Carbon Emission Prediction of Freeway Construction Phase Based on Back Propagation Neural Network Optimization

Abstract

As a large-scale transportation infrastructure project, the construction of a freeway will consume a large amount of high-energy and high-density raw material products and emit a large amount of carbon dioxide. Selecting route options with lower carbon emissions during the preliminary design phase of a project is one effective way to mitigate carbon emission pressure. This study collected 124 highway construction cases and calculated the carbon emissions generated during the construction of each case. By utilizing the grey relational analysis method, we assessed the degree of association between various indicators and carbon emissions, identifying the primary indicators influencing carbon emissions. Furthermore, we integrated multiple strategies to improve the northern goshawk optimization algorithm and optimize the BP neural network, thereby establishing a carbon emission prediction model for the highway construction phase. Using this model, we predicted the carbon emission data per kilometer of two different highway route options, which were 2.2959 t and 4.3009 t, respectively, and recommended the route option with lower carbon emissions. This model addresses the challenge faced by highway construction units in quantifying carbon emissions for different route options during the preliminary design phase, providing a basis for adjusting and comparing route options from a low-carbon perspective.

1. Introduction

As one of the greenhouse gases most closely associated with human activity, CO₂ emissions have been increasing over the past few decades causing a global radiative imbalance that contributes 63.5 percent of the total global radiative forcing [1]. At the end of the 20th century, mankind began to work together to address the environmental threats posed by greenhouse gases, signing the Paris Agreement and introducing policies and measures to control carbon emissions [2]. Carbon emissions from the transportation sector account for a high and rising share of carbon emissions from major industries [3]. Reducing the level of carbon emissions in this industry and building a green and efficient transportation system are of great significance to the implementation of energy saving and carbon reduction. In the transportation industry, freeway transportation is the absolute main body of CO₂ emissions and the focus of emission reduction, and controlling and reducing carbon emissions from freeway transportation are effective ways to alleviate the pressure of carbon emissions. Therefore, the study of freeway carbon emissions is crucial to the implementation of the low-carbon concept and the realization of carbon neutrality.

As a large-scale transportation infrastructure project, the construction of a highway will consume a large amount of high-energy and high-density raw materials and emit a large amount of carbon dioxide [4]. At present, there are various methods for calculating carbon emissions during the construction phase of highways, such as the emission factor [5], actual measurement [6], input–output and mass balance [7], etc., among which the emission factor method is more widely used due to its simple and easy-to-operate advantages. However, the above methods or those based on various types of energy consumption data or the use of monitoring facilities to calculate carbon emissions, which are mostly applicable to the completion of the project construction, cannot be used in the beginning of the design of highway projects to quickly and accurately quantify the carbon emissions generated by the construction of the project, and it is difficult to provide a basis for the adjustment of the route program, the comparison, and the selection. Once the design plan for a highway is finalized, pursuing energy conservation and carbon reduction during the construction stage can only involve seeking breakthroughs in minor aspects, such as material optimization, construction techniques, and management technologies, which have a relatively limited impact on the overall carbon emissions of the project. Determining the amount of carbon emissions in the design plan prior to engineering construction is crucial for reducing carbon emissions.

In order to solve the drawbacks of traditional calculation methods, scholars at home and abroad have begun to utilize different methods to construct carbon emission prediction models. Aggarwal et al. [8] analyzed the energy demand and carbon emissions of road transport in the Delhi region and estimated the energy demand and CO₂ emissions using an integrated framework (ASIF). In the study by Chen and others [9], continuous measurements of CO₂, TVOC, and HCHO were conducted in five rooms of SDE and NUS. The collection data were trained and tested by four machine learning algorithms, including a support vector machine (SVM), Gaussian processes (GPs), M5P, and a backpropagation neural network (BPNN). Khan et al. [10] proposed a new model based on data mining and supervised machine learning algorithms (regression and classification) and applied an ensemble technique (bagging and boosting) to the developed multilayer perceptron model to predict the GHG emissions generated from passenger and freight transportation on Canadian highways. Yanmin Qu [11] and others took the backbone highway network in Hubei Province as the research object and used two indicators, total CO₂ emission and transportation CO₂ emission intensity, to predict and compare different development modes, and they put forward rationalization suggestions for the development of highway transportation in Hubei Province according to the prediction results. In the study by Singh M [12], a scalable vehicle CO₂ emission prediction model is proposed which uses vehicle on-board diagnostics (OBD-II) port data. The proposed system uses real-time in-vehicle sensor data to estimate the CO₂ emissions of the vehicle using a recurrent neural network (RNN)-based long short-term memory (LSTM) model. Huitian Liu [13] and others took the 15-year transportation carbon emission data of 30 provinces as the basis and combined the two methods of the Pearson correlation coefficient and Spearman rank correlation coefficient to screen the influencing factors of transportation carbon emission as the prediction index; they constructed the prediction model by using various machine learning algorithms, such as decision tree, random forest, XGBoost, etc., and evaluated the prediction effect of different models with MSE, MAE, MAPE, and R² and obtained the prediction results of MSE, MAPE, and R². The prediction effects of different models were evaluated, and the conclusion that the XGBoost algorithm is the most suitable for constructing transportation CO₂ prediction models was obtained. Sun, W [14] used carbon emission data from Hebei Province; PCA was applied to reduce the dimensions of the influencing factors and extract two principal components as input variables. The parameters of the LSSVM model were obtained through PSO, and a prediction model was established, proving that the PSO-LSSVM prediction model has higher accuracy. Li, YM et al. [15] used a genetic algorithm to optimize input weights and bias thresholds in an extreme learning machine algorithm called the genetic algorithm extreme learning machine (GA-ELM) algorithm to predict industrial carbon dioxide emissions. Empirical results showed that the GA-ELM algorithm used five factors as inputs to predict industrial CO₂ emissions with higher accuracy and performance than extreme learning machines, backpropagation neural networks, and genetic algorithm optimized backpropagation neural networks.

