbon emission factors of building materials. The carbon emission factors of main building materials are shown in

Table 1. Carbon emission factor table of some building materials [28,29,30].

Name	Material Unit	EF	EF Unit	MCC	Replacement	Recovery
rock wool insulation board	m3	89.1	kgCO2/m3	0.008	1	—
Polyethylene foam strip	m	0.281	kgCO2/m	0	—	—
3 mm flat glass	m2	8.475	kgCO2/m2	0.008	1	—
ceramic floor tile	m2	18.33	kgCO2/m2	0.002	1	—
grade III reinforcement	t	2340	kgCO2/t	1	—	0.4
bolt	kg	2.14	kgCO2/kg	0.001	—	0.1
steel security door	m2	73.48	kgCO2/m2	0.036	1	0.5
cement-steel nail	kg	8.57	kgCO2/kg	0.001	—	0.1
concrete C25	m3	343	kgCO2/m3	2.361	—	—
concrete C30	m3	295	kgCO2/m3	2.367	—	—
concrete C35	m3	426	kgCO2/m3	2.372	—	—
clay standard brick	one thousand	442.863	kgCO2/one thousand	1.6	—	—
aerated concrete block	m3	191.5	kgCO2/m3	0.6	—	—
cement	t	735	kgCO2/t	1	—	—
slaked lime	t	1190	kgCO2/t	1	—	—
latex paint	kg	4.12	kgCO2/kg	0.001	—	—

.

The power carbon emission factor is released by the Ministry of Ecology and Environment of China based on the survey data of previous years. The power carbon emission factor of each region is generally released according to the capacity marginal emission factor (BM) and power marginal emission factor (OM) of the six power grid boundaries in North China and Northwest China, respectively, on time, and will be released in the form of the average emission factor from 2019 onwards. In the greenhouse gas emission report of power generation industry enterprises released in February 2023, the average emission factor of the national power grid in 2022 was updated to 0.5703 tCO₂/MWh, and the value of the power carbon emission factor in this paper is taken as this value.

In Xi’an, residential buildings in winter mainly use the municipal heat network plus floor radiant heating. The acquisition of the thermal carbon emission factor is particularly important for the calculation of energy consumption carbon emissions of residential buildings to eliminate heat load. The relevant departments of the state have not issued uniform carbon emission factors on heating, and the carbon emission factors of local purchased heat can be calculated by using the total heat production, fuel type consumed, and total fuel consumption in the local energy balance sheet. The thermal emission factor is calculated to be 0.06 tCO₂/GJ.

2.2.2. Building Carbon Emission Accounting Model

This paper discusses building carbon emissions from the perspective of the building life cycle, and divides the building life cycle into five stages: building materials production, building materials transportation, construction, operation and maintenance, and demolition and recycling. The carbon emissions of the whole life cycle can be obtained by adding the carbon emissions of each stage, as shown in Equation (1):

$$E_{\mathrm{LC}}=E_{\mathrm{sc}}+E_{\mathrm{ys}}+E_{\mathrm{jz}}+E_{\mathrm{yw}}+E_{\mathrm{ch}}$$

(1)

where E_LC denotes the building life cycle carbon emissions; E_sc denotes carbon emissions from building materials production; E_ys denotes carbon emissions of building materials transportation; E_jz denotes carbon emissions during construction; E_yw denotes carbon emissions in the building operation and maintenance stage; E_ch denotes carbon emissions in the stage of building demolition and recycling.

According to the research in the building norm and literature [21,25], the calculation formula of carbon emissions in each sub-stage of the building life cycle is as follows:

• Building material production stage

According to the IPCC report, the carbon emissions of the production stage of building materials come from the carbon emissions of the material production process, including the carbon emissions of processing, manufacturing, packaging, storage, and other links, that is, the process from the “cradle to the door”. Carbon emissions at the production stage of building materials are calculated according to Equation (2):

$$E_{\mathrm{sc}}={\displaystyle \sum _{i=1}^n{M}_{i}E{F}_{\mathrm{sc},i}}$$

(2)

where M_i denotes the usage amount of the i type of building materials; EF_sc,i denotes the carbon emission factor corresponding to the i type of building material. In this study, the main building materials, such as concrete, steel, cement mortar, and blocks, are considered. The total weight of the selected main building materials should be higher than 95% of the total weight of all building materials, or the building materials with a weight ratio of less than 0.1% should be ignored.

