# Modeling and Estimation of CO2 Emissions in China Based on Artificial Intelligence

Authors: Pan Wang; Yangyang Zhong; Zhenan Yao
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

Since China’s reform and opening up, the social economy has achieved rapid development, followed by a sharp increase in carbon dioxide (CO2) emissions. Therefore, at the 75th United Nations General Assembly, China proposed to achieve carbon peaking by 2030 and carbon neutrality by 2060. The research work on advance forecasting of CO2 emissions is essential to achieve the above-mentioned carbon peaking and carbon neutrality goals in China. In order to achieve accurate prediction of CO2 emissions, this study establishes a hybrid intelligent algorithm model suitable for CO2 emissions prediction based on China’s CO2 emissions and related socioeconomic indicator data from 1971 to 2017. The hyperparameters of Least Squares Support Vector Regression (LSSVR) are optimized by the Adaptive Artificial Bee Colony (AABC) algorithm to build a high-performance hybrid intelligence model. The research results show that the hybrid intelligent algorithm model designed in this paper has stronger robustness and accuracy with relative error almost within ±5% in the advance prediction of CO2 emissions. The modeling scheme proposed in this study can not only provide strong support for the Chinese government and industry departments to formulate policies related to the carbon peaking and carbon neutrality goals, but also can be extended to the research of other socioeconomic-related issues.


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## Body

## 1. Introduction

Global warming has become a fact generally accepted by the international community. Climate warming has seriously affected the living environment and social development of humankind. Although the cyclical changes in the natural environment itself affect global climate change, more and more studies have shown that human activities have accelerated the global warming process largely. Since the industrial revolution, with the development of social economy and the increasing intensity of human activities, the concentration of carbon dioxide (CO2) in the atmosphere has risen sharply [1]. Studies have shown that the main cause of global warming in the past 50 years is the massive emission of greenhouse gases. The main greenhouse gas is CO2, and its emissions are inextricably linked to the extensive use of fossil fuels and the widespread destruction of forests. [2–5]. The fourth assessment report of IPCC (Intergovernmental Panel on Climate Change) pointed out that China’s CO2 emissions exceeded that of the United States in 2006, ranking first in the world [6]. Moreover, China’s CO2 emissions have continued to increase in recent years. In 2012, the annual emissions reached 8106.43 million tons. Socioeconomic development is necessary to improve living standards and social welfare. To this end, the government must maintain a stable economic growth rate in the country. Therefore, all countries in the world are facing the dual challenges of CO2 emissions and social-economic development. On the one hand, it is necessary to curb the level of CO2 emissions caused by the consumption of fossil fuels, and on the other hand, the economic growth rate needs to be maintained [2, 7]. China’s economy has grown exponentially since China implemented its reform and opening-up policy. Studies have shown that China’s GDP has grown by an average of more than 9% per year in the past four decades [8–10]. However, this rapid GDP growth has been achieved through a massive increase in energy consumption and the accompanying increase in CO2 emissions. In recent years, due to the increasingly strong voice in the international community for the development of a low-carbon economy, the issue of CO2 emissions has attracted widespread attention from scholars around the world, and some research results have been achieved. Scholars’ research on CO2 emissions mainly focuses on two aspects, one is to explore the social and economic factors that affect CO2 emissions, and the other is to establish CO2 emissions prediction models.The factors affecting CO2 emissions are complex and diverse. In recent years, many experts have done a lot of research work on CO2 emissions and published some research results. Zha et al. [11] built an assessment framework for direct and indirect CO2 emissions from the tourist sector and used the SBM-Undesirable model to integrate the CO2 emission component in the efficiency evaluation framework. Liu et al. [12] examined the dynamic relationship between tourism income, economic growth, energy consumption, and CO2 emissions. Mujtaba et al. [13] examined the correlation between economic growth, energy consumption, population, trade openness, and CO2 emissions. By using the generalized method of moments (GMM) dynamic panel model, Al-Ayouty et al. [14] found a positive correlation between population and CO2 emissions. Aller et al. [15] comprehensively analyzed the factors associated with CO2 emissions using Bayesian model. The researchers’ study was based on data from different countries and the results varied widely [16], but there were some commonalities. Many researchers have found that economic growth and population growth are two of the most important factors that influence CO2 emissions. Economic growth affects CO2 emissions mainly through three channels: scale effect, structural effect and technical effect [17, 18]. The scale effect of the economy has a promoting effect on CO2 emissions, while the structural effect and technological effect have a curb effect on CO2 emissions [19]. In a study based on provincial panel data, Wang et al. [20] found that economic growth was an important driver of CO2 emissions growth. Using the generalized index method, Shao et al. [21] found that the scale effect of economy is the main contributor to the increase in CO2 emissions. Therefore, an increasing number of scholars are currently working to estimate the link between GDP growth and CO2 emissions [8, 22–26]. Guo et al. [27] found a positive correlation between population size and CO2 emissions. Ohlan [28] studied the relationship between population density, energy consumption, GDP growth, and CO2 emissions and found that population density has a strong positive impact on CO2 emissions, which is the main factor affecting CO2 emissions. In addition, many other factors can affect CO2 emissions [29]. Previous research results show that there are many factors affecting CO2 emissions, and the impact mechanism is relatively complex. The relationship between CO2 emissions and its influencing factors varies greatly due to regional differences [30].At present, the research on the impact mechanism of CO2 emissions is relatively mature. Recently, many researchers have begun to focus on the modeling and prediction of CO2 emissions issue. Sun et al. [31] have established CO2 emission prediction models based on BP neural network and least square support vector machine, respectively, and found that the least square support vector machine model has better prediction effect. Budiono et al. [32] used a multiple linear regression model to predict CO2 emissions from electricity production in Indonesia and the results show that the model predictions are very close to the actual data. Mardani et al. [33] proposed a neuro-fuzzy model to predict CO2 emissions, and the results show that the model can effectively predict CO2 emissions. Gao et al. [34] proposed a fractional grey Riccati model (FGRM (1, 1)); by testing 20 data sets from M-competition, it is shown that the proposed model can be used to predict short-term CO2 emissions. Zhao and Yang [35] tested the dynamic mode decomposition (DMD) for CO2 emission prediction, which proves that DMD model has ideal effect for short-term carbon dioxide prediction. Wen and Yuan [36] have designed a new hybrid prediction model (RF-DPSO-BP) for CO2 emission prediction and tested the validity of the model through the panel data test of Chinese commercial sector. It can be seen that machine learning methods have been gradually applied to CO2 emission modeling and prediction, and existing studies have also confirmed the feasibility and effectiveness of machine learning for CO2 emission prediction. However, few studies at the current stage consider the hyperparameters optimization problem of intelligent algorithms such as machine learning applied to CO2 emission modeling and prediction. Therefore, this research will focus on two aspects of China’s CO2 emissions. On the one hand, based on the data of China’s CO2 emissions and socioeconomic indicators, it will analyze the correlation between CO2 emissions and various socioeconomic indicators. On the other hand, considering that the CO2 emission modeling data belong to a small sample training set, this study will use the LSSVR to carry out research work. In order to solve the hyperparameter optimization problem of machine learning modeling, the improved artificial bee colony algorithm is mixed with LSSVR to build a CO2 emission prediction model based on the hybrid intelligent algorithm. The purpose of this hybrid intelligence model is to accurately predict future CO2 emissions, which can provide reliable theoretical support for Chinese government departments to formulate policies to achieve dual carbon (carbon peaking and carbon neutrality) goals. Finally, this study will give some policy recommendations to the Chinese government.


