A new multivariable grey model and its application to energy consumption in China

Abstract

Based on the nonlinearity of energy consumption systems and the influence of multiple factors, this paper presents a nonlinear multivariable grey prediction model with parameter optimization and estimates the parameters and the approximate time response function of the model. Next, a genetic algorithm is applied to optimize the nonlinear terms of the novel model to seek the optimal parameters, and the modelling steps are outlined. Then, to assess the effectiveness of the novel model, this paper adopts Chinese oil, gas, coal and clean energy as research objects, and three classical grey forecasting models and one time series method are chosen for comparison. The results indicate that the new model attains a high simulation and prediction accuracy, basically higher than that of the three grey prediction models and the time series method.

Keywords

Grey prediction model energy consumption simulated annealing optimization genetic algorithm

1 Introduction

At present, facing the profound adjustment of international energy supply and demand patterns, a new round of energy technological transformation is underway. As a major energy producer and consumer, China must seize this opportunity, implement new development concepts, focus on supply-side structural reform and actively promote energy consumption, supply, technology, institutional revolution and international cooperation. Additionally, the energy structure should be optimized to compensate for several energy development shortcomings, such as resource and environmental constraints, low quality and efficiency, poor infrastructure, and a lack of key technologies. Thus, efforts should be invested to enhance the competitiveness of the energy industry, build a clean, low-carbon, safe and efficient modern energy system and better support the sustained and stable development of the Chinese economy.

According to a preliminary calculation by the National Bureau of Statistics (NBS), the GDP of China reached 99086.5 billion yuan in 2019, and its economic aggregate approached the 100 trillion yuan mark. Translated at the average annual exchange rate, the economic aggregate reached 14.4 trillion dollars, ranking second in the world. As of 2019, the energy production of China has remained generally stable. Over the past decade, from the perspective of the total energy production, the total energy production of China has continued to grow. Primary energy production totalled 3.97 billion tons of standard coal, up to 5.1% year on year. The raw coal output reached 3.85 billion tons, up 4% year on year. The crude oil output was 191 million tons, up 0.9% year on year. The natural gas output amounted to 176.17 billion cubic metres, up to 10% year on year. Power generation reached 7503.43 billion kilowatt-hours, up 4.7% year on year. In the middle of this period, the total energy production only decreased in 2015 and 2016, and a steady growth was again attained in 2017, while the total energy production reached a historical high in 2019. From the perspective of the growth rate, the growth rate reached as high as 9.1% in 2010 and substantially decreased in 2012, with the growth rate dropping by 5.8% and continuing to decrease by approximately 4.2% in 2016. In 2017, the growth rate rebounded to 3.6%, and the growth rate over the past two years remained stable at 5% and 5.1%, still 4% lower than the high growth rate of 9.1% in 2010.

In addition, energy consumption has exhibited a steady growth trend. The total energy consumption in 2019 was 4.86 billion tons of standard coal, an increase of 3.3% over the previous year. Coal consumption increased by 1.0%, crude oil consumption increased by 6.8%, natural gas consumption increased by 8.6%, and electricity consumption increased by 4.5%. Over the past decade, the total energy consumption has continued to rise, with an increase of 1.25 billion tons of standard coal in 2019 over the 2010 level. According to energy consumption structure data in recent years, the proportion of coal consumption exhibited a downward trend, falling to lower than 60% in 2018. However, coal remains the main energy source in China in the short term. The proportion of clean energy consumption in the total energy consumption nearly doubled from 13% in 2011 to 23.4% in 2019. In general, in the energy composition of China, coal occupies the dominant position, oil and natural gas are highly dependent on foreign countries, and the proportion of clean energy consumption continues to increase.

The energy development of China occurs at a critical stage of transformation, thereby experiencing unprecedented opportunities and challenges. An important development goal and task of the 14th Five-Year Plan is to increase efforts to strengthen the clean energy industry and lay a firm foundation to achieve the goal of a 20% non-fossil energy proportion in the primary energy consumption by 2030. During the 14th Five-Year Plan period, China still faces a complicated international situation and domestic energy revolution, and coal still occupies a dominant position in the primary energy consumption structure of China for a long period of time in the future. To accelerate energy consumption transformation, enhancement of the clean energy level and efficient utilization of traditional fossil energy will become an important task in the energy development of China during the 14th Five-Year Plan period. Energy production should not only optimize the stock but also promote clean and efficient development and utilization of coal as the foundation and primary task of energy transformation and development [1, 2]. The mechanisms and policies that encourage the development of distributed energy should be improved, the energy price system should be standardized, the attributes of energy commodities should be restored, the decisive role of the market in resource allocation and the role of the government should be maximized, and an energy market system with fair competition conditions should be stablished.

Therefore, the prediction and analysis of energy consumption in China are very important. In this paper, a novel model is applied to four energy consumption forecasts in China, and the prediction results provide effective information for the Chinese government to formulate energy economic policies. The original data are obtained from the National Bureau of Statistics of China. Accurate energy consumption prediction provides greater insights into future energy supply conditions, helps adjust and improve the energy structure of a given country and promotes the diversification of energy development and utilization. On the basis of prediction data, it is also helpful to implement practical measures to allocate social resources in advance and ensure the healthy and rapid development of the Chinese economy.

2 Literature review

2.1 Research progress of energy consumption prediction

Aiming at the problem of energy consumption trend prediction, numerous scholars have proposed various learning methods from different perspectives. The existing methods mainly include time series models, regression analysis models, econometric models, artificial neural network models, and hybrid prediction models. For example, Ruiz et al. [3] proposed a time series clustering method based on extracted energy consumption data and applied it to the modelling and prediction of public building energy. Di Leo et al. [4] employed regression analysis to forecast the energy demand and considered data pertaining to local regions and all of Italy to verify the effectiveness of the model. De Albuquerquemello [5] established an oil price prediction model by studying the relationship between the changes in economic parameters in the United States and the United States oil supply and demand. Huang et al. [6] introduced the principles of decomposition and integration into the modelling method of artificial neural networks and proposed a novel international energy prediction method. Barak et al. [7] applied a combination of linear regression and the autoregressive integrated moving average (ARIMA) hybrid algorithm to predict energy consumption.