2.

Building material transport stage

Transport carbon emissions will be generated when all kinds of building materials are transferred to the construction site after processing in the factory. The direct source of transport carbon emissions is the power energy consumption of various transport vehicles. Different vehicles consume different types of energy and have different consumption values, and the length of the transport distance will also directly affect the total carbon emissions at this stage. Therefore, the calculation method of carbon emissions in the transport stage is shown in Equation (3):

$$E_{\mathrm{ys}}={\displaystyle \sum _{i=1}^n{M}_i{T}_{\mathrm{jc},i}}E{F}_{\mathrm{ys},i}$$

(3)

where T_jc,i denotes the corresponding transport distance of the i kind of building materials; EF_ys,i denotes the carbon emission coefficient of the transport mode corresponding to the i type of building materials. The transportation mode and transportation distance should be calculated according to the actual transportation of building materials. When the actual data are difficult to obtain, the recommended value of the specification can be used.

3.

Building construction stage

From the perspective of construction activities, on the one hand, the energy consumption of machinery and equipment on the construction site generates carbon emissions, including direct carbon emissions after fuel combustion and indirect emissions of purchased power, which is called the energy consumption of sub-projects. On the other hand, the implementation process of various measures also produces carbon emissions, including the energy consumption of construction auxiliary facilities such as scaffolding and formwork during the construction process, and the energy consumption of lighting and air conditioning equipment in on-site office and residential rooms, which will produce carbon emissions, known as the energy consumption of measure projects. However, the energy consumption of the measure project in the actual project is relatively small, accounting for about 5% of the energy consumption of the branch project, and the data collection of this part is difficult, so the actual calculation can only calculate the carbon emissions of the energy consumption of the branch project. Therefore, the carbon emission in the construction stage is calculated as Equation (4):

$$E_{\mathrm{jz}}={\displaystyle \sum _{i=1}^n{N}_{\mathrm{jz},i}E{F}_{\mathrm{ny},i}}$$

(4)

where N_jz,i denotes the total consumption of the i type of energy; EF_ny,i denotes the carbon emission factor of energy source i.

Energy consumption is calculated according to the volume of sub-projects as Equation (5):

$$N_{\mathrm{jz}}={\displaystyle \sum _{j=1}^n{Q}_{\mathrm{fx},j}{f}_{\mathrm{fx},j}}$$

(5)

where N_jz denotes the energy consumption of sub-projects; Q_fx,j denotes the engineering quantity of the j project in the sub-project during the construction process; f_fx,j denotes the energy consumption coefficient of the j item in the sub-project during the construction process.

The construction energy consumption calculation is optimal if based on the energy consumption ledger of each piece of mechanical equipment on the construction site. If there is no energy consumption record statistical list, it can be determined according to the energy consumption coefficient of the subdivision project. The energy consumption coefficient can be obtained by the mechanical energy consumption coefficient and the engineering quantity quota standard tabulation. When the above data are difficult to obtain, the construction carbon emission can be obtained by referring to the relevant literature data or prediction equation [31,32].

4.

Operation and maintenance stage

The carbon emissions in the building operation stage consists of two parts. First, the carbon emissions in the building operation are caused by the energy consumption in the use of refrigeration, heating, lighting, elevator, and other equipment. The second is the maintenance carbon emissions generated by the use of new building materials during the upgrading of building materials such as the envelope structure, elevator, and pipeline. Maintenance carbon emissions generally consist of two parts: carbon emissions from the production of new building materials and carbon emissions from construction, but the latter account for a relatively small proportion and data collection is difficult, so the maintenance stage can only calculate the carbon emissions consumed by new building materials. Therefore, building operation and maintenance carbon emissions can be calculated as Equation (6):

$$E_{\mathrm{yw}}=E_{\mathrm{oper}}+E_{\mathrm{main}}$$

(6)

where E_oper denotes carbon emission from building operation; E_main denotes building maintenance carbon emissions.