Most of the existing carbon emission prediction studies focus on the prediction of carbon emissions from freeways in the whole transportation industry or in a certain region, and there are fewer studies on the prediction of carbon emissions during the construction phase of a specific section of freeway. At the initial stage of highway design, there are usually different route options to choose from, but the carbon emissions that may be generated by highway construction at this stage are difficult to measure quickly and accurately, making it impossible to choose a more environmentally friendly, low-carbon route option. This paper takes the highway construction stage as the research object, collects sufficient engineering examples and calculates their carbon emissions, uses intelligent algorithms to explore the relationship between the relevant parameters of the route scheme and the carbon emissions, and constructs a carbon emissions prediction model. The model can quickly predict the carbon emissions of the route scheme in the preliminary design stage of the highway and provide a basis for the adjustment and comparison of routes from the perspective of green and low-carbon energy.

2. Materials and Methods

2.1. Carbon Emission Calculation Methodology

Analyzed using the life cycle assessment [16], the freeway construction phase contains three processes: material production, material transportation, and construction [17], which consume a large number of high-energy and high-density material products, and most of the materials cannot be directly mined; to obtain the materials, they need to be processed and synthesized through a series of procedures; the material production process burns energy as a driving force to generate a large amount of carbon emissions. The process of material production and processing at the construction site requires transportation by means of energy consumption, which in turn generates carbon emissions; the construction site operation involves the use of a large amount of mechanical equipment, and the consumption of fossil or electric power energy generates carbon emissions.

The freeway project is divided into a number of individual projects, and the carbon emissions of each individual project are composed of three stages, namely material production, material transportation, and construction; so, an inventory analysis of each individual project at different stages is carried out to determine the quantities of road construction materials, off-site processing machinery and equipment, transportation vehicles, and on-site construction machinery, and when combined with the carbon emission factor, the carbon emissions of the freeway construction stage can be calculated. The meanings of the specific parameters used in the process are shown in

Table 1. Parameters for calculating carbon emissions during the construction phase of freeways.

Parameters	Description of Definitions
$i$	Individual projects, i = 1, 2, …
$l$	l = 1, 2, 3 Corresponding to the three phases of material production, material transportation, and construction, respectively
$C_i^l$	Type l carbon emissions from individual projects in category
$r$	Types of road construction materials, r = 1, 2, …n
$s$	Type of transport machinery, s = 1, 2, …n
$t$	Type of construction machinery, t = 1, 2, …n
$Q_i^r$	Consumption of rth material for individual items of work in category i
$Q_i^s$	Shifts consumed by type y of transportation machinery for individual projects in category i
$Q_i^t$	Shifts consumed by type t of construction machinery for individual projects of category i
$f^r$	Carbon emission factors for category r materials
$f^s$	Carbon emission factors for category s transportation machinery
$f^t$	Carbon emission factor for category t construction machinery
$C_i$	Carbon emissions from individual projects in category i
$C$	Carbon emissions from freeway construction phase

.