The above models more accurately predict energy data, but these models usually require a high data volume during the establishment process. To obtain a highly accurate model, a large amount of data must be preprocessed [8]. After data cleaning and conversion, the selected data can be applied as the input of the neural network model, so more time and effort are needed in data processing.

In recent years, great changes have occurred in the global energy structure. Therefore, certain historical data offer a limited reference value given the current energy situation or future energy development trends. This situation leads to a sharp reduction in energy-related data. Moreover, modelling methods that require a large amount of data training to ensure the model accuracy are not applicable. Therefore, if there were a model requiring a small amount of time to obtain data and establish the model while simultaneously obtaining a good prediction accuracy, this model would be considered attractive [9]. In this paper, the research direction focused on the grey prediction model. Comparatively, the grey system prediction model yields more advantages in addressing uncertain systems with small samples and a poor data quality [10] and can produce more accurate prediction results even in the case of relatively scarce data [11, 12].

2.2 Research progress of the grey prediction model in energy consumption prediction

The grey prediction model can be applied to systems with uncertainty and scarce data. As mentioned earlier, due to the change in the energy structure and the influence of various other factors, not all historical data are suitable for current energy consumption forecasting. Therefore, the amount of usable data is currently very small. The grey model is a method that can suitably consider small samples to achieve the purpose of simulation and prediction. The model can simulate and predict with at least four data samples, which is suitable for energy prediction involving fewer data samples. Moreover, the grey prediction model has been successfully applied to the prediction of energy consumption. For example, Luo et al. [13] added nonlinear terms to the grey Riccati model, optimized these nonlinear terms with the simulated annealing (SA) optimization algorithm, and then predicted the consumption of clean energy. Ma et al. [14] proposed a novel polynomial grey prediction model to predict natural gas consumption in China. Ye et al. [15] proposed an interval grey optimized model to predict energy consumption. Xiao et al. [16] performed Box-Cox transformation to establish a new constrained grey Bernoulli optimization model to predict biomass energy consumption in China, the United States, Brazil and Germany. Zhao and Wu [17] developed a neighbourhood cumulative discrete grey model and applied it to predict non-renewable energy consumption in several countries.

The above literature reports different methods to study the prediction of energy consumption. Sequential data were basically applied to the energy consumption sequence itself, and the modelling object was a single time series without considering the influence of relevant factors on the system, so the modelling process was relatively simple. The grey univariate model contains a single variable and a first-order equation. [18 –26] and directly applies a univariate time series to modelling. However, the energy system possesses a complex structure and many influencing factors. At present, there are studies related to energy consumption and management, most of which are based on the comprehensive consideration of multiple factors. For example, Rezaei et al. [27] considered the joint production of a variety of clean energy sources and carried out technical and economic analyses of this production approach. Zhou et al. [28] proposed a stochastic method based on unscented transformation (UT) to predict the demand for electricity and heat more accurately. Gong et al. [29] developed a method to apply distributed energy management. These articles have considered the influence of various factors on the energy system in practical application scenarios and carried out in-depth analysis. In the grey system, many scholars have accounted for this aspect.

The modelling process of the multivariable grey prediction model [30 –32] fully considers the influence of relevant factors on system changes, thus compensating for the limitations of the univariate model and the deficiency of its limited simulation ability. For example, Wang et al. [33] used an optimized multivariable grey prediction model to predict the industrial energy consumption of China, and Zeng et al. [34] proposed a novel multivariable grey prediction model and applied it to energy consumption prediction. Dang et al. [35] established a new multivariable grey prediction model to estimate the total electricity consumption in Jiangsu Province, China, while Wu et al. [36] developed a multivariable grey prediction model that considers the change in the total population, which was employed to predict the electricity consumption in Shandong Province, China, with good results.

The above multivariable grey prediction model considers multiple factors of energy consumption to resolve the energy consumption prediction problem and provides good results, thus mitigating the defects whereby the univariate model does not consider the influence of multiple factors. However, the above models are basically linear models, and energy consumption systems are generally nonlinear systems. Therefore, this article is based on the classic GMC(1,N) model [37]. This paper obtains a nonlinear multivariate grey prediction model by adding nonlinear terms, and the optimized model relies on a genetic algorithm to optimize the nonlinear terms. Then, the novel model is applied to four major energy consumption cases in China, and the fossil fuel energy consumption of coal, oil and natural gas and clean energy consumption are forecast over the next five years.

2.3 Contribution and organization

To solve the nonlinearity of the energy consumption system and the influence of multiple factors, a nonlinear grey multivariable grey prediction model is proposed, and parameter estimation and time response equations of the model are obtained. Moreover, this model achieves a good effect in the prediction of energy consumption given a nonlinearity data structure and multiple factors.

To improve the accuracy of the novel model, the genetic algorithm is used to optimize nonlinear terms, select value ranges of the nonlinear terms and obtain locally optimal nonlinear terms. The novel model chooses oil, natural gas, coal and clean energy in China as research objects to analyse the effectiveness of the model, and the results are superior to those obtained with three other grey prediction models and a time series method.

According to the effectiveness analysis results for the proposed model, the novel model is adopted to predict the consumption of three kinds of fossil and clean energy sources in China over the next five years. The forecast results reveal that China does not reach a consumption peak within the next five years. The growth of coal and oil energy occurs gradually, and the fastest growth is observed for clean energy and natural gas.

The other sections of this article are arranged as follows: section 3 proposes the GOMC(1,N) model and outlines the optimal modelling steps. Section 4 considers three kinds of fossil and clean energy sources in China in an empirical analysis of the model and predicts the consumption of these four kinds of energy sources in China over the next five years. Section 5 provides a summary and prospects.

3 GOMC(1,N) model

This section first introduces the definition and related conclusions of the traditional GMC(1,N) model [38], then establishes a nonlinear GOMC(1,N) model and optimizes the nonlinear terms of the model with a genetic algorithm.