$$E_{\mathrm{oper}}=Y\times {\displaystyle \sum _{i=1}^n{Q}_i\times E{F}_{\mathrm{ny}.i}}$$

(7)

where Y denotes the running time of the building; Q_i denotes the net energy consumption of type i in the operation of the building (i.e., fossil energy consumption after excluding renewable energy).

$$E_{\mathrm{main}}={\displaystyle \sum _{t=1}^n{R}_t\times E{F}_{\mathrm{wh},t}\times D_{\mathrm{cyc},t}}$$

(8)

where R_t denotes the usage amount of the t kind of building materials that need to be replaced in the building maintenance part; EF_wh,t denotes the carbon emission factor corresponding to the replacement of the t type of building materials; D_cyc,t denotes the renewal rate of the t building material over the life of the building.

5.

Building demolition and recycling stage

The building demolition process is divided into three sub-processes: demolition process, waste transportation, and building materials recycling. Among these, the calculation logic of the demolition process is the same as that of the building construction process, and the calculation logic of the waste transportation process is the same as that of the building materials transportation process. The recycling of building materials refers to the negative carbon emissions generated during the recycling of steel, aluminum alloy, and other building materials, that is, the carbon emissions reduced during the production of new building materials, which is taken as a negative value in the calculation. The calculation method is shown in Equation (9):

$$E_{\mathrm{ch}}=E_{\mathrm{demo}}+E_{\mathrm{tran}}+E_{\mathrm{recyc}}$$

(9)

where E_demo denotes carbon emissions in the process of building demolition; E_tran denotes the carbon emissions/kgCO₂ from the removal of waste transportation; E_recyc indicates that the recycling process of recyclable building materials reduces carbon emissions and takes a negative value.

$$E_{\mathrm{demo}}={\displaystyle \sum _{i=1}^n{N}_{\mathrm{demo},i}E{F}_{\mathrm{ny},i}}$$

(10)

where N_demo,i denotes the total consumption of the i energy of each division and project in the process of building demolition.

The energy consumption is calculated according to the sub-project quantity as Equation (11):

$$N_{\mathrm{demo}}={\displaystyle \sum _{j=1}^n{Q}_{\mathrm{demo},j}{f}_{\mathrm{demo},j}}$$

(11)

where N_demo denotes the energy consumption of sub-projects; Q_demo,j denotes the engineering quantity of the j project in the subdivision project in the process of demolition; f_demo,j denotes the energy consumption coefficient of the j item in the subdivision project during the demolition process.

$$E_{\mathrm{tran}}={\displaystyle \sum _{i=1}^n{F}_i{T}_{\mathrm{fq},i}}E{F}_{\mathrm{ys},i}$$

(12)

where F_i denotes the quality of the i waste; T_fq,i denotes the transport distance of the i type of waste, and the transport distance should be based on the actual occurrence value. If the data are insufficient, it should be estimated at 30 km [33].

$$E_{\mathrm{recyc}}={\displaystyle \sum _{i=1}^n{M}_{\mathrm{recyc},i}{f}_{i}E{F}_{\mathrm{recyc},i}}$$

(13)

where M_recyc,i denotes the consumption of the t kind of recyclable building materials; f_i denotes the recycling coefficient of the t kind of recyclable building materials; EF_recyc,i denotes the carbon emission factor corresponding to the t kind of recyclable building material.

The calculation process of carbon emissions during building demolition construction is complicated and data acquisition is difficult, and the carbon emissions at this stage account for less than 5% of the life cycle, so the proportional method can also be used to estimate when the data acquisition is difficult. According to experience, the carbon emissions during building demolition construction account for 8.95% of the carbon emissions during construction [34].