• Carbon emissions at the material production stage:

  $$C_i^1={\displaystyle {\sum }_{r=1}^n{Q}_i^r}\times f^r$$

  (1)
• Carbon emissions at the material transportation stage:

  $$C_i^2={\displaystyle {\sum }_{s=1}^n{Q}_i^s}\times f^s$$

  (2)
• Carbon emissions during the construction phase:

  $$C_i^3={\displaystyle {\sum }_{t=1}^n{Q}_i^t}\times f^t$$

  (3)

Carbon emissions from individual projects:

$$C_i={\displaystyle {\sum }_{l=1}^3{C}_i^l}$$

(4)

Carbon emissions during the freeway construction phase:

$$C={\displaystyle {\sum }_{i=1}^9{C}_i}$$

(5)

2.2. Neural Network Construction Method

Common intelligent algorithms include regression algorithms [18], support vector machines [19], random forests [20], backpropagation neural networks [21], memetic neural networks [22], convolutional neural networks [23], etc., and after gaining an understanding of the intelligent algorithms and conducting an applicability analysis, this paper selects three algorithms: long short-term memory (LSTM), the backpropagation (BP) neural network, and the convolutional neural network (CNN) to build prediction models. It verifies the feasibility of using intelligent algorithms to accurately and rapidly predict carbon emissions during the construction phase of highway projects at the preliminary design stage. The prediction model based on the BP neural network performs better, demonstrating superior generalization and fault tolerance capabilities. Therefore, the BP neural network-based prediction model is chosen for further optimization and improvement.

The backpropagation neural network is a multilayer feed-forward neural network that is trained by the error backpropagation algorithm. It contains an input layer, a hidden layer, and an output layer, and through a special feedback mechanism, it can learn to calculate the error in reverse and adjust the network weights to achieve learning and optimization [24]. The input data are processed by the activation function in the implicit layer and forward-propagated to the output layer to obtain the output value; the loss function is used to calculate the error between the actual output of the network and the desired output, and the mean square error is commonly used as the loss function; the gradient of the loss function with respect to the weights is calculated by the chain rule, and this is used to update the network weights so as to minimize the loss function; a gradient descent rule is used to continually update the network weights and thresholds, until the network error satisfies the condition or the number of iterations reaches the set value. The structure of BP neural network is shown in Figure 1.

In this paper, the tansig function is used as the activation function of the hidden layer to construct the BP neural network to increase the nonlinear fitting ability of the model, and the purelin function is used as the activation function of the output layer to keep the output unchanged. With the predictive indicators as the input layer, the number of nodes in the input layer is the number of predictive indicators; with the carbon emissions as the output layer, the number of nodes in the output layer is 1. The number of nodes in the hidden layer determines the expressive ability and complexity of the network, and if the number of nodes is too small, it will lead to insufficient fitting ability; too many will easily lead to overfitting; this is determined according to empirical Equation (6) [24].

$$l=\sqrt{m+n}+a$$

(6)

where $l,m,n$—Refers to the number of nodes in the hidden layer, input layer, and output layer, respectively; $a$—Refers to a constant between 1 and 10.

2.3. Optimization Methods for Neural Networks

Although the BP neural network has strong self-learning ability, excellent nonlinear fitting capability, and good generalization performance, it is highly sensitive to initial weights, which affect the gradient values and the weight update amount during each iteration, thereby influencing the final training results. Optimizing the initial weights through algorithms can enhance the stability of the model. In recent years, commonly used neural network optimization methods include genetic algorithms [25], particle swarm optimization [26], northern goshawk optimization [27], the sine cosine algorithm [28], and the opposite study of refraction [29]. The advantages, disadvantages, and applicable scopes of the different algorithms are summarized in

Table 2. Comparison of commonly used optimization algorithms.

Algorithms	Superiority	Limitations	Applicable Scenarios
Genetic Algorithms	Strong global search capability, high adaptability, high parallelism, and good robustness.	High computational complexity, parameter sensitivity, slow convergence speed, and poor interpretability.	Complex nonlinear problems, multi-objective optimization, discrete or mixed optimization.
Particle Swarm Optimization	Fast convergence speed, few parameters, simple implementation, and strong adaptability.	Prone to local optima, parameter sensitivity, limited support for discrete problems, and poor robustness.	Continuous optimization problems, single-objective optimization, fast convergence scenarios.
Northern Goshawk Optimization	Strong global search capability, fast convergence speed, few parameters, and strong adaptability.	Limited research, with limited effectiveness for high-dimensional problems.	Continuous and discrete optimization problems, global search and fast convergence scenarios, low-dimensional or moderate-dimensional problems.
The Sine Cosine Algorithm	Simple implementation, strong global search capability, few parameters, and strong adaptability.	Slow convergence speed, limited support for discrete problems.	Continuous optimization problems, global search scenarios, low-dimensional or moderate-dimensional problems.
The Opposite Study of Refraction	Enhanced global search capability, improved convergence speed, strong adaptability, and few parameters.	Increased computational complexity, with limited effectiveness for high-dimensional problems.	Continuous, discrete, and mixed optimization problems, combined with other algorithms.

.

Considering the characteristics of the model constructed in this paper, this study integrates the sine cosine algorithm, refraction opposition-based learning, and northern goshawk optimization to optimize the BP neural network.