3.1 Definition and properties of the GMC(1,N) model

Definition 1. The raw data are defined as X⁽⁰⁾ = {X⁽⁰⁾ (1) , X⁽⁰⁾ (2) , ⋯ , X⁽⁰⁾ (n)}, and after accumulation, the sequence is recorded as X⁽¹⁾ = {X⁽¹⁾ (1) , X⁽¹⁾ (2) , ⋯ , X⁽¹⁾ (n)}, where: $X^{(1)} (k) = \sum_{j = 1}^{k} X^{(0)} (j), k = 1, 2, 3, \dots, n$

Definition 2. The GMC(1,N) model is defined as follows:

$\begin{matrix} X_{1}^{(0)} (rp + t) + b_{1} Z_{1}^{(1)} (rp + t) \\ = b_{2} Z_{2}^{(1)} (t) + b_{3} Z_{3}^{(1)} (t) + \dots + b_{n} Z_{n}^{(1)} (t) + u \end{matrix}$ (1) where r is the number of data points used for modelling, rp is the time delay coefficient, rf is the number of points used for prediction, and b₁, b₂, ⋯ , b_n and u denote the parameters to be estimated. In addition, the differential equation is as follows:

$\begin{matrix} \frac{{dX}_{1}^{(1)} (rp + t)}{dt} + b_{1} X_{1}^{(1)} (t) \\ = b_{2} X_{2}^{(1)} (t) + b_{3} X_{3}^{(1)} (t) + \dots + b_{n} X_{n}^{(1)} (t) + u \end{matrix}$ (2)

The above equation is denoted as the whitening equation of the GMC(1,N) model, and the following applies: $X_{1}^{(1)} (rp + t) = \sum_{k = rp + 1}^{rp + t} X_{1}^{(0)} (k), t = 1, 2, \dots, r + rf$ $Z_{1}^{(1)} (rp + t) = \frac{X_{1}^{(1)} (rp + t) + X_{1}^{(1)} (rp + t - 1)}{2}$

Theorem 1. The least-square estimation equation of the GMC(1,N) model parameters is: $[b_{1}, b_{2}, \dots, b_{n}, u]^{T} = (B^{T} B)^{- 1} B^{T} Y_{n}$ where: $\begin{matrix} B = [\begin{matrix} - Z_{1}^{(1)} (rp + 2) & Z_{2}^{(1)} (2) & \dots & Z_{n}^{(1)} (2) & 1 \\ - Z_{1}^{(1)} (rp + 3) & Z_{2}^{(1)} (3) & \dots & Z_{n}^{(1)} (3) & 1 \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ - Z_{1}^{(1)} (rp + n) & Z_{2}^{(1)} (n) & \dots & Z_{n}^{(1)} (n) & 1 \end{matrix}], \\ Y = [\begin{matrix} X^{(0)} (rp + 2) \\ X^{(0)} (rp + 3) \\ ⋮ \\ X^{(0)} (rp + n) \end{matrix}] \end{matrix}$

Theorem 2. Equation (2) is expressed as: $f (t) = \sum_{j = 2}^{n} b_{j} X_{j}^{(1)} (t) + u$

The solution of Equation (2) is:

$\begin{matrix} X_{1}^{(1)} (rp + t) = & X_{1}^{(1)} (rp + 1) e^{- b_{1} (t - 1)} \\ + \int_{1}^{t} e^{- b_{1} (t - τ)} f (t) dt \end{matrix}$ (3)

With the use of the integral trapezoidal equation, the following is obtained: $\begin{matrix} \int_{1}^{t} e^{- b_{1} (t - τ)} f (t) dt = u (t - 2) \\ \times \sum_{τ = 2}^{t} \frac{1}{2} [e^{- b_{1} (t - τ)} f (τ) + e^{- b_{1} (t - τ + 1)} f (τ - 1)] \end{matrix}$

Moreover, u (t - 2) is the unit step function, which is defined as: ${\begin{matrix} u (t - 2) = 0, t < 2 \\ u (t - 2) = 1, t ⩾ 2 \end{matrix}$

The value of u (t - 2) can be determined by the range of values of t. Then, the reduction equation is: ${\hat{X}}_{1}^{(0)} (rp + t) = {\hat{X}}_{1}^{(1)} (rp + t) - {\hat{X}}_{1}^{(1)} (rp + t - 1)$

3.2 Establishment of the GOMC(1,N) model

In this section, the grey GOMC(1,N) model is first established, the parameter estimation and time response equations of the model are then obtained, and the nonlinear terms of the model are optimized with the genetic algorithm. The traditional GMC(1,N) model remains a linear model in nature and achieves a low efficiency in predicting complex nonlinear time series, which limits its applicability. Therefore, this section first establishes a nonlinear model below.

Definition 3. X⁽⁰⁾, X⁽¹⁾, Z⁽¹⁾ are defined according to definition 1, and the model can be built as:

$\begin{matrix} X_{1}^{(0)} (rp + t) + b_{1}^{'} Z_{1}^{(1)} (rp + t) \\ = b_{2}^{'} Z_{2}^{(1)} (t) + b_{3}^{'} Z_{3}^{(1)} (t) + \dots + b_{n}^{'} Z_{n}^{(1)} (t) + c (t - 1)^{τ} + u \end{matrix}$ (4)

This model is referred to as the nonlinear GMC(1,N) optimization model, abbreviated as the GOMC(1,N) model. The following whitening equation can be obtained from Equation (4):

$\begin{matrix} \frac{{dX}_{1}^{(1)} (rp + t)}{dt} + b_{1}^{'} X_{1}^{(1)} (t) \\ = b_{2}^{'} X_{2}^{(1)} (t) + b_{3}^{'} X_{3}^{(1)} (t) + \dots + b_{n}^{'} X_{n}^{(1)} (t) + c (t - 1)^{τ} + u \end{matrix}$ (5)

where c (k - 1) ^τ and u are nonlinear correction terms, r is the number of data points used for modelling, and rp is the time delay coefficient. If there is no time delay, then. rf is the number of points used for pre rp = 0 diction, and $b_{1}^{'}, b_{2}^{'}, \dots, b_{n}^{'}, c$ and u denote the parameters to be estimated. Via the least-squares method, the parameter estimation function of theorem 3 can be obtained.