## 2. Theory and Methodology

### 2.1. Methodology of Least Square Support Vector Regression

The basic idea of LSSVR is to use the known sample data to obtain a best fitting function [37] and then input new sample data according to this function to calculate the corresponding output value. Given a training sample set,(1)T=x1,y1,…,xl,yl∈Rn×Yl,where xi∈Rn,yi∈Y=R,i=1,2,…,l. The sample input is mapped to a high-dimensional space by nonlinear mapping, and the LSSVR function is constructed as follows:(2)yx=ωΤφx+b,where ω is weight vector and b is deviation. The solution of (2) can be transformed into an optimization problem, as in (3)minω,b,ξ,R=12ω2+c2∑i=1lξ2,s.t,yi=ωΤφxi+b+ξi,where c is penalty parameter and ξi≥0 is relaxation factor. The function model of LSSVR can be solved by using Lagrange function and KKT optimization condition:(4)yx=∑i=1laiKx,xi+b,where ai is Lagrange multiplier and Kx,xi is a kernel function. In this study, the Gauss radial basis function with strong fitting ability is used as the kernel function of LSSVR, as in (5)Kx,xi=exp−x−xi222σ2.


### 2.2. Methodology of Adaptive Artificial Bee Colony (AABC) Algorithm

#### 2.2.1. Artificial Bee Colony Algorithm

As a new biomimetic optimization algorithm, artificial bee colony (ABC) has been widely used in recent years. In the ABC algorithm, a honey source is used to represent a function solution, and the quality of the honey source reflects the merits of the solution.In the ABC algorithm, the bee colony is composed of a lead bee, a follower bee, and a scout bee, and the problem is solved by information exchange, conversion, and mutual cooperation between the three types of bee colonies. When solving the optimization problem, the spatial point is regarded as the location of the honey source, each point represents a possible solution, andN represents the number of honey sources. The quality of honey source xi (i=1,2,3,…,N) corresponds to the fitness value of the solution. Suppose the dimension of the problem to be solved is D, at the tth iteration, the position of the honey source is Xit=xi1txi2t…xiDtT, where t is the current number of iterations, and the maximum number of iterations is T. xid∈Ld,Ud, and Md and Nd respectively represent the two boundaries of the search space, d=1,2,3,…,D. The ABC algorithm is initialized, and the initial position of the honey source is randomly generated in the search space according to formula (6). Then, the lead bee searches for a new source of honey is according to formula (7).(6)xid=Md+rand0,1Nd−Md,(7)vid=xid+ηxid−xjd,where d represents a dimension in the solution space; j∈1,2,3,…,N,j≠i; η is a random number between [−1, 1], representing the magnitude of the disturbance.The fitness of the two honey sources is then evaluated and the retention ofxi or vi is determined according to the greedy algorithm. The fitness value of the solution is calculated according to (8), where the function value of the solution is represented. The probability that the honey source found by the lead bee is followed is calculated according to (9).(8)fiti=11+fi,fi≥0,1+absfi,fi<0,(9)Pi=fiti∑i=1Nfiti.The follower bee uses roulette to choose to lead bee; that is, a uniformly distributed random numberr is generated in 0,1. When Pi>r, the follower bee will generate a new honey source around the honey source and use the greedy algorithm to determine the retained honey source. If a better honey source is not found after t iterations reach the threshold limit, the honey source xit is discarded. At this time, the lead bee becomes a scout bee, a new honey source xit+1 is randomly generated in the search space instead of xit, and the calculation formula of xit is (10). On the contrary, the honey source xit is retained. At this time, t=t+1, and it is judged whether the algorithm reaches the termination condition and the optimal solution is output.(10)xit+1=Ld+rand0,1Ud−Ld,t≥limit,xit,t<limit.


#### 2.2.2. Improved Artificial Bee Colony Algorithm

Two key problems are involved in the ABC algorithm. One is the selection of the search step size. The search range and search accuracy of the population are controlled by the step sizeη, but the value of η is completely random. When the value of η is too large, it is easy to jump out of the true global optimal solution; when the value of η is too small, it is easy to converge earlier and obtain a local optimal solution. According to the analysis of bee feeding behavior, there should be a large search step in the early stage of the search, so as to quickly gather around the global optimal solution and improve the convergence speed. In the later stage of the search, the optimal solution obtained by the algorithm search is close to the real optimal solution. At this time, the search step size should be gradually reduced to achieve a detailed search around the optimal solution. For this reason, this study designs a self-adaption. The step size of the search strategy is adapted to the decreasing operator, and the calculation formula is (11)vid=xid+ηxid−xjd,η=η01−12logTt,where η0∈0,1;t=1,2,3,…,T.Another key issue is the selection of honey sources in the ABC algorithm. In the standard ABC algorithm, only the honey source with high fitness is selected, and the honey source with low fitness is quickly eliminated. This will lead to a decline in the diversity of the population, which will make it difficult for the algorithm to achieve global optimality. Aiming at this problem, this study designs a new adaptive probability selection mechanism, which is calculated as(12)Pi=λfiti∑i=1Nfiti+1−λ1/fiti∑i=1N1/fiti,λ=et/Tln2−1,where λ∈0,1. In the early stage of the algorithm, t/T⟶0,λ⟶0. At this time, the honey source with poor fitness has the possibility of being selected, thereby improving the ability of the algorithm to obtain the generalization; in the later stages of the algorithm’s operation, t/T⟶1,λ⟶1. At this time, only the honey source with high fitness is selected. Thereby, the convergence speed of the algorithm is accelerated, and the convergence precision of the algorithm is also improved.In summary, this study designs the adaptive step-down operator to update the step size of the search strategy and designs the adaptive probability selection mechanism to solve the honey source selection problem, improves the ABC algorithm, and establishes an AABC algorithm.


## 2.1. Methodology of Least Square Support Vector Regression

The basic idea of LSSVR is to use the known sample data to obtain a best fitting function [37] and then input new sample data according to this function to calculate the corresponding output value. Given a training sample set,(1)T=x1,y1,…,xl,yl∈Rn×Yl,where xi∈Rn,yi∈Y=R,i=1,2,…,l. The sample input is mapped to a high-dimensional space by nonlinear mapping, and the LSSVR function is constructed as follows:(2)yx=ωΤφx+b,where ω is weight vector and b is deviation. The solution of (2) can be transformed into an optimization problem, as in (3)minω,b,ξ,R=12ω2+c2∑i=1lξ2,s.t,yi=ωΤφxi+b+ξi,where c is penalty parameter and ξi≥0 is relaxation factor. The function model of LSSVR can be solved by using Lagrange function and KKT optimization condition:(4)yx=∑i=1laiKx,xi+b,where ai is Lagrange multiplier and Kx,xi is a kernel function. In this study, the Gauss radial basis function with strong fitting ability is used as the kernel function of LSSVR, as in (5)Kx,xi=exp−x−xi222σ2.