2.3.1. Northern Goshawk Optimization

Northern goshawk optimization is a swarm intelligence optimization algorithm proposed by Mohammad Dehghani; it is able to optimize the weight thresholds of BP neural networks to improve the overall and local optimal performance, thus improving the accuracy of BP neural network models. The algorithm simulates the process of preying on prey by a hawk in a vast space, which is divided into two phases: exploration and exploitation [30]. At the beginning of the algorithm, the northern goshawk acts as a searcher and randomly initializes population members in the search space [31].

Population size matrix:

$$X={\left[\begin{array}{c}{X}_1\\ ⋮\\ X_i\\ ⋮\\ X_N\end{array}\right]}_{N\times m}={\left[\begin{array}{ccccc}{x}_{1,1}& \cdots & x_{1,j}& \cdots & x_{1,m}\\ ⋮& & ⋮& & ⋮\\ x_{i,1}& \cdots & x_{i,j}& \cdots & x_{i,m}\\ ⋮& & ⋮& & ⋮\\ x_{N,1}& \cdots & x_{N,j}& \cdots & x_{N,m}\end{array}\right]}_{N\times m}$$

(7)

where $X_{i,j}$—Position of the jth dimension of the ith goshawk; $N,m$—Refers to the size of the population and the dimension of the solution problem, respectively.

Objective function vector:

$$F={\left[\begin{array}{c}{F}_1\\ ⋮\\ F_i\\ ⋮\\ F_N\end{array}\right]}_{N\times 1}={\left[\begin{array}{c}F\left(X_1\right)\\ ⋮\\ F\left(X_i\right)\\ ⋮\\ F\left(X_N\right)\end{array}\right]}_{N\times 1}$$

(8)

where $F_i$—Refers to the value of the objective function for the ith goshawk.

During the exploration phase, the northern goshawk randomly selects prey and pursues it with the following mathematical expression:

$$P_i=X_k;i=1,2,\dots ,N;k=1,2,\dots i-1,i+1,\dots ,N$$

(9)

$$X_{i,j}^{new,P1}=\{\begin{array}{c}{x}_{i,j}+r\cdot \left(P_{i,j}-I{x}_{i,j}\right),F_{Pi}<F_i\\ x_{i,j}+r\cdot \left(x_{i,j}-P_{i,j}\right),F_{Pi}\ge F_i\end{array}$$

(10)

$$X_i=\{\begin{array}{c}{X}_{i,j}^{new,P1},F_i^{new,P1}<F_i\\ X_i,F_i^{new,P1}\ge F_i\end{array}$$

(11)

where $P_i$—Prey location of the ith goshawk; $F_{Pi}$—The value of the objective function for the prey location of the ith goshawk; $X_{i,j}^{new,P1}$—The new location of the jth dimension of the ith goshawk after the survey phase update; $F_{i,j}^{new,P1}$—Objective function values for the jth dimension of the ith northern goshawk after the survey phase update; $k,r$—Random integers in the range [1, N] and random numbers in the range [0, 1], respectively.

After the northern goshawk attacks the prey, the prey tries to escape; in the case of pursuit, it is assumed that this hunt is in the attack position with radius R. The mathematical expression for this phase is as follows:

$$x_{i,j}^{new,P2}=x_{i,j}+R\cdot \left(2r-1\right)\cdot x_{i,j}$$

(12)

$$R=0.02\left(1-{\displaystyle \frac{t}{T}}\right)$$

(13)

$$X_i=\{\begin{array}{c}{X}_{i,j}^{new,P2},F_i^{new,P2}<F_i\\ X_i,F_i^{new,P2}\ge F_i\end{array}$$

(14)

where $t,T$—The current iteration number and the maximum iteration number, respectively; $X_{i,j}^{new,P2}$—New location of the ith northern goshawk after the development phase update; $F_{i,j}^{new,P2}$—The value of the objective function for the first northern eagle after the development phase update.

2.3.2. Improving the Northern Goshawk Optimization by Incorporating Multiple Strategies

The northern goshawk optimization has the advantages of a simple principle and high accuracy in searching for superiority, but it also has the limitations of slower convergence speed and poorer balance between global and local searching abilities; so, it is first improved by integrating various strategies to improve the northern goshawk optimization (NGO) and to improve the convergence speed and searching ability of the algorithm; then, the BP neural network is optimized by using improved northern goshawk optimization.

• Introducing the Opposite Study of Refraction

The opposite study of refraction combines the principle of light refraction with inverse learning, which expands the range of the optimization search on the basis of inverse learning and significantly enhances the ability to jump out of local extremes [32]; its schematic diagram is shown in Figure 2. The opposite study of refraction is used to initialize the individual northern goshawk optimization, which is able to expand the search range by calculating the inverse solution of the current solution to discover a better alternative solution [33].