2.2.3. Functional Unit

This study completed the calculation of carbon emissions at each stage of the life cycle of 57 residential buildings in Xi’an. The index of “carbon emission intensity” was adopted for carbon emission evaluation in this study. For the stages that do not involve a time scale, such as building materials production and transportation, carbon emission intensity was expressed by the carbon emission per unit building area (kgCO₂/m²). The carbon emission intensity of the stages related to the time scale, such as operation and maintenance and life cycle, is expressed by the carbon emission per unit of construction area per unit year, namely LCCO₂, (kgCO₂/(m²·a)).

2.3. Carbon Emission Prediction Model in the Design Stage of Building Scheme

Many scholars have carried out research on the prediction of building carbon emissions and proposed many prediction models. However, some of these models have special research boundaries and only focus on one or several life cycle stages. Some prediction methods are complex and require many parameters, which makes it difficult to popularize projects. This study aims to train a convenient and efficient pre-assessment model for building carbon emissions that can be used by designers at any time. Considering the size of the sample library, this paper adopts the multiple linear regression model for prediction.

2.3.1. Introduction to the Prediction Model

A linear regression model consisting of one independent variable and one dependent variable is called unitary linear regression. Multiple linear regression is developed from unitary linear regression, that is, to explore the quantitative dependency between a dependent variable and multiple independent variables. The mathematical model of multiple linear regression is shown as Equation (14):

$$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\cdots +{\beta }_n{x}_n+\epsilon$$

(14)

where y denotes the dependent variable; x₁, x₂, x₃, …, x_n denotes n independent variables; β₀ denotes the constant term, also known as the intercept; β₁, β₂, …, β_n denotes the partial regression coefficient, referred to as the regression coefficient. β_i (i = 1, 2, …, n) denotes the average change in the dependent variable y when the independent variable x_i changes by one unit. ε denotes the residual term, representing random error, and the residual follows the normal distribution N(0, σ²).

The multiple linear regression equation obtained from the sample estimation is shown as Equation (15):

$$\widehat{y}=b_0+b_1{x}_1+b_2{x}_2+\cdots +b_n{x}_n$$

(15)

where $\widehat{y}$ denotes the estimated value of y and the average value of y when a group of independent variables x₁, x₂, x₃, …, x_n; b₁, b₂, …, b_n are the sample estimate values of the model parameters.

When using the multiple linear regression model, the following conditions should be met: (1) there is a causal relationship between the independent variables and the dependent variables in theory; (2) the dependent variable is a continuous variable; (3) there is a linear relationship between the respective variables and the dependent variables; (4) the residual should satisfy the normality, independence, and homogeneity of variance; and (5) there is no multicollinearity between independent variables.

2.3.2. Evaluation Index

In this study, the adjusted determination coefficient (R²_adj), root mean square error (RMSE), and mean absolute error (MAE) were used as evaluation indexes.

The R²_adj is developed from the coefficient of determination (R²). The coefficient of determination, also known as goodness of fit, is used to describe the degree of fit of the data to the model and denotes the degree of interpretation of the independent variable to the dependent variable. The value of R² is between [0,1]; the closer it is to 1, the better the fitting effect, and an R² value of 1 indicates that the independent variable can explain all the dependent variables. The coefficient of determination has important shortcomings in the use of linear regression models; with the increase in the number of independent variables, R² becomes larger and larger, indicating better fitting of the model. However, the larger R² is actually caused by the greater number of independent variables, which deviates from the interpretation of the fitting effect of the model. Therefore, based on the coefficient of determination, the corrected coefficient of determination R²_adj is proposed, which includes the number of independent variables in the formula to avoid the above problems, as shown in Equations (16) and (17).

The mean absolute error denotes the mean of the absolute error between the predicted and observed values, as shown in Equation (18). The RMS error is the sample standard deviation of the residual difference between the experimental and predicted values, as shown in Equation (19). The smaller the mean absolute error and the root mean square error, the better.