## 2.2. Methodology of Adaptive Artificial Bee Colony (AABC) Algorithm

### 2.2.1. Artificial Bee Colony Algorithm

As a new biomimetic optimization algorithm, artificial bee colony (ABC) has been widely used in recent years. In the ABC algorithm, a honey source is used to represent a function solution, and the quality of the honey source reflects the merits of the solution.In the ABC algorithm, the bee colony is composed of a lead bee, a follower bee, and a scout bee, and the problem is solved by information exchange, conversion, and mutual cooperation between the three types of bee colonies. When solving the optimization problem, the spatial point is regarded as the location of the honey source, each point represents a possible solution, andN represents the number of honey sources. The quality of honey source xi (i=1,2,3,…,N) corresponds to the fitness value of the solution. Suppose the dimension of the problem to be solved is D, at the tth iteration, the position of the honey source is Xit=xi1txi2t…xiDtT, where t is the current number of iterations, and the maximum number of iterations is T. xid∈Ld,Ud, and Md and Nd respectively represent the two boundaries of the search space, d=1,2,3,…,D. The ABC algorithm is initialized, and the initial position of the honey source is randomly generated in the search space according to formula (6). Then, the lead bee searches for a new source of honey is according to formula (7).(6)xid=Md+rand0,1Nd−Md,(7)vid=xid+ηxid−xjd,where d represents a dimension in the solution space; j∈1,2,3,…,N,j≠i; η is a random number between [−1, 1], representing the magnitude of the disturbance.The fitness of the two honey sources is then evaluated and the retention ofxi or vi is determined according to the greedy algorithm. The fitness value of the solution is calculated according to (8), where the function value of the solution is represented. The probability that the honey source found by the lead bee is followed is calculated according to (9).(8)fiti=11+fi,fi≥0,1+absfi,fi<0,(9)Pi=fiti∑i=1Nfiti.The follower bee uses roulette to choose to lead bee; that is, a uniformly distributed random numberr is generated in 0,1. When Pi>r, the follower bee will generate a new honey source around the honey source and use the greedy algorithm to determine the retained honey source. If a better honey source is not found after t iterations reach the threshold limit, the honey source xit is discarded. At this time, the lead bee becomes a scout bee, a new honey source xit+1 is randomly generated in the search space instead of xit, and the calculation formula of xit is (10). On the contrary, the honey source xit is retained. At this time, t=t+1, and it is judged whether the algorithm reaches the termination condition and the optimal solution is output.(10)xit+1=Ld+rand0,1Ud−Ld,t≥limit,xit,t<limit.


### 2.2.2. Improved Artificial Bee Colony Algorithm

Two key problems are involved in the ABC algorithm. One is the selection of the search step size. The search range and search accuracy of the population are controlled by the step sizeη, but the value of η is completely random. When the value of η is too large, it is easy to jump out of the true global optimal solution; when the value of η is too small, it is easy to converge earlier and obtain a local optimal solution. According to the analysis of bee feeding behavior, there should be a large search step in the early stage of the search, so as to quickly gather around the global optimal solution and improve the convergence speed. In the later stage of the search, the optimal solution obtained by the algorithm search is close to the real optimal solution. At this time, the search step size should be gradually reduced to achieve a detailed search around the optimal solution. For this reason, this study designs a self-adaption. The step size of the search strategy is adapted to the decreasing operator, and the calculation formula is (11)vid=xid+ηxid−xjd,η=η01−12logTt,where η0∈0,1;t=1,2,3,…,T.Another key issue is the selection of honey sources in the ABC algorithm. In the standard ABC algorithm, only the honey source with high fitness is selected, and the honey source with low fitness is quickly eliminated. This will lead to a decline in the diversity of the population, which will make it difficult for the algorithm to achieve global optimality. Aiming at this problem, this study designs a new adaptive probability selection mechanism, which is calculated as(12)Pi=λfiti∑i=1Nfiti+1−λ1/fiti∑i=1N1/fiti,λ=et/Tln2−1,where λ∈0,1. In the early stage of the algorithm, t/T⟶0,λ⟶0. At this time, the honey source with poor fitness has the possibility of being selected, thereby improving the ability of the algorithm to obtain the generalization; in the later stages of the algorithm’s operation, t/T⟶1,λ⟶1. At this time, only the honey source with high fitness is selected. Thereby, the convergence speed of the algorithm is accelerated, and the convergence precision of the algorithm is also improved.In summary, this study designs the adaptive step-down operator to update the step size of the search strategy and designs the adaptive probability selection mechanism to solve the honey source selection problem, improves the ABC algorithm, and establishes an AABC algorithm.


## 2.2.1. Artificial Bee Colony Algorithm

As a new biomimetic optimization algorithm, artificial bee colony (ABC) has been widely used in recent years. In the ABC algorithm, a honey source is used to represent a function solution, and the quality of the honey source reflects the merits of the solution.In the ABC algorithm, the bee colony is composed of a lead bee, a follower bee, and a scout bee, and the problem is solved by information exchange, conversion, and mutual cooperation between the three types of bee colonies. When solving the optimization problem, the spatial point is regarded as the location of the honey source, each point represents a possible solution, andN represents the number of honey sources. The quality of honey source xi (i=1,2,3,…,N) corresponds to the fitness value of the solution. Suppose the dimension of the problem to be solved is D, at the tth iteration, the position of the honey source is Xit=xi1txi2t…xiDtT, where t is the current number of iterations, and the maximum number of iterations is T. xid∈Ld,Ud, and Md and Nd respectively represent the two boundaries of the search space, d=1,2,3,…,D. The ABC algorithm is initialized, and the initial position of the honey source is randomly generated in the search space according to formula (6). Then, the lead bee searches for a new source of honey is according to formula (7).(6)xid=Md+rand0,1Nd−Md,(7)vid=xid+ηxid−xjd,where d represents a dimension in the solution space; j∈1,2,3,…,N,j≠i; η is a random number between [−1, 1], representing the magnitude of the disturbance.The fitness of the two honey sources is then evaluated and the retention ofxi or vi is determined according to the greedy algorithm. The fitness value of the solution is calculated according to (8), where the function value of the solution is represented. The probability that the honey source found by the lead bee is followed is calculated according to (9).(8)fiti=11+fi,fi≥0,1+absfi,fi<0,(9)Pi=fiti∑i=1Nfiti.The follower bee uses roulette to choose to lead bee; that is, a uniformly distributed random numberr is generated in 0,1. When Pi>r, the follower bee will generate a new honey source around the honey source and use the greedy algorithm to determine the retained honey source. If a better honey source is not found after t iterations reach the threshold limit, the honey source xit is discarded. At this time, the lead bee becomes a scout bee, a new honey source xit+1 is randomly generated in the search space instead of xit, and the calculation formula of xit is (10). On the contrary, the honey source xit is retained. At this time, t=t+1, and it is judged whether the algorithm reaches the termination condition and the optimal solution is output.(10)xit+1=Ld+rand0,1Ud−Ld,t≥limit,xit,t<limit.


## 2.2.2. Improved Artificial Bee Colony Algorithm

Two key problems are involved in the ABC algorithm. One is the selection of the search step size. The search range and search accuracy of the population are controlled by the step sizeη, but the value of η is completely random. When the value of η is too large, it is easy to jump out of the true global optimal solution; when the value of η is too small, it is easy to converge earlier and obtain a local optimal solution. According to the analysis of bee feeding behavior, there should be a large search step in the early stage of the search, so as to quickly gather around the global optimal solution and improve the convergence speed. In the later stage of the search, the optimal solution obtained by the algorithm search is close to the real optimal solution. At this time, the search step size should be gradually reduced to achieve a detailed search around the optimal solution. For this reason, this study designs a self-adaption. The step size of the search strategy is adapted to the decreasing operator, and the calculation formula is (11)vid=xid+ηxid−xjd,η=η01−12logTt,where η0∈0,1;t=1,2,3,…,T.Another key issue is the selection of honey sources in the ABC algorithm. In the standard ABC algorithm, only the honey source with high fitness is selected, and the honey source with low fitness is quickly eliminated. This will lead to a decline in the diversity of the population, which will make it difficult for the algorithm to achieve global optimality. Aiming at this problem, this study designs a new adaptive probability selection mechanism, which is calculated as(12)Pi=λfiti∑i=1Nfiti+1−λ1/fiti∑i=1N1/fiti,λ=et/Tln2−1,where λ∈0,1. In the early stage of the algorithm, t/T⟶0,λ⟶0. At this time, the honey source with poor fitness has the possibility of being selected, thereby improving the ability of the algorithm to obtain the generalization; in the later stages of the algorithm’s operation, t/T⟶1,λ⟶1. At this time, only the honey source with high fitness is selected. Thereby, the convergence speed of the algorithm is accelerated, and the convergence precision of the algorithm is also improved.In summary, this study designs the adaptive step-down operator to update the step size of the search strategy and designs the adaptive probability selection mechanism to solve the honey source selection problem, improves the ABC algorithm, and establishes an AABC algorithm.