Theorem 3. The parameter list is defined as $P = {(b_{1}^{'}, b_{2}^{'}, \dots, b_{n}^{'}, c, u)}^{T}$ , where:

$B = (\begin{matrix} - Z_{1}^{(1)} (rp + 2) & Z_{2}^{(1)} (2) & \dots & Z_{n}^{(1)} (2) & (2 - 1)^{τ} & 1 \\ - Z_{1}^{(1)} (rp + 3) & Z_{2}^{(1)} (3) & \dots & Z_{n}^{(1)} (3) & (3 - 1)^{τ} & 1 \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ - Z_{1}^{(1)} (rp + n) & Z_{2}^{(1)} (n) & \dots & Z_{n}^{(1)} (n) & (n - 1)^{τ} & 1 \end{matrix})$

$P = (\begin{matrix} b_{1}^{'} \\ b_{2}^{'} \\ ⋮ \\ b_{n}^{'} \\ c \\ u \end{matrix}), Y_{R} = (\begin{matrix} X_{1}^{(0)} (rp + 2) \\ X_{1}^{(0)} (rp + 3) \\ ⋮ \\ X_{1}^{(0)} (rp + n) \end{matrix})$

Then, parameter $P = {(b_{1}^{'}, b_{2}^{'}, \dots, b_{n}^{'}, c, u)}^{T}$ satisfies:

$P = {(b_{1}^{'}, b_{2}^{'}, \dots, b_{n}^{'}, c, u)}^{T} = (B^{T} B)^{- 1} B^{T} Y$ (6)

Proof. The above result can be proven with the least-squares method.

Based on theorem 2, the following theorem can be obtained:

Theorem 4. $f (t) = \sum_{j = 2}^{n} b_{j}^{'} X_{j}^{(1)} (t) + c (t - 1)^{τ} + u$

The solution of Equation (5) is:

$\begin{matrix} X_{1}^{(1)} (rp + t) = X_{1}^{(1)} (rp + 1) e^{- b_{1}^{'} (t - 1)} + u (t - 2) \\ \times \sum_{τ = 2}^{t} \frac{1}{2} [e^{- b_{1}^{'} (t - τ)} f (τ) + e^{- b_{1}^{'} (t - τ + 1)} f (τ - 1)] \end{matrix}$ (9) where u (t - 2) is the unit step function and defined as: ${\begin{matrix} u (t - 2) = 0, t < 2 \\ u (t - 2) = 1, t ⩾ 2 \end{matrix}$

And the reduction equation is:

${\hat{X}}_{1}^{(0)} (rp + t) = {\hat{X}}_{1}^{(1)} (rp + t) - {\hat{X}}_{1}^{(1)} (rp + t - 1)$ (10)

3.3 Optimization of the nonlinear correction term of the GOMC(1,N) model

Section 3.2 reveals that the parameters P = (b₁, b₂, ⋯ , b_n, c, u) ^T of the model can be obtained by determining the order τ, which is the nonlinear quantity. In this section, to verify the effectiveness of the model, this paper mainly adopts two indicators to evaluate the model, namely, the absolute percentage error (APE) and average absolute percentage error (MAPE), which are defined as follows: $APE = (\frac{x^{(0)} (k) - {\hat{x}}^{(0)} (k)}{x^{(0)} (k)}) \times 100 %, k = 1, 2, 3 \dots n$

$MAPE = \frac{1}{n} (\sum_{i = 1}^{n} | \frac{x^{(0)} (i) - {\hat{x}}^{(0)} (i)}{x^{(0)} (i)} |) \times 100 %$ (11)

Optimization of the nonlinear terms mainly targets the order τ in Equation (4). This model uses the genetic algorithm proposed by Holland et al. [39] to search the order. The model applies the evolutionary principle of survival of the fittest and elimination of the unfit in the biological world to optimize the selection of encoded parameter individuals. The appropriate fitness function is obtained, and the fitness value of all individuals is calculated. After selection, mutation and crossover, the overall fitness level of the population is continuously improved, which not only inherits suitable information from the previous generation but also performs better than the previous generation. Then, the cycle is repeated until the desired conditions are met, and the calculation steps are listed in Table 1.

Table 1

Algorithm: The algorithm of GA to find the optimal τ
Set the objective function
Input: The original series and the number of modeling data
Output: The best order
for τ ∈ (0, + ∞] do
Substitute r to $\hat{P} = {(B^{T} B)}^{- 1} B^{T} Y$ and obtain parameters $P = {(b_{1}^{'}, b_{2}^{'}, \dots, b_{n}^{'}, c, u)}^{T}$
Substitute parameters to discrete equation Equation (6) and compute the simulation value to get
${\hat{x}}^{(1)} (k)$
Compute ${\hat{x}}^{(0)} (k)$ in Equation (9,10)
Compute MAPE in Equation (11)
End
Update the minimum value MAPE
Return the best r by using GA.

Based on the definition of the GOMC(1,N) model and genetic algorithm, the whole prediction process of the proposed model is as follows:

The original series x⁽⁰⁾ is input.

The 1-AGO series x⁽¹⁾ of x⁽⁰⁾ and the mean sequence z⁽¹⁾ of the 1-AGO series are computed.

The data of step 1 are substituted into Equation (6) and the initial nonlinear order to obtain parameters $b_{1}^{'}, b_{2}^{'}, \dots, b_{n}^{'}, c, u$ .

The coefficients obtained in the previous step are substituted into the time response equation, and the restored value ${\hat{x}}^{(0)} (k)$ is then computed.

The data of the above three steps are substituted into Equation (11) to construct the GOMC model and compute the MAPE.

The GA algorithm is applied to optimize the nonlinear terms and compute the lowest MAPE value.

The optimal τ value is substituted to reconstruct the GOMC model and compute the simulated data ${\hat{x}}^{(0)} (k)$ and MAPE.