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^n{\left(y_i-\widehat{y}\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(16)

$${R^2}_{adj}=1-\frac{n-1}{n-p-1}\left(1-R^2\right)$$

(17)

$$RMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{\left(\widehat{y}-y_i\right)}^2}}{n}}$$

(18)

$$MAE=\frac{{\displaystyle \sum _{i=1}^n\left|{\widehat{y}}_i-y_i\right|}}{n}$$

(19)

where $y_i$ is the actual value, ${\widehat{y}}_i$ is the predicted value, $\overline{y}$ is the average value, p is the number of variables, n is the number of samples.

3. Data Collection

3.1. Data Source

From the previous discussion, we know that a major problem in the current research on the building life cycle model lies in insufficient consideration of the project implementation stage and insufficient understanding of the life cycle carbon emission calculation in the feasibility study and scheme design stage. Design work in these two stages largely determines the carbon emission statistics of the building life cycle. Therefore, this study proposes a two-dimensional framework for carbon emissions in the building life cycle, in which it is proposed that carbon emissions in the feasibility study stage should be estimated by the index method, and carbon emissions in the scheme design stage should be pre-evaluated by the regression formula method. The formulation of such formulas requires a large number of case data as the training basis. Data are derived from life cycle carbon emission inventories for a large number of projects during the preliminary design or construction drawing design stage.

This study collected and analyzed the design data of 57 residential buildings, including the professional design drawings of the architecture, the structure, HVAC, the construction drawing design stage project budget, the building energy saving design report, and other materials. The selected architectural cases are distributed in Yanta District, Lianhu District, Chang’an District and Huyi District, Xi’an City, Shaanxi Province. Xi’an is located in Guanzhong Plain, which belongs to the warm temperate semi-humid continental monsoon climate zone, with a mild climate and moderate rainfall. The thermal division of Xi’an buildings is a cold area, and the heating period is 82 days.

3.2. Data Description

The construction time of the selected case buildings is concentrated from 2017 to 2021. The basic introduction of 57 residential buildings is shown in Figure 3. The construction area is evenly distributed below 20,000 square meters. The number of building floors is concentrated in high-rise buildings, with 25 floors and above accounting for nearly half. The building structure is mainly a shear wall structure and frame shear wall structure, in which the shear wall occupies the absolute majority. The case of this study is evenly distributed and has a wide coverage in terms of building attributes such as area, building height, number of households, body shape coefficient, and average window to wall ratio. The research results have strong explanatory significance for the carbon emission characteristics of residential buildings in Xi’an City.

4. Results and Discussion

4.1. Analysis of Building Life Cycle Carbon Emission Characteristics

After detailed accounting of carbon emissions at each stage of the building life cycle, LCCO₂, the carbon emission intensity index of the building life cycle, can be easily obtained, as shown in Figure 4. As can be seen from the figure, the operation and maintenance stage and building materials production stage are the life cycle stages that contribute most of the carbon emissions, and the sum of the two stages contributes 92.3% of the carbon emissions. The calculation or prediction of carbon emissions in the life cycle of buildings is essentially the calculation or prediction of carbon emissions in the production, operation, and maintenance stage of building materials. The carbon emission intensity of the operation and maintenance stage is between 35 and 40 kgCO₂/(m²·a), the carbon emission intensity of the building materials production stage is between 10 and 15 kgCO₂/(m²·a), and the carbon emission intensity of the whole life cycle is about 45~55 kgCO₂/(m²·a). In addition, the carbon emissions of the building materials transportation and construction stage are similar and small, and the sum does not exceed 5%. The low carbon emissions ratio of the two is the main reason why the proportion method is used to estimate them in many studies. In all cases, the carbon emissions of the demolition and recycling stage are negative, which means that the carbon emissions saved by the recycling of building materials are greater than the combined carbon emissions of the demolition itself and the waste transportation at that stage. There is little difference in the carbon emission intensity of the same life cycle stage among all cases, and the frequency distribution diagram of carbon emission intensity of each major stage is drawn, as shown in Figure 5.