It is assumed that $x_{i,j}$ is an individual northern goshawk generated by the random initialization of the NGO algorithm in the search space, and $x_{i,j}^{\ast }$ is a solution using refractive inverse position, which can be obtained according to the principle of the opposite study of refraction:

$$x_{i,j}^{\ast }={\displaystyle \frac{a_j+b_j}{2}}+{\displaystyle \frac{a_j+b_j}{2\mu }}-{\displaystyle \frac{x_{i,j}}{\mu }}$$

(15)

$$\mu =h/h^{\ast }$$

(16)

where $a_j$, $b_j$—Refers to the minimum and maximum values in the optimization search range, respectively; $x_{i,j}$—Position of the ith goshawk in the jth dimension within the population; $\mu$—Scaling factor for lenses; $h$, $h^{\ast }$—Refers to the lengths of the incident and refracted rays, respectively.

2.

Introducing the Sine Cosine Algorithm

The sine cosine algorithm (SCA) is a new swarm intelligence optimization algorithm proposed by Seyedali Mirjalili; it uses the oscillatory change characteristics of the sine cosine model to act on the individual positions to increase the diversity of the individuals and continuously approach the global optimum [34]. The sine cosine algorithm is used to replace the position update formula in the exploration phase of the northern goshawk optimization, and the step search factor of the sine cosine algorithm is improved by replacing $r_1$ with ${r_1}^{\prime }$, which balances the global search and local exploitation capabilities of the northern goshawk optimization. The formula for the new position of the jth dimension of the ith northern goshawk after the exploration phase update is as follows [35]:

$$x_{i,j}^{new,P1}=\{\begin{array}{c}{x}_{i,j}^{\ast }+{r_1}^{\prime }\times \sin \left(r_2\right)\times \left|r_3{P}_{i,j}-x_{i,j}^{\ast }\right|,r_4<0.5\\ x_{i,j}^{\ast }+{r_1}^{\prime }\times \cos \left(r_2\right)\times \left|r_3{P}_{i,j}-x_{i,j}^{\ast }\right|,r_4\ge 0.5\end{array}$$

(17)

$${r_1}^{\prime }={\left(1-{\left({\displaystyle \frac{t}{T}}\right)}^{\eta }\right)}^{1/\eta }$$

(18)

where $x_{i,j}^{\ast }$—The location of the jth dimension of the ith goshawk of the solution is learned using the opposite study of refraction update; $P_{i,j}$—The current prey position of the jth dimension of the ith northern goshawk of the solution; $r_2$, $r_3$, $r_4$—Random numbers, $r_2\in \left[0,2\pi \right]$, $r_3\in \left[0,2\right]$, $r_4\in \left[0,1\right]$; $\eta$—Adjustment coefficient, $\eta \ge 1$.

The optimization of the BP neural network using the improved northern eagle algorithm is shown in Figure 3.

2.4. Data Sources

Since there is no special database for the carbon emissions of the highway construction stage, only the bill of quantities of actual cases can be collected, combined with the corresponding carbon emission factors through the calculation of the highway construction stage using the carbon emission calculation method, to obtain the emissions [36]. In this paper, a total of 124 highway projects were collected, including the bill of quantities and the related predictive index values, and the carbon emissions of a project were calculated and associated with its predictive indexes to form the sample data, part of which is shown in Figure 4.

3. Model Predictions and Analysis of Results

3.1. Selection of Predictive Indicators

3.1.1. Selection of Relevant Variables

At present, there are fewer related researches using intelligent algorithms to predict carbon emissions in the construction phase of freeways; this paper consults relevant experts in the field on the basis of combing and summarizing the carbon emission prediction research of related projects; it obtains the information from the indicators that can be used as the indicators for predicting carbon emissions in the construction phase of freeways and obtains a preliminary list of the indicators for carbon emission prediction, as shown in

Table 3. Preliminary list of indicators for carbon emission projections.

No.	Indicator Name	Unit	No.	Indicator Name	Unit
1	Area of freeway land	acres	11	Excavation	m3
2	Number of interconnections	individual	12	Fill volume	m3
3	Total cost	million dollars	13	Electricity consumption	kw·h
4	Total length of route	km	14	Asphalt consumption	t
5	Length of roadbed	km	15	Cement consumption	t
6	Length of road surface	km	16	Diesel consumption	kg
7	Bridge culvert length	km	17	Aggregate consumption	m3
8	Tunnel length	km	18	Reinforcing steel consumption	kg
9	Length of intersection works	km	19	Gasoline consumption	kg
10	Number of service areas	individual	20	Coal consumption	t

.

3.1.2. Predictive Indicator Identification

There are a large number of carbon emission prediction indicators in the preliminary list, and in order to ensure that the constructed prediction model is accurate and referential while being easy to use and convenient, the indicators need to be screened.