4 Application of the GOMC(1,N) model in prediction of the energy consumption of China

4.1 Analysing the validity of the novel model in energy consumption prediction in China

China is the largest developing country worldwide, and the formulation and implementation of energy measures have attracted global attention. Therefore, this article applies the novel model to four energy consumption prediction cases in China and analyses the prediction results to provide effective information to the Chinese government to formulate energy economy policies. The original data originate from the National Bureau of Statistics of China, as indicated in Table 2. In this section, a trend change diagram for each factor is generated. As shown in Fig. 1, the GDP, oil, natural gas and clean energy show an obvious linear upward trend, while coal exhibits an unsaturated S-shaped change trend. Moreover, the population reveals a stable trend, and the growth rate decreases. Among these factors, the population and GDP are the main influencing factors of the four types of energy. The models considered in the comparative experiment are the traditional GM(1,N) model [40], GMC(1,N) model [37], OBGM(1,N) model [41], NGM(1,N) model [42] and nonlinear autoregressive with external input neural network (NARX) model. The first three examples are fossil energy consumption projections, and the last example is a clean energy consumption projection.

Table 2
Raw energy data for the different variables

Year Total oil consumption Total coal consumption Total gas consumption Total clean energy consumption Total population GDP

2010 62752.75 249568.42 14425.92 33900.91 134091 412119.3

2011 65023.22 271704.19 17803.98 32511.61 134735 487940.2

2012 68363.46 275464.53 19302.62 39007.39 135404 538580

2013 71292.12 280999.36 22096.39 42525.13 136072 592963.2

2014 74090.24 279328.74 24270.94 48116.08 136782 643563.1

2015 78672.62 273849.48 25364.4 52018.5 137462 688858.2

2016 80626.51 270207.78 27020.78 57963.93 138271 746395.1

2017 84323.45 270911.52 31397.03 61897 139008 832035.9

2018 87696 273760 36192 66352 139538 919281.1

2019 91854 280422 39366 74358 140005 990865.1

Year	Total oil consumption	Total coal consumption	Total gas consumption	Total clean energy consumption	Total population	GDP
2010	62752.75	249568.42	14425.92	33900.91	134091	412119.3
2011	65023.22	271704.19	17803.98	32511.61	134735	487940.2
2012	68363.46	275464.53	19302.62	39007.39	135404	538580
2013	71292.12	280999.36	22096.39	42525.13	136072	592963.2
2014	74090.24	279328.74	24270.94	48116.08	136782	643563.1
2015	78672.62	273849.48	25364.4	52018.5	137462	688858.2
2016	80626.51	270207.78	27020.78	57963.93	138271	746395.1
2017	84323.45	270911.52	31397.03	61897	139008	832035.9
2018	87696	273760	36192	66352	139538	919281.1
2019	91854	280422	39366	74358	140005	990865.1

Fig. 1

Comparison of the trends of the different factors.

The unit of energy consumption is 10000 tons of standard coal, the unit of the population is ten thousand people, and the unit of the GDP is 100 million yuan.

Case 1: Forecast of the coal consumption in China

In the first case, coal consumption was selected as the research object. Data from 2010 to 2015 were used to build the model, and data from 2016 to 2019 were considered for model testing. The results for each model are summarized in Table 3, where the optimal τ value of the GOMC(1,N) model is 2.3900, and the optimal background value coefficient of the OBGM(1,N) model is 0.2324. According to the calculation results, a data trend chart is generated, as shown in Fig. 2.

Table 3

Simulation and prediction results for each model in regard to coal consumption in China.

Raw	GM	APE	NGM	APE	OBGM	APE	GMC	APE	NARX	APE	GOMC	APE
data	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)		(%)	(1,N)	(%)
249568.42	249568.4200	0.0000	2.4957E+05	0.0000E+00	2.4957E+05	0.0000	2.4957E+05	0.0000E+00	235997.0793	5.4379	249568.42	0.0000
271704.19	242601.8406	10.7110	2.7170E+05	0.0000E+00	2.7574E+05	1.4848	1.2330E+06	3.5381E+02	242275.3389	10.8312	229402.6578	15.5690
275464.53	314050.0992	14.0075	5.0176E+06	1.9215E+03	2.6483E+05	–3.8596	2.7693E+07	9.9532E+03	244596.2774	11.2059	265096.9649	3.7637
280999.36	294533.3046	4.8164	1.5297E+07	5.3439E+03	3.1921E+05	13.5982	7.1947E+08	2.5594E+05	257127.5439	8.4953	284084.5453	–1.0979
279328.74	285391.2008	2.1704	6.2632E+07	2.2522E+04	1.5518E+05	–44.4462	1.8807E+10	6.7329E+06	259889.6515	6.9592	290230.6448	–3.9029
MAPE_SIM (%)		7.9263		7.4469E+03		15.8472		1.7498E+06		8.5859		6.0834
273849.48	283575.4284	3.5516	2.3640E+08	8.6225E+04	6.2315E+05	127.5518	4.9175E+11	1.7957E+08	261055.6821	4.6718	283036.6024	3.3548
270207.78	284559.7033	5.3114	9.1096E+08	3.3723E+05	1.1292E+06	–517.9000	1.2858E+13	4.7585E+09	258185.7011	4.4492	269930.4942	–0.1026
270911.52	286204.6379	5.6451	3.4915E+09	1.2887E+06	5.0347E+06	1758.4000	3.3619E+14	1.2410E+11	252165.7131	6.9195	267480.8647	–1.2663
273760.00	287607.9110	5.0584	1.3401E+10	4.8952E+06	1.5434E+07	–5737.8000	8.7904E+15	3.2110E+12	244448.2084	10.7071	276741.8309	1.0892
280422.00	288856.0498	3.0076	5.1415E+10	1.8335E+07	5.2659E+07	18679.0000	2.2984E+17	8.1963E+13	234787.8821	16.2734	280324.579	–0.0347
MAPE_PRE (%)		4.5148		2.4942E+07		5364.0675		1.7061E+13		8.6042		1.1695

Fig. 2

Trend comparison diagram of the model data in Case 1.

According to the results in Table 3, NGM(1,N), GMC(1,N) and OBGM(1,N) yield large errors at the two stages, indicating that these three models are not suitable for the prediction of coal consumption in China. GM(1,N), NARX and GOMC(1,N) yield small errors at the two stages, and GOMC(1,N) yields the smallest errors. Moreover, the error in the optimized model is significantly smaller, indicating that GOMC(1,N) is more suitable for the prediction of coal consumption than are the other models. To analyse the results more intuitively, Fig. 2 shows a trend comparison diagram of the simulation and prediction results for the GM(1, N), GOMC(1, N) and NARX models, as listed in Table 3, to the raw data, and an error comparison of the three models is shown in Fig. 3.