The distribution fitting plots based on a probability density function for the carbon emission intensity of the building life cycle, building material production stage, building material transportation stage, and operation and maintenance stage all conform to the characteristics of the lognormal distribution on the whole, and are skewed to the right to different degrees. The expected carbon emission intensity of the life cycle and building materials production stage is 50.0 kgCO₂/(m²·a) and 665.6 kgCO₂/m², respectively, with a high concentration. The expected value of the two parts can be used as a reference value for estimating carbon emissions in the feasibility study stage by the indicator method. The expected value of the transport stage of building materials is about 7.6% of the production stage of building materials, which is close to the estimated value in the literature, in which the transport stage accounts for about 10% of the carbon emissions in the production stage, considering that the frequency distribution of this stage is not highly concentrated and skewed to the right. The carbon emission intensity in the operation and maintenance stage is highly concentrated, and the expected value is 1769.9 kgCO₂/m², which can be used as an estimate when the operation energy consumption simulation is inconvenient.

4.2. Construction of Prediction Model

4.2.1. Linear Analysis of Variables

The life cycle carbon emissions (LCCE, unit tCO₂) of a building are generally related to the basic parameters of the building, such as the area, floor number, and number of households, and also to the thermal parameters, such as the heat transfer coefficient of the exterior wall (Wall-K), exterior window (Windows-K), and roof (Roof-K). In search of sufficiently complete explanatory variables, in this study, area, floor number, story height, building height, number of households, building surface area, building volume, shape factor, standard floor area, south window wall ratio (S-WWR), north window wall ratio (N-WWR), east window wall ratio (E-WWR), west window wall ratio (W-WWR), average window wall ratio (M-WWR), Wall-K, Windows-K, and Roof-K were collected from architectural design drawings, HVAC design drawings, and building energy saving design books. The explanatory variables are X₁, X₂, …, X₁₇. Because the orientation of all building samples in the case database is in the north and facing south, and located in Xi’an, the two variables of orientation and location are ignored.

In order to verify the linear relationship between the respective variables and the dependent variables, a scatter plot covering the regression line is drawn in Figure 6.

As can be seen from the figure, 17 explanatory variables and dependent variables all had linear relationships, meeting the basic requirements of linear regression models. In addition, the six variables of building area, number of floors, height, number of households, surface area, and volume have a strong correlation with the dependent variables, especially the building area, indicating that building area is an important explanatory variable of LCCE. The linear relationship between the remaining variables and the dependent variables is not significant, and further analysis is needed.

During model training, if there is an order of magnitude difference between the values of each explanatory variable, the role of the independent variable with a larger value in the model trained by the original data will be amplified, while the role of the independent variable with a smaller value will be weakened, and the model will have a certain degree of distortion. In order to eliminate the difference of orders of magnitude and give all explanatory variables the same weight, it is necessary to standardize the original data before model training. Data standardization includes Min-Max standardization, Z-Score standardization, mean normalization, and other methods. In this study, the Z-Score standardization method, which is most commonly used in regression analysis, was adopted for data standardization.

4.2.2. Correlation Analysis and VIF Validation

In Figure 7, red denotes a positive correlation, while blue denotes a negative correlation. The greater the absolute value of the corresponding number of the two variables, the stronger the correlation. It can be seen that X₁ (area), X₂ (floor number), X₄ (building height) X₅ (number of households), X₆ (building surface area), X₇ (building volume), X₉ (standard floor area), and LCCE have a strong correlation, and all pass the significance test. X₈ (shape factor), X₁₅ (Wall-K), X₁₆ (Windows-K), and X₁₇ (Roof-K) have a weaker correlation, but also passed the significance test. However, correlation analysis cannot be used as the sole criterion for variable screening because there may be collinearity between different variables, so it is necessary to carry out collinearity diagnosis for each variable. The variance inflation factor (VIF) is a measure of the severity of co-linearity in multiple linear regression models. The value of VIF is greater than 1, and the closer it is to 1, the weaker the multicollinearity will be; otherwise, the more serious it will be. It is considered that there is no multicollinearity; when 1 < VIF < 10, there is no multicollinearity. When 10 ≤ VIF < 100, there is a strong collinearity. When VIF ≥ 100, it is considered that there is severe collinearity, which is unacceptable [35]. For example, through collinearity diagnosis of the above 17 independent variables, it is found that the VIF values of building surface area and building volume are both greater than 100. In fact, there is an obvious logical relationship between the shape factor variables in the variable group and the two variables. The collinearity of such variables with a strong logical relationship is typical in collinearity problems, which can be solved by retaining some variables. The remaining explanatory variables were re-tested by the same screening method, and the 11 independent variables finally determined by the prediction model were obtained, as shown in

Table 2. Independent variables for predictive model after VIF diagnosis.