The common feature selection methods include grey relational analysis [37], principal component analysis [38], analytic hierarchy process [38], and recursive feature elimination [39], among others. The advantages, disadvantages, and applicable scopes of these methods are summarized in

Table 4. Comparison of commonly used feature selection methods.

Methods	Superiority	Limitation	Applicable Scenarios
GRA	Applicable to small sample sizes, capable of handling incomplete information, and computationally simple.	The results only provide a ranking of correlations, lacking in-depth explanations of causal relationships.	Applicable to small sample sizes, high uncertainty, and incomplete information data.
PCA	Effective dimensionality reduction, eliminates redundant information, unsupervised learning, and high computational efficiency.	The results are principal components, with limited interpretability, requiring further analysis of the actual significance of the components. Sensitive to missing data, necessitating data imputation or deletion of missing samples.	Dimensionality reduction for high-dimensional data, data denoising, and analysis of linearly separable data.
AHP	Combines qualitative and quantitative analysis, structured decision making, with intuitive results.	Highly subjective, with high computational complexity and stringent requirements for consistency testing.	Multi-objective, multi-criteria decision making, and small-scale data analysis.
REF	Suitable for high-dimensional data, model-driven, and highly flexible.	High computational complexity, sensitive to missing data, requiring data preprocessing.	Feature selection for high-dimensional data, model-driven feature importance analysis.

.

In the sample data of this study, carbon emissions were calculated based on the engineering bill of quantities from actual cases combined with the carbon emission factor method. During the process of collecting the engineering bill of quantities from the actual cases, there were instances where certain indicators were either inaccurate or missing. Among the feature selection methods mentioned above, the grey relational analysis (GRA) method determines the degree of association based on the similarity between the geometric shapes of different factor sequences. It can assess the correlation between various prediction indicators and carbon emissions, screening out important, highly correlated, and representative indicators as prediction indicators. This approach ensures the accuracy of the prediction model while reducing operational complexity. For subsequent predictions of newly built highway projects, one only needs to extract the data of these indicators from the relevant case materials and input them into the trained model to obtain accurate and rapid estimates of the carbon emissions generated by constructing a highway based on that route plan. In this paper, the GRA method is utilized to screen indicators with strong correlations from the initial indicator list as input values, involving five processes: determining the research sequence, non-dimensionalization of the sequence, calculation of grey relational coefficients, calculation of grey relational degrees, and ranking of correlation degrees.

• Determining the study series

In this paper, the carbon emissions generated during the construction phase of the freeway are regarded as the reference sequence, and the 20 predicted indicators in the preliminary list are used as the comparison sequence; the original dataset is shown in

Table 5. Dataset for analysis of carbon emission projection indicators.

X0	477,494.8	897,112.49	987,458.8	115,651.4	317,403.5	242,627.2	346,074.0
X1	1290.903	4486.1	0	1095.6	731.173	1139.38	1441.61
X2	124	59	0	21	4	10	9
X3	802,820.3	533,520.6	239,295.7	92,994.78	162,455.8	98,104.82	142,140.9
X4	9.071	45.285	16.535	10.02	10.156	12.132	17.11
X5	0.249	28.98	0	4.812	1.891	4.367	6.437
X6	0.249	28.98	0	4.812	1.891	8.052	6.437
X7	5.901	8.426	0	2.618	5.225	2.067	3.252
X8	0	1.909	16.535	2.59	1.927	1.618	2.341
X9	2.921	5.97	0	0	1.113	4.08	5.08
X10	1	1	0	0	0	0	0
X11	14,889	6,342,896	0	795,336	390,755	1,690,480	3,114,817
X12	22,949	5,422,121.6	0	823,430	421,413	1,296,981	285,133
X13	24,255,439	63,407,259	94,199,184	4,168,590	27,256,986	19,032,582	30,386,956
X14	5122.89	33,252.23	4018.54	91.56	3883.28	568.83	55.24
X15	263,626.18	516,252.6	575,252.59	73,837.16	179,725.48	162,129.18	228,969.91
X16	4,763,706.4	21,246,383	5,379,334.1	4,407,012.9	2,922,809.5	3,899,906.2	6,546,169.3
X17	575,654.7	2,351,603.6	961,535.55	438,086.05	551,200.04	326,197.14	450,571.48
X18	78,339.13	95,319.5	48,620.38	8942.25	44,789.05	25,432.29	37,779.82
X19	120,474.82	748,112.67	827,689.8	27,808.57	80,113.69	119,510.04	150,976.68
X20	2.18	12.89	9.57	0.89	2.12	10.91	4.74

, where X0 is the reference sequence corresponding to the carbon emissions during the construction phase of the freeway, and X1~X20 correspond to the indicators with the serial numbers 1~20 in the preliminary list of the predicted indicators of the carbon emissions, respectively.