## 3. Data Preparation and Analysis

### 3.1. Data Preparation

Database preparation is a very important step for neural network modeling. In this study, the data used were derived from five socioeconomic indicators related to CO2 emissions in China from the World Development Indicators database published by the World Bank, including fixed capital consumption (FCC), power consumption (PC), oil consumption (OC), gross domestic product (GDP), population (P), and CO2 emissions. The experimental samples totaled 47 sets of data from 1971 to 2017. Figure 1 is a data view of each indicator. It can be seen that the five socioeconomic indicators related to CO2 emissions are showing an increasing trend year by year.Figure 1
Time-dependent curve of socioeconomic indicators related to CO2 emissions. (a) FCC. (b) PC per capita. (c) OC per capita. (d) GDP. (e) Population. (f) CO2 emissions.
(a)(b)(c)(d)(e)(f)Table1 presents the statistical analysis of the six variables. As shown in Table 1, the value of the standard deviation of CO2 emissions was found to be equal to 3.2443 × 106. Further, the same statistics for FCC, PC, OC, GDP, and P were found to be equal to 5.302, 1.3254 × 103, 610.2162, 2.3125 × 1013 and 1.6623 × 108 respectively. The remainder of the results derived from this analysis is set out in Table 1.Table 1
Summary of the social and economic indicators related to CO2 emissions for China.
FCC (%)PC (kw·h)OC (kgoe)GDP (RMB Yuan)PCO2 emissions (kiloton)Minimum value2.5739151.9893464.93322.4569 × 10118.4111 × 1088.7663 × 105Maximum value22.33994.5916 × 1032.4066 × 1038.2712 × 10131.3864 × 1091.0932 × 107Average9.69121.2906 × 1031.0732 × 1031.6128 × 10131.1599 × 1094.1852 × 106Standard deviation5.30201.3254 × 103610.21622.3125 × 10131.6623 × 1083.2443 × 106


### 3.2. Data Analysis

In order to evaluate the relationship between socioeconomic-related indicators and CO2 emissions, this study used two analytical methods to characterize the sensitivity of various socioeconomic indicators to CO2 emissions. A single factor regression analysis was used to obtain a graph of the relationship between each indicator and CO2 emissions, as shown in Figure 2. In the regression analysis, the coefficient R2 is used to measure the degree of influence of different indicators on CO2 emissions, and R2 represents the proportion of the population variance, which can be obtained by (13)R2=1−∑i=1nfxi−yi∑i=1nfxi2−∑i=1nyi2/n.Figure 2
Cross-plots of economic indicators and CO2 emissions. (a) FCC-CO2 emissions. (b) PC-CO2 emissions. (c) OC-CO2 emissions. (d) GDP-CO2 emissions. (e) P-CO2 emissions.
(a)(b)(c)(d)(e)It can be seen from Figure2 that there is a positive correlation between each indicator and CO2 emissions, and R2 is very large, indicating that there is a good correlation between various economic indicators and CO2 emissions. Fixed capital consumption, electricity consumption, and oil consumption are all linearly related to CO2 emissions. However, both GDP and total population are nonlinearly related to CO2 emissions.In addition to the simple regression method, we also used the correlation coefficient analysis method to analyze the relationship between economic indicators and CO2 emissions. The analysis results are shown in Figure 3. It can be seen that in addition to the total population indicators, other economic indicators have very high correlation coefficients. Both the crossplot method and the correlation coefficient analysis method show that there is a good correlation between the five socioeconomic indicators selected in this study and the CO2 emissions, which can be used as the input independent variable of the CO2 emission prediction model.Figure 3
Graph of correlation matrix.In order to reflect the dynamic development of various social and economic indicators and the changes in CO2 emissions during the study period, we calculated the annual growth rates of various socioeconomic indicators and CO2 emissions. Figure 4 shows the annual growth rate of socioeconomic indicators and CO2 emissions. It can be seen from the figure that except for a few years, the annual growth rate of FCC tends to be stable and the fluctuation is small; the annual growth rate of the population shows a trend of decreasing year by year. The annual growth rate of each parameter fluctuates greatly, and the change is relatively complicated.Figure 4
The annual growth rate of socioeconomic indicators and CO2 emissions. (a) FCC growth rates. (b) PC growth rates. (c) OC growth rates. (d) GDP growth rates. (e) P growth rates. (f) CO2 emissions growth rates.
(a)(b)(c)(d)(e)(f)Table2 presents the statistical analysis of growth rates for the six variables. As shown in Table 2, the value of the standard deviation of CO2 emissions growth rate was found to be equal to 4.7735. Further, the same statistics for FCC, PC, OC, GDP, and P growth rates were found to be equal to 17.7822, 3.7368, 3.7586, 7.4978, and 0.5206, respectively. The remainder of the results derived from this analysis is set out in Table 2. Figure 5 presents the descriptive statistics in the form of a boxplot.Table 2
Summary of the social and economic indicators related to CO2 emissions for China.
FCCPCOCGDPPCO2 emissionsInitial growth rate10.02027.84442.63173.8872.48786.2675Average growth rate5.88827.75363.704413.71971.09365.7432Minimum nonnegative growth rate0.08721.4889−3.93010.3062.59420.4803Maximum growth rate112.730815.451913.568236.34182.487817.9247Standard deviation17.78223.73683.75867.49780.52064.7735Figure 5
Boxplot showing the differences in values of each variable.


## 3.1. Data Preparation

Database preparation is a very important step for neural network modeling. In this study, the data used were derived from five socioeconomic indicators related to CO2 emissions in China from the World Development Indicators database published by the World Bank, including fixed capital consumption (FCC), power consumption (PC), oil consumption (OC), gross domestic product (GDP), population (P), and CO2 emissions. The experimental samples totaled 47 sets of data from 1971 to 2017. Figure 1 is a data view of each indicator. It can be seen that the five socioeconomic indicators related to CO2 emissions are showing an increasing trend year by year.Figure 1
Time-dependent curve of socioeconomic indicators related to CO2 emissions. (a) FCC. (b) PC per capita. (c) OC per capita. (d) GDP. (e) Population. (f) CO2 emissions.
(a)(b)(c)(d)(e)(f)Table1 presents the statistical analysis of the six variables. As shown in Table 1, the value of the standard deviation of CO2 emissions was found to be equal to 3.2443 × 106. Further, the same statistics for FCC, PC, OC, GDP, and P were found to be equal to 5.302, 1.3254 × 103, 610.2162, 2.3125 × 1013 and 1.6623 × 108 respectively. The remainder of the results derived from this analysis is set out in Table 1.Table 1
Summary of the social and economic indicators related to CO2 emissions for China.
FCC (%)PC (kw·h)OC (kgoe)GDP (RMB Yuan)PCO2 emissions (kiloton)Minimum value2.5739151.9893464.93322.4569 × 10118.4111 × 1088.7663 × 105Maximum value22.33994.5916 × 1032.4066 × 1038.2712 × 10131.3864 × 1091.0932 × 107Average9.69121.2906 × 1031.0732 × 1031.6128 × 10131.1599 × 1094.1852 × 106Standard deviation5.30201.3254 × 103610.21622.3125 × 10131.6623 × 1083.2443 × 106