Fig. 3

APE comparison of the various models in Case 1.

Because the errors in the NGM, GMC and OBGM models are too large, which influences the comparison effect of the other models, these models are not shown in the trend comparison chart. The GM(1,N) model basically overestimates the actual trend, the NARX results are all below the original data curve, and the trend of the GOMC(1,N) model is the closest to the actual trend line. The trend chart in Fig. 2 shows that GOMC(1,N) at the other nodes is closer to the original data except that the difference at the first node is larger.

As shown in Fig. 3, the APE value of GOMC(1,N) was basically the lowest except in 2011, and the value was close to zero in three years. All the above information indicates that the GOMC model effectively predicts coal consumption in China.

Case 2: Forecast of the oil consumption in China

The object of the second case study is oil consumption in China, which is the same as that in the previous case. The data of the first five years are used to build the model, and the data of the next five years are applied for model testing. The calculation results for each model are summarized in Table 4, where the optimal parameter of GOMC(1,N) is τ = 1.3979, and the optimal background value parameter of OBGM(1,N) is 0.6652. A data trend chart is also generated, as shown in Fig. 4.

Table 4

Simulation and prediction results of oil consumption in China for each model

Raw	GM	APE	NGM	APE	OBGM	APE	GMC	APE	NARX	APE	GOMC	APE
data	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)		(%)	(1,N)	(%)
62752.75	62752.7500	0.0000	62752.7500	0	62752.7500	0	62752.7500	0.0000	62585.4628	0.2666	62752.7500	0
65023.22	55991.9966	13.8892	65023.2200	0	66857.3905	2.8208	57348.8656	11.8020	62309.4936	4.1735	64044.8368	1.5047
68363.46	74421.1583	8.8610	–86286.6955	–226.2176	69849.5486	2.1738	63546.6930	7.0458	68510.2877	0.2148	68138.6580	0.3288
71292.12	73053.8363	2.4711	108401.5624	52.0527	72995.3786	2.3891	67460.8386	5.3741	71411.7832	0.1678	71396.7926	0.1468
74090.24	74414.7815	0.4380	126574.0415	–270.8377	75890.5112	2.4298	70550.6162	4.7774	75244.9018	1.5585	74337.2781	0.3334
MAPE_SIM (%)		6.4149		137.277		2.4534		7.2500		1.2762		0.5784
78672.62	76614.8923	–2.6156	170466.3184	116.6781	85309.7110	8.4363	73210.3920	–6.9430	78728.1720	0.0706	77028.7039	2.0896
80626.51	79718.5786	–1.1261	190542.8696	–336.3278	81968.0400	1.6639	75825.4665	–5.9547	82991.0725	2.9327	79745.7842	1.0924
84323.45	84268.3456	–0.0653	268757.8325	218.7225	87024.1350	3.2028	79017.7160	–6.2921	85509.9937	1.4071	83193.7840	1.3397
87696.00	88844.2261	1.3093	288500.3173	–428.9777	91789.2220	4.6675	82823.1312	–5.5565	87489.7656	0.2352	87627.2664	0.0784
91854.00	92609.4143	0.8224	412477.1341	349.0573	95593.7830	4.0714	86618.3787	–5.6999	91515.1802	0.3689	92485.1557	0.6871
MAPE_PRE (%)		1.1877		1449.7635		4.4084		6.0893		1.0029		1.0574

Fig. 4

Trend comparison diagram of the model data in Case 2.

The results in Table 4 indicate that the NGM(1,N) model yields the largest errors at the two stages. The modelling errors of the GM(1,N) and GMC(1,N) models are similar, while the GOMC(1,N) model attains the highest accuracy, and MAPE_SIM is 7% lower than that of the unoptimized model. Moreover, MAPE_PRE is improved by 5%. MAPE_PRE of the NARX model is slightly lower than that of the GOMC(1,N) model, but its MAPE_SIM value is higher, while the simulation effect is not as good as that of the GOMC(1,N) model. This indicates that the GOMC(1,N) model is more suitable for oil consumption prediction in China than are the other models. To facilitate a clear comparison of the various models, a trend graph of the four models and a relative error graph of the four models are shown in Figs. 4 and 5, respectively.

Fig. 5

APE comparison of the various models in Case 2.

As shown in Fig. 4, the GM(1,N) and OBGM(1,N) models basically overestimate the actual trend, the GMC(1,N) model overestimates the actual trend at the modelling stage and underestimates the actual values at the forecasting stage, and the NARX model exhibits a slight fluctuation trend, fluctuating around the curve of the real values at both the prediction and simulation stages. The GOMC(1,N) model trend is close to the actual trend. Moreover, in the APE comparison shown in Fig. 5, the APE value of the GOMC(1,N) model is the lowest in every year, and the lowest APE values are those of the NARX(1,N) and GOMC(1,N) models. The performance of the GOMC(1,N) model is relatively stable, which indicates that the GOMC(1,N) model can effectively predict oil consumption in China.

Case 3: Forecast of the natural gas consumption in China

The third object is the third largest energy source in the energy structure of China, which is also the energy source experiencing great development in recent years. In this case, the 2010–2018 data are used to build the model, and the data of the last year are considered to test the model. The results for the five models are listed in Table 5, where the optimal parameter of GOMC(1,N) is τ = 5.1988, and the optimal background value parameter of OBGM(1,N) is 0.0015. Then, according to the obtained data, a data trend comparison chart is generated, as shown in Fig. 6. A relative error diagram is shown in Fig. 7.