2.

Dimensionless data processing

Since different indicators have different meanings and units, they need to be dimensionless so that different indicators can be mapped to similar value intervals before they can be compared. In this paper, mean normalization is used to conduct the dimensionless processing of data.

$$x={\displaystyle \frac{x-\overline{x}}{\sigma }}$$

(19)

where $\overline{x}$—Average of raw series; $\sigma$—Standard deviation of the original series.

3.

Calculation of correlation coefficients

The carbon emission series differed from the series of 20 indicators, and the absolute values were taken to find out the maximum difference of two levels and the minimum difference of two levels, and the correlation coefficients between each indicator and carbon emissions were found.

Two levels of maximum difference:

$$M=\underset{a}{\max }\underset{b}{\max }\left|x_{a0}-x_{ab}\right|$$

(20)

Two levels of minimum difference:

$$m=\underset{a}{\min }\underset{b}{\min }\left|x_{a0}-x_{ab}\right|$$

(21)

Correlation coefficients:

$${\xi }_{ab}=\left(m+\rho M\right)/\left|x_{a0}-x_{ab}\right|+\rho M$$

(22)

where $\rho$—The resolution coefficient, which generally takes the value in the range of [0, 1], is taken as $\rho =0.5$ in this paper; ${\xi }_{ab}$—Correlation coefficients.

4.

Calculating correlation

The correlation coefficient measures the degree of similarity between the comparison series and the reference series at each point in time. Since the correlation coefficient has multiple values, it is not easy to compare them as a whole. It is common practice to calculate the average of the correlation coefficients at each point in time as a composite indicator of the degree of association between the comparison series and the reference series.

Degree of association:

$$r_i={\displaystyle \frac{1}{n}}{\displaystyle \sum _{a=1}^n{\xi }_{ab}}$$

(23)

where $r_i$—Correlation between the ith comparison sequence and the reference sequence.

5.

Analysis of associated findings

The calculation results show that the value of the correlation between each indicator and the carbon emissions of the freeway construction stage is between 0 and 1, and the larger the correlation, the closer the relationship between the indicator and the carbon emissions. It is usually considered that there is a strong correlation between the two when $r_i>0.8$, a certain correlation between the two when $0.5\le r_i\le 0.8$, and no correlation between the two when $r_i<0.5$. Figure 5 shows that the indicator with the strongest correlation with the carbon emissions in the construction phase of the freeway is the consumption of cement, and the indicator with the weakest correlation is the number of service areas.

Analyzed by the gray correlation method, 10 indicators, including cement consumption, gravel consumption, steel consumption, diesel consumption, total route length, tunnel length, bridge culvert length, crossing length, roadbed length and pavement length, are strongly correlated with carbon emissions, and the rest of the indicators have a certain degree of correlation with carbon emissions. In order to ensure the accuracy of the prediction model and at the same time reduce the operational complexity, the 10 indicators with strong correlation are selected as the prediction indicators.

3.2. Model Parameterization and Training

The model is constructed based on the MATLAB R2022b platform, and the 124 samples organized in the previous section are divided into the training set and test set for subsequent model training and testing. Considering the accuracy of the training results and computing speed, the data cut-off is set to 0.85, i.e., 104 of the 124 samples are randomly selected as the training set data for network learning and training, and the remaining samples are used to test and verify the training effect of the network. At the initial stage of constructing a prediction model using neural networks, this paper selected three algorithms for experimentation: long short-term memory (LSTM), the backpropagation neural network (BPNN), and the convolutional neural network (CNN). The performance of the different models was evaluated using root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R²), with the specific results presented in the

Table 6. Comparison of model evaluation indicators.

Model	RMSE	MAE	R2
BP	3.074	2.269	0.996
LSTM	7.842	4.971	0.985
CNN	6.567	5.159	0.981

. The prediction model based on the BP neural network demonstrated superior performance across all three evaluation metrics. Therefore, the subsequent optimization efforts focused solely on the BP neural network. The following discussion highlights the specific performance of the prediction model before and after optimization.

The learning rate is one of the most important hyperparameters in the BP neural network, as it determines the step size for weight updates during each iteration. According to empirical guidelines, a larger learning rate (e.g., 0.1) is suitable for simple tasks, while a smaller learning rate (e.g., 0.001) is recommended for more complex tasks. During the parameter tuning process, we tested a series of learning rates (0.0001, 0.001, 0.01, and 0.1) and found that the prediction model performed best when the learning rate was set to 0.01. Therefore, this learning rate was used in both the pre- and post-improvement BP neural network models for prediction.