## 3.2. Data Analysis

In order to evaluate the relationship between socioeconomic-related indicators and CO2 emissions, this study used two analytical methods to characterize the sensitivity of various socioeconomic indicators to CO2 emissions. A single factor regression analysis was used to obtain a graph of the relationship between each indicator and CO2 emissions, as shown in Figure 2. In the regression analysis, the coefficient R2 is used to measure the degree of influence of different indicators on CO2 emissions, and R2 represents the proportion of the population variance, which can be obtained by (13)R2=1−∑i=1nfxi−yi∑i=1nfxi2−∑i=1nyi2/n.Figure 2
Cross-plots of economic indicators and CO2 emissions. (a) FCC-CO2 emissions. (b) PC-CO2 emissions. (c) OC-CO2 emissions. (d) GDP-CO2 emissions. (e) P-CO2 emissions.
(a)(b)(c)(d)(e)It can be seen from Figure2 that there is a positive correlation between each indicator and CO2 emissions, and R2 is very large, indicating that there is a good correlation between various economic indicators and CO2 emissions. Fixed capital consumption, electricity consumption, and oil consumption are all linearly related to CO2 emissions. However, both GDP and total population are nonlinearly related to CO2 emissions.In addition to the simple regression method, we also used the correlation coefficient analysis method to analyze the relationship between economic indicators and CO2 emissions. The analysis results are shown in Figure 3. It can be seen that in addition to the total population indicators, other economic indicators have very high correlation coefficients. Both the crossplot method and the correlation coefficient analysis method show that there is a good correlation between the five socioeconomic indicators selected in this study and the CO2 emissions, which can be used as the input independent variable of the CO2 emission prediction model.Figure 3
Graph of correlation matrix.In order to reflect the dynamic development of various social and economic indicators and the changes in CO2 emissions during the study period, we calculated the annual growth rates of various socioeconomic indicators and CO2 emissions. Figure 4 shows the annual growth rate of socioeconomic indicators and CO2 emissions. It can be seen from the figure that except for a few years, the annual growth rate of FCC tends to be stable and the fluctuation is small; the annual growth rate of the population shows a trend of decreasing year by year. The annual growth rate of each parameter fluctuates greatly, and the change is relatively complicated.Figure 4
The annual growth rate of socioeconomic indicators and CO2 emissions. (a) FCC growth rates. (b) PC growth rates. (c) OC growth rates. (d) GDP growth rates. (e) P growth rates. (f) CO2 emissions growth rates.
(a)(b)(c)(d)(e)(f)Table2 presents the statistical analysis of growth rates for the six variables. As shown in Table 2, the value of the standard deviation of CO2 emissions growth rate was found to be equal to 4.7735. Further, the same statistics for FCC, PC, OC, GDP, and P growth rates were found to be equal to 17.7822, 3.7368, 3.7586, 7.4978, and 0.5206, respectively. The remainder of the results derived from this analysis is set out in Table 2. Figure 5 presents the descriptive statistics in the form of a boxplot.Table 2
Summary of the social and economic indicators related to CO2 emissions for China.
FCCPCOCGDPPCO2 emissionsInitial growth rate10.02027.84442.63173.8872.48786.2675Average growth rate5.88827.75363.704413.71971.09365.7432Minimum nonnegative growth rate0.08721.4889−3.93010.3062.59420.4803Maximum growth rate112.730815.451913.568236.34182.487817.9247Standard deviation17.78223.73683.75867.49780.52064.7735Figure 5
Boxplot showing the differences in values of each variable.


## 4. Results and Discussion

### 4.1. Model Establishment

Formulas (7) and (9) in the original ABC algorithm are respectively replaced by the adaptive step size updated formula (11) and the adaptive honey source selection formula (12), composing an improved ABC algorithm called adaptive ABC algorithm. The AABC algorithm is combined with LSSVR to construct an artificial intelligence model for CO2 emissions prediction. Figure 6 shows the flow of model construction. Considering that the dimensions of each socioeconomic indicator are different and the numerical values show large differences in magnitude, which is not conducive to modeling and calculation, we need to normalize the data first. Set the parameters of AABC, including the number of bee colonies NP, the maximum number of searches for honey sources limit, the maximum number of iterations T of the algorithm, the number of parameters to be optimized D, and the range of values of each parameter. Then, set the objective function. In this study, the minimum root mean square error (RMSE) fitted by LSSVR is taken as the objective function of the AABC algorithm, and its reciprocal is defined as the fitness function. Finally, through the iterative optimization of AABC algorithm, the optimal parameters of LSSVR are obtained; that is, the AABC-LSSVR model is successfully constructed, which can be used for the prediction of CO2 emissions.Figure 6
Flow chart of modeling for CO2 emissions prediction.


### 4.2. Model Performance

As mentioned above, the data in this study are the socioeconomic and CO2 emissions data from 1971 to 2017 in China, totaling 47 groups. The 47 groups of data are divided into three parts: training, validation, and testing, of which 70% are trained. The validation and testing sections each accounted for 15%.When initializing the parameters of the ABC and AABC optimization algorithms, the size of the artificial bee colony is 50, the number of honey sources is half of the size of the bee colony, the dimensionD of the solution problem is 2, the maximum number of iterations T is 300, and the maximum number of searches is limit 100. The penalty parameter c and the kernel function parameter σ have values ranging from [0.05, 1000] to [0.0001, 50], respectively. According to the aforementioned modeling process, the program was coded with MATLAB R2018b, which can be used to obtain the LSSVR and AABC-LSSVR models, respectively. Figure 7 shows the optimization results of the AABC algorithm. The optimum c and σ were synchronously obtained as follows: best c=2.8284, best σ=0.0625.Figure 7
Parameter optimization results of LSSVR by using AABC algorithm.Figure8 is an iterative optimization curve for the AABC-LSSVR model. It can be seen from the figure that under the control of adaptive regulation, in the early stage, the iterative curve drops rapidly (MSE value decreases rapidly), indicating that the iterative step size of the population is larger and the convergence speed is faster; in the medium term, the iterative curve is stable. The state indicates that some honey sources with low fitness are retained, so that the diversity of the population is supplemented; in the later stage, the iterative curve drops rapidly again to reach the convergence value, indicating that only the honey source with high fitness is selected at this time. It can be seen that the AABC has strong adaptability and effectiveness in searching for key parameters of the LSSVR algorithm.Figure 8
Iterative optimization curve of AABC-LSSVR model.The predictive performance of the LSSVR and AABC-LSSVR models with the same inputs is evaluated using the coefficient of determination (R2), as shown in Figures 9 and 10. It can be seen from Figures 9(a) and 10(a) that LSSVR has a strong fitting ability in the training set part, which is slightly inferior to the AABC-LSSVR model. However, as can be seen from Figures 9(b), 9(c) and 10(b), 10(c), the LSSVR model is significantly less effective in the verification and testing part than the AABC-LSSVR model, especially in the test section. It shows that the optimization effect of AABC on LSSVR is very obvious, which improves the fitting performance of LSSVR. It also shows that the AABC-LSSVR model proposed in this study has strong generalization ability in the prediction of CO2 emissions and is trustworthy.Figure 9
Comparison of the CO2 emissions prediction results with LSSVR model and real CO2 emissions. (a) LSSVR—training results. (b) LSSVR—validation results. (c) LSSVR—testing results. (d) LSSVR—all results.
(a)(b)(c)(d)Figure 10
Comparison of the CO2 emissions prediction results with AABC-LSSVR model and real CO2 emissions. (a) AABC-LSSVR—training results. (b) AABC-LSSVR—validation results. (c) AABC-LSSVR—testing results. (d) AABC-LSSVR—all results.
(a)(b)(c)(d)Figures9(d) and 10(d) show crossplot of real CO2 emissions versus predicted values. Coefficient of determination (R2) for LSSVR prediction is equal to 0.9427 which verifies robustness of LSSVR model. While coefficient of determination (R2) for AABC-LSSVR prediction is equal to 0.997 which verifies strong robustness of improved LSSVR model. It is sufficient to claim that the robustness of LSSVR was improved by using AABC algorithm.In addition to coefficient of determination (R2), error distribution was also employed for assessment of the LSSVR and AABC-LSSVR performance. Figure 11 allows more statistical analysis of LSSVR and AABC-LSSVR performance by using error distribution information. As shown in Figure 11(a), mean and standard deviation of error distribution for LSSVR model are in turn equal to 2.1152 × 105 and 2.1152 × 105, which are relatively larger than that of AABC-LSSVR model (see Figure 11(b)). It means that the prediction error of AABC-LSSVR model is more acceptable.Figure 11
Absolute error histogram with 20 bins of each model. (a) LSSVR model. (b) AABC-LSSVR model.
(a)(b)Figure12 provides an opportunity to compare relative error between LSSVR and AABC-LSSVR for all data points. From Figure 12(a), it can be seen that relative error of AABC-LSSVR for almost all data points is located in the range of [−5% 5%], which is an acceptable value. Figure 12(b) presents the descriptive statistics in the form of a boxplot for relative error data. Small relative error of mean and fluctuation range of data reveals high performance of AABC-LSSVR model in CO2 emissions prediction.Figure 12
Results of relative error analysis for each model. (a) Relative error of models in prediction of CO2 emissions. (b) Boxplot showing the differences in relative error of each model.
(a)(b)In summary, we can see that AABC-LSSVR outperformed LSSVR owing to higherR2 and lower relative error. This study states AABC algorithm is very effective for LSSVR and AABC-LSSVR predicted values are in good agreement with reality.