Table 5

Simulation and prediction results of natural gas consumption in China for each model

Raw	GM	APE	NGM	APE	OBGM	APE	GMC	APE	NARX	APE	GOMC	APE
data	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)		(%)	(1,N)	(%)
14425.92	14425.9200	0	14425.9200	0.0000	14425.9200	0.0000	14425.9200	0.0000	14499.1536	0.5077	14425.9200	0.0000
17803.98	15276.8872	14.194	17620.1443	–1.0326	17590.2932	1.2002	16462.5122	7.5347	17815.4945	0.0647	17519.0397	1.6004
19302.62	21171.6507	9.6828	23253.2793	20.4670	19793.5381	2.5433	16073.7801	16.7275	19284.7481	0.0926	19931.6832	3.2590
22096.39	22215.6182	0.5396	26834.4179	21.4425	22007.1709	0.4038	12180.2480	44.8768	23729.3388	7.3901	21909.7717	0.8446
24270.94	23874.6923	1.6326	29283.2525	20.6515	23877.5633	1.6208	–1316.0736	105.4224	24259.3765	0.0476	23514.3931	3.1171
25364.40	25617.8193	0.9991	31061.3799	22.4605	25411.3072	0.1849	–40881.3146	261.1760	25364.7936	0.0016	24994.3520	1.4589
27020.78	27921.8743	3.3348	32958.7027	21.9754	27302.3937	1.0422	–152065.8967	662.7739	26741.0262	1.0353	26693.8961	1.2097
31397.03	31379.2043	0.0568	36785.0569	17.1609	31227.6285	0.5395	–460581.5030	1566.9588	27894.9919	11.1540	29001.4840	7.6298
36192.00	34907.2492	3.5498	42021.6636	16.1076	36265.2771	0.2025	1310608.0677	3721.2646	26418.7863	27.0038	32711.8281	9.6159
MAPE_SIM (%)		4.2487		17.6623		0.9671		798.3418		5.2553		3.5919
39366.00	37801.7127	3.9737	47036.3672	19.4848	40770.5790	3.5680	3644070.9031	9356.8991	21970.7036	44.1886	39365.9236	0.0002
MAPE_PRE (%)		3.9737		19.4848		3.5680		9356.8991		44.1886		0.0002

Fig. 6

Trend comparison diagram of the model data in Case 3.

Fig. 7

APE comparison of the various models in Case 3.

The results in Table 5 indicate that the errors in the NGM(1,N) and GMC(1,N) models are large at the two stages, and the modelling error in the OBGM(1,N) model is the smallest, while the modelling error in the GOMC(1,N) model is only smaller to that in the OBGM(1,N) model. The prediction error in the GOMC(1,N) model is the smallest, which is close to 0, and significantly improves the error in the model before optimization. This demonstrates that GOMC is more suitable for natural gas consumption prediction than are the other models.

As shown in Fig. 6, the NGM(1,N), GM(1,N) and OBGM(1,N) models basically overestimate the actual consumption trend, and the NARX model reveals an obvious downward trend on the last few sets of data, which is obviously not in line with the actual situation. Only the GOMC(1,N) model trend is close to the actual trend. In the comparison chart of the APE values shown in Fig. 7, the OBGM(1,N) model yields the lowest APE value at the model establishment stage, while at the prediction stage, the APE value of the GOMC(1,N) model is close to 0. In conclusion, the GOMC(1,N) model can effectively predict natural gas consumption in China.

Case 4: Forecast of clean energy consumption in China

The fourth case concerns clean energy consumption in China. The data from 2011–2018 are used for model building, and the data of the last year are used for model testing. The results for the five models are listed in Table 6, in which the optimal parameter of GOMC(1,N) is τ = 2.1658, and the optimal parameter of OBGM(1,N) is 0.5373. A data trend chart is also produced, as shown in Fig. 8.

Table 6

Simulation and prediction results for each model regarding clean energy consumption in China

Raw	GM	APE	NGM	APE	OBGM	APE	GMC	APE	NARX	APE	GOMC	APE
data	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)	(1,N)	(%)		(%)	(1,N)	(%)
32511.61	32511.61	0.0000	32511.61	0.0000	32511.61	0.0000	32511.61	0.0000	28844.89161	11.2782	32511.61	0.0000
39007.39	34854.6739	10.6460	38831.2834	–0.4515	38785.4883	0.5689	38302.1086	1.8081	30859.6592	20.8877	37978.8253	2.6368
42525.13	52621.5661	23.7423	49892.5793	17.3249	43081.2339	1.3077	42576.522	–0.1209	39520.91967	7.0646	42474.1683	0.1198
48116.08	54480.6354	13.2275	58893.5454	22.3989	47557.6525	1.1606	46900.6772	2.5260	46717.28185	2.9071	47203.9893	1.8956
52018.5	55361.7119	6.4270	66520.7619	27.8790	52438.7812	0.8079	51415.2635	1.1597	51088.17914	1.7884	52309.9309	0.5602
57963.93	58190.4972	0.3909	73550.4612	26.8901	57523.3229	0.7601	56092.6959	3.2283	56326.58506	2.8248	57849.531	0.1974
61897	63714.1787	2.9358	79589.7359	28.5842	62180.0577	0.4573	60440.6844	2.3528	61013.22167	1.4278	63527.1486	2.6336
66352	69674.735	5.0077	84248.5743	26.9722	66263.5893	0.1332	63937.0457	3.6396	64416.25675	2.9174	69026.3623	4.0306
MAPE_SIM (%)		8.9110		21.5001		0.7423		2.1193	61547.8794	6.3870		1.7249
74358	74660.7059	0.4071	87990.3594	18.3334	69923.321	5.9640	66478.6898	10.5965	61547.8794	17.2276	74388.7946	0.0414
MAPE_PRE (%)		0.4071		18.3334		5.9640		10.5965		17.2276		0.0414

Fig. 8

Trend comparison diagram of the model data in Case 4.

The results in Table 6 reveal that the NGM(1,N) model yields the largest error at the two stages, the OBGM(1,N) model yields the smallest MAPE_SIM value, and MAPE_SIM of the GOMC(1,N) model is second only to that of the OBGM(1,N) model, with an error lower than 2%. However, the GOMC(1,N) model attains the best MAPE_PRE value, which is close to 0, and the error in the model before optimization is significantly improved. Through data comparison, it is found that the error at the modelling stage is reduced by 0.4%, and the error effect at the prediction stage is increased by 10%, indicating that GOMC(1,N) is more suitable for clean energy consumption prediction than are the other models. To compare the models, a trend diagram of the four models is shown in Fig. 8, and a relative error diagram of the four models is shown in Fig. 9.

Fig. 9

APE comparison of the various models in Case 4.