Independent Variable	Name	VIF
X1	Floor area	5.177
X2	Floor Number	4.934
X3	Story height	1.359
X5	Household number	5.451
X8	Form factor	1.907
X10	S-WWR	1.648
X11	N-WWR	2.184
X14	M-WWR	2.567
X15	Wall-K	3.879
X16	Window-K	3.752
X17	Roof-K	4.06

.

4.2.3. Model Construction Result

Before the model was constructed, the prediction set and validation set were divided according to the ratio of 8:2. The rationality of the division into the prediction set and verification set is directly related to the effectiveness of model testing. This study divided the data set according to the Y-value sequence method. The specific method was as follows: the data set was arranged in ascending order according to the value of the dependent variable (i.e., LCCE value), and the fifth group of every five data sets was taken as the verification set from top to bottom, with a total of 46 prediction sets and 11 verification sets. According to the above model introduction and variable selection results, with life cycle carbon emissions as the dependent variable and 11 explanatory variables as the independent variables, a multiple linear regression model was constructed for the prediction set as follows:

$$\begin{array}{ll}\mathrm{y}=& 1390+2.414x_1+76x_2+144x_3+7.98x_4-10232x_5\\ & +3207x_6+6559x_7-11869x_8+2280x_9+522x_{10}-2430x_{11}\end{array}$$

(20)

where y denotes the building life cycle carbon emissions; x₁ denotes the area; x₂ denotes the floor number; x₃ denotes the story height; x₄ denotes the number of households; x₅ denotes the shape factor; x₆ denotes S-WWR; x₇ denotes N-WWR; x₈ denotes M-WWR; x₉ denotes Wall-K; x₁₀ denotes Windows-K; x₁₁ denotes Roof-K.

The R²_adj of the model was 0.985, which indicates that the model has high reliability. The Durbin–Watson test was used for model independence, and this model’s value was 1.889, indicating that residuals and independent variables were independent of each other, and there was no autocorrelation in the error of the regression model. As shown in Figure 8a, the frequency histogram was drawn for the standardized residual of the model, and it is obvious that the residual of the training model basically accords with the normal distribution. The standardized predicted values were used to make a scatter plot of the standardized residuals. As shown in Figure 8b, the standardized residuals were randomly and evenly distributed on both sides above and below the horizontal line 0, and the variances were considered to be basically equal, thus proving the homogeneity of variances.

4.3. Validation of Predictive Models

The accuracy of the prediction model is the most important evaluation criterion for the fitting effect of the model. The calculated values and predicted values of the above fitted multiple linear regression model were compared graphically, as shown in Figure 9, in which the calculated values and predicted values of the prediction set and the verification set are also compared. As can be seen from the figure, the predicted values are all near the y = x line; 75% of the samples are within ±10% of the error line; the dispersion of the predicted values is small; and the prediction performance of the model is good. In order to more intuitively express the difference between the calculated value and the predicted value of carbon emissions in the sample set, a line chart was drawn, as shown in Figure 10. Meanwhile, three evaluation indexes of the model, R²_adj, MAE, and RMSE, are calculated in

Table 3. Evaluation index of the life cycle carbon emission prediction model.

Model	R2adj	Mean Value	MAE	RMSE	MAE Error	RMSE Error
LCCE prediction model	0.985	30,505	2684	3418	8.80%	11.20%

.