### 4.3. Discussion

The model of CO2 emission prediction has been constructed based on AABC and LSSVR algorithms, and the performance of the model has been tested. The results also show that the AABC-LSSVR model has strong robustness and generalization ability, and the prediction accuracy is acceptable and trustworthy. Therefore, the AABC-LSSVR model will be used to predict China’s CO2 emissions for the next five years (2018–2022). Considering that the socioeconomic indicators for the next five years are also unknown, this study will reduce the uncertainty of prediction by setting different scenarios, and these scenarios will adopt different input independent variable data. The characteristics of China’s social and economic indicators have been analyzed in the past few years, and the annual growth rate of each indicator has been calculated. Therefore, four scenarios will be set to generate model input independent variable data, as shown in Table 3. These data are all calculated by (14). Scenario (a) is based on the growth rate calculated in 2017 as the compound annual growth rate. Scenario (b) is based on the average growth rate between 1971 and 2017 as the compound annual growth rate. Scenario (c) is based on the nonnegative minimum growth rate between 1971 and 2017 as the compound annual growth rate. Scenario (d) is based on the nonnegative maximum growth rate between 1971 and 2017 as the compound annual growth rate.(14)ftn=ft01+cagrn,where a is the value after n years and b is the initial value.Table 3
The forecasting scenarios of the social and economic indicators related to CO2 emissions for China (from 2018 to 2022).
ScenarioYearFCC (%)PC (kw·h)OC (kgoe)GDP (yuan)PScenario (a)201824.57844.5917 × 1032.4699 × 1038.5927 × 10131.4209 × 109201927.04125.3402 × 1032.5349 × 1038.9267 × 10131.4562 × 109202029.75075.7591 × 1032.6017 × 1039.2737 × 10131.4925 × 109202132.73186.2108 × 1032.6701 × 1039.6342 × 10131.5296 × 109202236.01176.698 × 1032.7404 × 1031.0008 × 10141.5676 × 109Scenario (b)201823.66134.9553 × 1032.4978 × 1039.4060 × 10131.4016 × 109201925.06085.3478 × 1032.5925 × 1031.0697 × 10141.4169 × 109202026.54325.7714 × 1032.6908 × 1031.2164 × 10141.4324 × 109202128.11326.2286 × 1032.7928 × 1031.3833 × 10141.4481 × 109202229.77626.7219 × 1032.8986 × 1031.5731 × 10141.4639 × 109Scenario (c)201822.35934.6599 × 1032.4139 × 1038.4858 × 10131.3931 × 109201922.37884.7293 × 1032.4214 × 1038.7059 × 10131.3997 × 109202022.39834.7997 × 1032.4288 × 1038.9318 × 10131.4065 × 109202122.41794.8712 × 1032.4362 × 1038.1635 × 10131.4132 × 109202222.43754.9437 × 1032.4437 × 1038.4012 × 10131.4201 × 109Scenario (d)201847.52385.301 × 1032.7332 × 1031.1277 × 10141.4209 × 1092019101.09786.1202 × 1033.1039 × 1031.5375 × 10141.4562 × 1092020215.06637.0658 × 1033.5251 × 1032.0963 × 10141.4925 × 1092021457.51228.1576 × 1034.0035 × 1032.8582 × 10141.5296 × 1092022973.26949.4181 × 1034.5466 × 1033.8968 × 10141.5676 × 109By substituting the five indicators of CO2 emissions in each of the scenarios in Table 3 into the AABC-LSSVR model, the predictions of CO2 emissions in four different scenarios can be obtained, as shown in Figure 13.Figure 13
The forecast results of CO2 emissions for China in the next five years (2018–2022). (a) Prediction values of CO2 emissions in four scenarios. (b) The growth rates of CO2 emissions.
(a)(b)As can be seen from Figure13(a), China’s CO2 emissions in the next five years (2018–2022) have shown an upward trend year by year in the above four scenarios. In scenario (a), CO2 emissions increase from 1.0932 × 107 kilotons in 2017 to 1.3026 × 107 kilotons in 2022. In scenario (b), CO2 emissions increase from 1.0932 × 107 kilotons in 2017 to 1.3575 × 107 kilotons in 2022. The CO2 emissions in scenario (c) increase from 1.0932 × 107 kilotons in 2017 to 1.1338 × 107 kilotons in 2022. The CO2 emissions in scenario (d) increase from 1.0932 × 107 kilotons in 2017 to 2.2509 × 107 kilotons in 2022. It can be seen from Figure 13(b) that the annual growth rate of China’s CO2 emissions in the next five years under the four scenarios is quite different. Scenario (a) has an average annual growth rate of 3.57%; scenario (b) has an average annual growth rate of 4.43%; scenario (c) has an average annual growth rate of 0.735%; scenario (d) has an average annual growth rate of 15.54%. In summary, the forecast of China’s CO2 emissions in the next five years under the four scenarios indicates that China’s CO2 emissions in 2022 will fluctuate between 1.1338 × 107 kilotons and 2.2509 × 107 kilotons.The analysis results of the scenarios set above show that future CO2 emissions are closely related to their influencing factors, and changes in any key influencing factor will cause strong fluctuations in CO2 emissions. Referring to the social and economic development of China in the past period, prediction of CO2 emissions in the next few years using the hybrid intelligence model is proposed in this study. The results show that China’s CO2 emissions will continue to rise in the future. The Chinese government should formulate special policies for relevant social-economic indicators to effectively control future CO2 emissions and complete the carbon peaking and carbon neutrality goals as soon as possible.