3.2.1. Carbon Emission Prediction Model Constructed Based on BP Neural Network

The model target error is set to 10⁻⁸, the minimum error verification is satisfied after nine iterations, the training duration is 0.5 s, the learning rate is 0.01, the MSE is 9.448, the RMSE is 3.0738, the MAE is 2.269, and the R² is 0.99569; the comparison of the predicted and true values is shown in Figure 6.

3.2.2. Carbon Emission Prediction Model Constructed Based on SCNGO Improved BP Neural Network

The SCNGO-BP model training time is 49 s, the initial population size is 36, the maximum number of iterations is 50, the neural network learning rate is set to 0.01, and the minimum error validation is satisfied after 17 iterations; the MSE is 3.1355, the RMSE is 1.7707, the MAE is 1.395, and the R² is 0.999; the comparison of the predicted and expected values is shown in Figure 7.

3.3. Performance Comparison of Different Network Models

In order to verify whether there is a significant difference between the prediction models before and after the optimization of the BP neural network by the SCNGO algorithm, the models are used to predict the sample test set, and the prediction errors of the two models are shown in Figure 8.

Among the 20 prediction samples, there are 12 SCNGO-BP prediction values with significantly smaller errors, and 3 with errors similar to those of BP, with a clear trend of error reduction. Compared with the BP neural network prediction model, the optimization of the SCNGO algorithm is mainly reflected in two aspects; firstly, the maximum error value is reduced from 8.34834 to 2.39037, and secondly, the error range is narrowed from −8.35 to 5.23 to −1.57 to 2.40, which has a significant effect.

3.4. Carbon Emission Projections for the Construction Phase of a Freeway

After completing the construction of the SCNGO-BP carbon emission prediction model and verifying its performance, it can predict the carbon emissions during the construction phase of the actual freeway project, which provides a theoretical basis for judging the low-carbon degree of the route design scheme and the comparison between the different route schemes.

Options 1 and 2 represent two different route design options within the same section of a highway construction project. The relevant carbon emission prediction indicator data for these schemes are presented in

Table 7. Carbon emissions during the construction phase.

Name	Unit	Option 1	Option 2
Total length of route	km	12.076	11.042
Tunnel length	km	0	0
Bridge culvert length	km	1.72	3.288
Roadbed length	km	10.29	7.719
Length of road surface	km	12.076	11.042
Length of intersection works	km	0.066	0.035
Cement consumption	t	195,748.785	336,360.475
Diesel consumption	kg	3,258,082.072	3,602,238.344
Reinforcing steel consumption	t	579,723.477	833,359.914
Aggregate consumption	m3	25,826.544	35,080.451

. The carbon emissions during the construction phase of these schemes are predicted using the previously established carbon emission prediction model for highway construction projects.

After calculation, the carbon emission per kilometer generated by the road construction and construction of Option 1 is about 2.2959 t, and the carbon emission per kilometer generated by the road construction and construction of Option 2 is about 4.3009 t. The carbon emission generated by Option 1 is lower, and Option 1 is the more preferred option from the low-carbon point of view.

4. Conclusions

This paper focuses on the construction phase of highway projects as its research object. It analyzes the degree of correlation between various indicators and carbon emissions using the grey relational analysis method. Relevant data from engineering examples are collected, and their carbon emissions are calculated accordingly. These data serve as samples to construct a carbon emission prediction model for the construction phase of highway projects using intelligent algorithms. The main conclusions drawn are as follows:

• The four materials of cement, crushed stone, steel reinforcement, and diesel exhibit substantial consumption during highway construction and have a strong correlation with carbon emissions. Similarly, tunnel length, bridge and culvert length, and intersection length, serving as key linear indicators in highway construction projects, are also closely related to carbon emissions.
• The optimization of the BP neural network through the integration of a multi-strategy improved northern goshawk optimization (SCNGO) algorithm yields significant results, which are primarily manifested in two aspects: a reduction in the maximum error value and a tightening of the error range. The predictions of the carbon emissions during the construction phase of different route schemes for actual highway projects, based on the SCNGO-BP prediction model, align closely with reality.

The carbon emission prediction model for the construction phase of highway projects developed in this paper enables the rapid and accurate quantification of carbon emissions generated by engineering construction at the initial design stage of highway projects. It addresses the challenge faced by highway construction units in quantifying carbon emissions for different route schemes during the preliminary design phase, thereby providing a basis for route scheme adjustment and comparison from a low-carbon perspective.

However, this study also has certain limitations. Specifically, in order to reduce the operational complexity of the prediction model, the process of screening prediction indicators using the grey relational analysis method did not take into account the mutual interactions between the indicators. In subsequent research, we will continue to delve deeper into this area and explore more reasonable methods for determining prediction indicators. In addition, we will continue to explore optimization methods for neural networks, pay attention to the current research on predicting carbon emissions during the construction phase of highways, and continuously improve the prediction model of carbon emissions during the construction phase of highways.