In order to see more clearly the deviation of the predicted value relative to the calculation value, the sample data in Figure 10 are arranged in ascending order according to the LCCE value. On the whole, the difference between the predicted value and the calculated value of each building carbon emission is small, and most of the difference is around 3000 tCO₂. Considering the differences in the research boundaries, carbon emission factors, and data acquisition in the field of building carbon emission, this error is very significant for building carbon emissions. As shown in Table 3, the adjusted determination coefficient, R²_adj, of the prediction model is 0.985, indicating that the fitted model has a fairly high reliability, and the 11 independent variables selected can explain most of the changes in the dependent variables. The mean absolute error, MAE, is within 2684 tCO₂, and the root mean square error is about 3418 tCO₂, which is consistent with the conclusions in Figure 10. Compared with the calculated average carbon emissions of 30,505 tCO₂, the error of these two parameters relative to the average value of the dependent variable is 8.80% and 11.20% respectively, both of which are about 10% and consistent with the conclusions of Figure 9.

In contrast to the experimental research, the research results of different scholars in the field of building carbon emissions may be quite different. The reason for this is that the research boundaries cannot be strictly consistent based on different research purposes, and the basic data for carbon emission calculation obtained from different building cases also have different levels of precision. Because of these two reasons, it is difficult to obtain highly accurate prediction models, like those in experimental research, in this field. The R²_adj of the multiple linear regression model proposed in this study is 0.985, and the model’s ability to explain the dependent variables is at a relatively high level. This model is expected to provide a simple and reliable tool for architects to estimate the life cycle carbon emission level of the project in the initial stage of architectural design. Of course, the model should further improve the interpretation accuracy and reduce the number of explanatory variables in future studies, so as to make the model more concise and reliable.

5. Conclusions

After calculating the life cycle carbon emissions of 57 buildings in Xi’an, this study analyzed the carbon emission characteristics of residential buildings in this area, and then proposed a carbon emission prediction model for the design stage of building schemes. The main contents and conclusions are as follows:

(1)

This study proposed a two-dimensional carbon emission framework for the building life cycle, which combines five project implementation stages, namely the feasibility study, scheme design, preliminary design, construction drawing design, and completed operation, with all stages of the building life cycle, and provided carbon emission pre-assessment methods for each building project implementation stage, so as to grasp the level of building carbon emission in the early stage of design. This study guided the selection of the design scheme and provided data support for the formulation of the carbon reduction scheme.

(2)

The life cycle carbon emissions of 57 residential buildings in Xi’an were calculated, and it was found that the life cycle carbon emission intensity was about 45~55 kgCO₂/(m²·a). The operation and maintenance stage and building materials production stage contributed most of the carbon emissions, and the sum of the two stages contributed 92.3% of the carbon emissions. The distribution fitting graph based on the probability density function for the carbon emission intensity of the building life cycle, building material production and transportation, stage and building operation and maintenance stage is in line with the lognormal distribution on the whole, and its expected value can be used as a reference value for estimating building carbon emissions by the index method of the feasibility study stage.

(3)

Eleven independent variables affecting building carbon emissions, namely area, floor number, story height, number of households, shape factor, S-WWR, N-WWR, M-WWR, Wall-K, Windows-K, and Roof-K were studied and determined. On this basis, a multiple linear regression model was proposed for carbon emission pre-assessment in the design stage of building schemes. The model error is about 10%.

Architectural designers need to know the life cycle carbon emission level and characteristics of the building project before the building is completed, so as to reduce the carbon emission intensity index by changing the materials and modifying the design, and thereby meet various laws and regulations. However, at present, most common building carbon emission calculation methods are based on inventory statistics, and the calculation process requires the support of a large number of building design data. In fact, this stage has approached the building construction, and even if the carbon emission intensity index of the building is found to be excessive, the building design cannot be changed. Therefore, there is an urgent need for a carbon emission prediction method that allows the design to be easily changed and is suitable for the early stage of the architectural design (such as the architectural scheme design stage), during which architectural design data and design parameters are scarce. The multiple linear regression prediction model proposed in this paper effectively solves this problem. The research method and the construction process of the prediction model described in this paper can provide guidance for the future research of the same type, and the proposed prediction model is conducive to the optimization and emission reduction of the future building design process.