## 4.1. Model Establishment

Formulas (7) and (9) in the original ABC algorithm are respectively replaced by the adaptive step size updated formula (11) and the adaptive honey source selection formula (12), composing an improved ABC algorithm called adaptive ABC algorithm. The AABC algorithm is combined with LSSVR to construct an artificial intelligence model for CO2 emissions prediction. Figure 6 shows the flow of model construction. Considering that the dimensions of each socioeconomic indicator are different and the numerical values show large differences in magnitude, which is not conducive to modeling and calculation, we need to normalize the data first. Set the parameters of AABC, including the number of bee colonies NP, the maximum number of searches for honey sources limit, the maximum number of iterations T of the algorithm, the number of parameters to be optimized D, and the range of values of each parameter. Then, set the objective function. In this study, the minimum root mean square error (RMSE) fitted by LSSVR is taken as the objective function of the AABC algorithm, and its reciprocal is defined as the fitness function. Finally, through the iterative optimization of AABC algorithm, the optimal parameters of LSSVR are obtained; that is, the AABC-LSSVR model is successfully constructed, which can be used for the prediction of CO2 emissions.Figure 6
Flow chart of modeling for CO2 emissions prediction.


## 4.2. Model Performance

As mentioned above, the data in this study are the socioeconomic and CO2 emissions data from 1971 to 2017 in China, totaling 47 groups. The 47 groups of data are divided into three parts: training, validation, and testing, of which 70% are trained. The validation and testing sections each accounted for 15%.When initializing the parameters of the ABC and AABC optimization algorithms, the size of the artificial bee colony is 50, the number of honey sources is half of the size of the bee colony, the dimensionD of the solution problem is 2, the maximum number of iterations T is 300, and the maximum number of searches is limit 100. The penalty parameter c and the kernel function parameter σ have values ranging from [0.05, 1000] to [0.0001, 50], respectively. According to the aforementioned modeling process, the program was coded with MATLAB R2018b, which can be used to obtain the LSSVR and AABC-LSSVR models, respectively. Figure 7 shows the optimization results of the AABC algorithm. The optimum c and σ were synchronously obtained as follows: best c=2.8284, best σ=0.0625.Figure 7
Parameter optimization results of LSSVR by using AABC algorithm.Figure8 is an iterative optimization curve for the AABC-LSSVR model. It can be seen from the figure that under the control of adaptive regulation, in the early stage, the iterative curve drops rapidly (MSE value decreases rapidly), indicating that the iterative step size of the population is larger and the convergence speed is faster; in the medium term, the iterative curve is stable. The state indicates that some honey sources with low fitness are retained, so that the diversity of the population is supplemented; in the later stage, the iterative curve drops rapidly again to reach the convergence value, indicating that only the honey source with high fitness is selected at this time. It can be seen that the AABC has strong adaptability and effectiveness in searching for key parameters of the LSSVR algorithm.Figure 8
Iterative optimization curve of AABC-LSSVR model.The predictive performance of the LSSVR and AABC-LSSVR models with the same inputs is evaluated using the coefficient of determination (R2), as shown in Figures 9 and 10. It can be seen from Figures 9(a) and 10(a) that LSSVR has a strong fitting ability in the training set part, which is slightly inferior to the AABC-LSSVR model. However, as can be seen from Figures 9(b), 9(c) and 10(b), 10(c), the LSSVR model is significantly less effective in the verification and testing part than the AABC-LSSVR model, especially in the test section. It shows that the optimization effect of AABC on LSSVR is very obvious, which improves the fitting performance of LSSVR. It also shows that the AABC-LSSVR model proposed in this study has strong generalization ability in the prediction of CO2 emissions and is trustworthy.Figure 9
Comparison of the CO2 emissions prediction results with LSSVR model and real CO2 emissions. (a) LSSVR—training results. (b) LSSVR—validation results. (c) LSSVR—testing results. (d) LSSVR—all results.
(a)(b)(c)(d)Figure 10
Comparison of the CO2 emissions prediction results with AABC-LSSVR model and real CO2 emissions. (a) AABC-LSSVR—training results. (b) AABC-LSSVR—validation results. (c) AABC-LSSVR—testing results. (d) AABC-LSSVR—all results.
(a)(b)(c)(d)Figures9(d) and 10(d) show crossplot of real CO2 emissions versus predicted values. Coefficient of determination (R2) for LSSVR prediction is equal to 0.9427 which verifies robustness of LSSVR model. While coefficient of determination (R2) for AABC-LSSVR prediction is equal to 0.997 which verifies strong robustness of improved LSSVR model. It is sufficient to claim that the robustness of LSSVR was improved by using AABC algorithm.In addition to coefficient of determination (R2), error distribution was also employed for assessment of the LSSVR and AABC-LSSVR performance. Figure 11 allows more statistical analysis of LSSVR and AABC-LSSVR performance by using error distribution information. As shown in Figure 11(a), mean and standard deviation of error distribution for LSSVR model are in turn equal to 2.1152 × 105 and 2.1152 × 105, which are relatively larger than that of AABC-LSSVR model (see Figure 11(b)). It means that the prediction error of AABC-LSSVR model is more acceptable.Figure 11
Absolute error histogram with 20 bins of each model. (a) LSSVR model. (b) AABC-LSSVR model.
(a)(b)Figure12 provides an opportunity to compare relative error between LSSVR and AABC-LSSVR for all data points. From Figure 12(a), it can be seen that relative error of AABC-LSSVR for almost all data points is located in the range of [−5% 5%], which is an acceptable value. Figure 12(b) presents the descriptive statistics in the form of a boxplot for relative error data. Small relative error of mean and fluctuation range of data reveals high performance of AABC-LSSVR model in CO2 emissions prediction.Figure 12
Results of relative error analysis for each model. (a) Relative error of models in prediction of CO2 emissions. (b) Boxplot showing the differences in relative error of each model.
(a)(b)In summary, we can see that AABC-LSSVR outperformed LSSVR owing to higherR2 and lower relative error. This study states AABC algorithm is very effective for LSSVR and AABC-LSSVR predicted values are in good agreement with reality.


## 4.3. Discussion

The model of CO2 emission prediction has been constructed based on AABC and LSSVR algorithms, and the performance of the model has been tested. The results also show that the AABC-LSSVR model has strong robustness and generalization ability, and the prediction accuracy is acceptable and trustworthy. Therefore, the AABC-LSSVR model will be used to predict China’s CO2 emissions for the next five years (2018–2022). Considering that the socioeconomic indicators for the next five years are also unknown, this study will reduce the uncertainty of prediction by setting different scenarios, and these scenarios will adopt different input independent variable data. The characteristics of China’s social and economic indicators have been analyzed in the past few years, and the annual growth rate of each indicator has been calculated. Therefore, four scenarios will be set to generate model input independent variable data, as shown in Table 3. These data are all calculated by (14). Scenario (a) is based on the growth rate calculated in 2017 as the compound annual growth rate. Scenario (b) is based on the average growth rate between 1971 and 2017 as the compound annual growth rate. Scenario (c) is based on the nonnegative minimum growth rate between 1971 and 2017 as the compound annual growth rate. Scenario (d) is based on the nonnegative maximum growth rate between 1971 and 2017 as the compound annual growth rate.(14)ftn=ft01+cagrn,where a is the value after n years and b is the initial value.Table 3
The forecasting scenarios of the social and economic indicators related to CO2 emissions for China (from 2018 to 2022).
ScenarioYearFCC (%)PC (kw·h)OC (kgoe)GDP (yuan)PScenario (a)201824.57844.5917 × 1032.4699 × 1038.5927 × 10131.4209 × 109201927.04125.3402 × 1032.5349 × 1038.9267 × 10131.4562 × 109202029.75075.7591 × 1032.6017 × 1039.2737 × 10131.4925 × 109202132.73186.2108 × 1032.6701 × 1039.6342 × 10131.5296 × 109202236.01176.698 × 1032.7404 × 1031.0008 × 10141.5676 × 109Scenario (b)201823.66134.9553 × 1032.4978 × 1039.4060 × 10131.4016 × 109201925.06085.3478 × 1032.5925 × 1031.0697 × 10141.4169 × 109202026.54325.7714 × 1032.6908 × 1031.2164 × 10141.4324 × 109202128.11326.2286 × 1032.7928 × 1031.3833 × 10141.4481 × 109202229.77626.7219 × 1032.8986 × 1031.5731 × 10141.4639 × 109Scenario (c)201822.35934.6599 × 1032.4139 × 1038.4858 × 10131.3931 × 109201922.37884.7293 × 1032.4214 × 1038.7059 × 10131.3997 × 109202022.39834.7997 × 1032.4288 × 1038.9318 × 10131.4065 × 109202122.41794.8712 × 1032.4362 × 1038.1635 × 10131.4132 × 109202222.43754.9437 × 1032.4437 × 1038.4012 × 10131.4201 × 109Scenario (d)201847.52385.301 × 1032.7332 × 1031.1277 × 10141.4209 × 1092019101.09786.1202 × 1033.1039 × 1031.5375 × 10141.4562 × 1092020215.06637.0658 × 1033.5251 × 1032.0963 × 10141.4925 × 1092021457.51228.1576 × 1034.0035 × 1032.8582 × 10141.5296 × 1092022973.26949.4181 × 1034.5466 × 1033.8968 × 10141.5676 × 109By substituting the five indicators of CO2 emissions in each of the scenarios in Table 3 into the AABC-LSSVR model, the predictions of CO2 emissions in four different scenarios can be obtained, as shown in Figure 13.Figure 13
The forecast results of CO2 emissions for China in the next five years (2018–2022). (a) Prediction values of CO2 emissions in four scenarios. (b) The growth rates of CO2 emissions.
(a)(b)As can be seen from Figure13(a), China’s CO2 emissions in the next five years (2018–2022) have shown an upward trend year by year in the above four scenarios. In scenario (a), CO2 emissions increase from 1.0932 × 107 kilotons in 2017 to 1.3026 × 107 kilotons in 2022. In scenario (b), CO2 emissions increase from 1.0932 × 107 kilotons in 2017 to 1.3575 × 107 kilotons in 2022. The CO2 emissions in scenario (c) increase from 1.0932 × 107 kilotons in 2017 to 1.1338 × 107 kilotons in 2022. The CO2 emissions in scenario (d) increase from 1.0932 × 107 kilotons in 2017 to 2.2509 × 107 kilotons in 2022. It can be seen from Figure 13(b) that the annual growth rate of China’s CO2 emissions in the next five years under the four scenarios is quite different. Scenario (a) has an average annual growth rate of 3.57%; scenario (b) has an average annual growth rate of 4.43%; scenario (c) has an average annual growth rate of 0.735%; scenario (d) has an average annual growth rate of 15.54%. In summary, the forecast of China’s CO2 emissions in the next five years under the four scenarios indicates that China’s CO2 emissions in 2022 will fluctuate between 1.1338 × 107 kilotons and 2.2509 × 107 kilotons.The analysis results of the scenarios set above show that future CO2 emissions are closely related to their influencing factors, and changes in any key influencing factor will cause strong fluctuations in CO2 emissions. Referring to the social and economic development of China in the past period, prediction of CO2 emissions in the next few years using the hybrid intelligence model is proposed in this study. The results show that China’s CO2 emissions will continue to rise in the future. The Chinese government should formulate special policies for relevant social-economic indicators to effectively control future CO2 emissions and complete the carbon peaking and carbon neutrality goals as soon as possible.


## 5. Conclusions

Based on China’s CO2 emissions from 1971 to 2017 and related socioeconomic indicators, including FCC, electricity consumption, OC, GDP, and total population, a new hybrid intelligent algorithm model for China’s CO2 emissions forecast is proposed in this research. In view of the shortcomings of the standard ABC algorithm, in this study, an adaptive step search formula and an adaptive probability selection formula are designed to enhance the optimization ability of ABC, thus forming the AABC algorithm to optimize the hyperparameters of the LSSVR model. Finally, the ABC-LSSVR and AABC-LSSVR models are established respectively to predict China’s CO2 emissions. The results show that the absolute value of the relative error of the AABC-LSSVR model is almost controlled within 5%, which can confidently indicate that the AABC-LSSVR model has better accuracy and generalization ability for CO2 emissions prediction. It can be seen that the hyperparameter optimization problem of machine learning can be effectively solved by establishing a hybrid intelligent algorithm, thereby greatly improving the reliability of the prediction results in the research of CO2 emissions advance forecast. According to the forecast results of China’s CO2 emissions from 2018 to 2022 by the AABC-LSSVR model, China’s CO2 emissions will continue to grow in the future for a long time and will fluctuate between 1.1338 × 107 kilotons and 2.2509 × 107 kilotons by 2022. If the Chinese government needs to achieve the dual carbon goal as soon as possible, it is necessary to introduce targeted policies to restrict the social and economic indicators closely related to CO2 emissions, so as to effectively curb CO2 emissions in the future.We make the following policy recommendations to the Chinese government based on the conclusions of the analysis above. First, in order to use fixed capital scientifically and rationally and reduce its physical loss as much as possible, it is necessary to improve the management awareness and management level of enterprises. Second, it is necessary to optimize the energy structure and increase the substitution ratio of new energy to traditional energy. China’s energy structure is dominated by petrochemical energy, and a large amount of CO2 is released in the process of energy consumption. Therefore, increasing the proportion of clean energy such as solar energy and wind energy in the energy consumption structure can effectively reduce CO2 emissions, thereby alleviating the conflict between CO2 emissions and economic development. Third, China’s industrial structure and export trade structure need to be adjusted. Manufacturing, which has long been China’s main export sector, is highly dependent on upstream sectors, leading to more energy consumption and CO2 emissions. The modern service industry relies more on human capital investment, and its asset-light characteristics can greatly reduce the energy consumption of upstream and downstream industrial chains, which can reduce CO2 emissions from the source. Therefore, the transformation of the industrial structure from manufacturing to modern service industry can not only improve economic efficiency, but also reduce environmental costs. Fourth, China still needs to vigorously develop its economy to increase residents’ income. There is a clear relationship between people’s consumption concept and behavior and economic level; that is, the higher the social affluence is, the more likely people will pay attention to the environment and consider whether their behavior will have an impact on the environment. People in high-income societies will obviously reduce “high-carbon” consumption and are more inclined to buy low-carbon products to promote CO2 emission reduction. Fifth, according to the share of CO2 emissions, the government should focus on controlling high-emission sectors, such as electricity, heat, gas, and water production and supply industries, and encourage innovation and promotion of energy-saving technologies in these sectors. In addition, since technological progress is an effective way to reduce CO2 emissions, government departments should strongly support enterprises and scientific research institutions to develop low-carbon emissions, CO2 capture, and storage technology research and development. Sixth, China’s urbanization is in an accelerated stage, and the government should vigorously promote a population structure that is conducive to sustainable development, to effectively control CO2 emissions. Human activities are the main reason for the increase of CO2 emissions. The government needs to guide people to green travel and low-carbon life, so that people can actively contribute to CO2 emission reduction through their own behaviors and achieve the purpose of effectively controlling the impact of population factors on CO2 emissions.In addition, machine learning has become a key technology in CO2 emission forecasting research. Although the hybrid intelligence model proposed in this study has achieved good results, it still has the possibility of further optimization. CO2 emissions and related influencing factors are time series data. On the one hand, researchers can try to extract features from the original data to the maximum extent for algorithm modeling through feature engineering. On the other hand, researchers can try to expand the deep learning framework of the recurrent neural network series to this study. In short, only continuous in-depth research in the future can continuously improve the accuracy of advanced forecasting of CO2 emissions.



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*Source: 6822467-2022-07-07.xml*