As shown in Fig. 8, the NGM(1,N), GM(1,N) and OBGM(1,N) models basically overestimate the actual consumption trend, while the NARX model underestimates the actual consumption trend, and only the GOMC(1,N) model trend is close to the actual trend. In the APE comparison chart shown in Fig. 9, the APE values of the OBGM(1,N) and GOMC(1,N) models are relatively low at the modelling stage, but the APE values of the GOMC(1,N) model are close to zero at the prediction stage. In summary, the GOMC(1,N) model can effectively predict clean energy consumption in China.

To illustrate the effectiveness of the model, different simulations and predictions were performed in the four cases. The first two examples involved 5 data simulations and 5 data predictions, where transverse comparison selected the same number of simulations and predictions in these two cases, while Cases 3 and 4 chose to predict one data point, while 9 and 8 simulations, respectively, in longitudinal comparison further illustrated the effectiveness of the model. The validity of the novel model proposed in this paper is verified through the above four cases, and it is observed that the GOMC(1,N) model always attains a high precision in the process of model comparison. As described in the Introduction, energy consumption is affected by various factors. Therefore, the energy consumption trend and various related factors are comprehensively considered in modelling, and the nonlinear term is optimized with the genetic algorithm, which results in a higher overall model performance than that of the other models, thus verifying the rationality of the novel model.

4.2 Energy consumption forecast over the next five years

The population and GDP factors are predicted with the GM(1,1) model, which uses the data from 2010–2019, and the other four energy sources are predicted with the GOMC(1,N) model. The parameters, errors and prediction results of the forecast process are listed in Table 7. To directly represent the consumption trends of the four types of energy sources over the next five years, trends of the data of the different energy sources are shown in Fig. 10. Combined with this chart, it is observed that the consumption of all kinds of energy sources in China will continue to rise and will not reach a peak within five years. In addition, the consumption of clean energy and natural gas will grow the fastest, which is good news for China.

Table 7

Year Total oil consumption Total coal consumption Total gas consumption Total clean energy consumption Total population GDP

2020 95485.2687 281916.0645 43240.82098 80200.3039 140908.1869 1082005.8543

2021 99712.74 310261.6585 48375.21607 87128.7653 141607.3693 1181600.8567

2022 104243.7873 358071.6489 54155.85906 94740.7841 142310.0210 1290363.2443

2023 109116.0718 431797.9703 60601.08776 103120.5235 143016.1593 1409136.8442

2024 114369.0846 538954.9428 67750.11433 112356.2007 143725.8013 1538843.1547

r 0.9209 2.2781 1.3675 2.2971 – –

MAPE 0.3392% 2.8280% 2.2018% 1.1312% 0.0511% 0.8824%

Year	Total oil consumption	Total coal consumption	Total gas consumption	Total clean energy consumption	Total population	GDP
2020	95485.2687	281916.0645	43240.82098	80200.3039	140908.1869	1082005.8543
2021	99712.74	310261.6585	48375.21607	87128.7653	141607.3693	1181600.8567
2022	104243.7873	358071.6489	54155.85906	94740.7841	142310.0210	1290363.2443
2023	109116.0718	431797.9703	60601.08776	103120.5235	143016.1593	1409136.8442
2024	114369.0846	538954.9428	67750.11433	112356.2007	143725.8013	1538843.1547
r	0.9209	2.2781	1.3675	2.2971	–	–
MAPE	0.3392%	2.8280%	2.2018%	1.1312%	0.0511%	0.8824%

Fig. 10

Forecast data comparison of the four energy sources.

According to Table 7 and Fig. 10, it can be observed that energy consumption in the future will still be dominated by coal, while the consumption of natural gas and other clean energy will experience an upward trend. The national energy structure will change. The national energy structure will change, and natural gas is a kind of low-carbon and clean energy source. In 2004, the Chinese government clearly proposed to vigorously develop natural gas and increase the proportion of natural gas in the primary energy structure. The promotion and use of natural gas play a beneficial role in environmental governance. Moreover, the Natural Gas Utilization Policy promulgated by the Chinese government also reflects their emphasis on the use of natural gas and the attitude of prioritizing the development of urban natural gas. With the support and promotion across China, the utilization rate of other clean energy sources will also show an upward trend. Therefore, it is an inevitable trend that the usage rate of natural gas and other clean energy sources will gradually increase under the current policy circumstances.

5 Conclusion

Based on the complexity of the energy consumption system, this paper adds nonlinear terms to the classic GMC(1,N) model and uses a genetic algorithm to optimize these nonlinear terms. Hence, a nonlinear grey multivariate prediction model, the GOMC(1,N) model, is proposed. Through case analysis, it is found that the GOMC(1,N) model achieves a better effect than that of the GM(1,N), NGM(1,N), OBGM(1,N) and GMC(1,N) models, which verifies that the GOMC(1,N) model obtained by adding nonlinear terms and optimizing these nonlinear terms can effectively predict energy consumption. In addition, by predicting several energy consumption cases over the next five years, the predicted trend is consistent with the actual situation according to the characteristics of the energy structure in China. Therefore, the novel model proposed in this paper can effectively predict energy consumption.

Based on the data trends of the different energy sources predicted with the model over the next five years, the following policy recommendations are made:

The trend of continued oil consumption growth in China in the future is inspiring. Since the reform and opening up, rapid economic growth has made China the second largest economy in the world. China should grasp the current development situation and accelerate the process of oil industry internationalization and marketization to ensure the oil supply. China should encourage opening of the market so that oil and gas development companies can compete. Moreover, China should continue to promote efforts to open up oil and gas licences and encourage investment in shale oil and gas.

In the future, the consumption of natural gas and clean energy will experience an upward trend, which will also affect the consumption of oil and coal. This phenomenon yields a restraining effect on the consumption of oil and coal, indicating that China should appropriately increase the use of natural gas and clean energy to reduce the consumption of oil and coal and avoid the excessive consumption of coal and oil. Efforts should be invested to identify suitable alternative energy sources, transform the utilization technology of fossil energy, further tap the energy saving potential, reduce the level of primary energy consumption, and decrease energy waste and environmental pollution attributed to energy consumption.

The investment in clean energy industries should be increased, technology for the development and use of clean energy should be upgraded, and relevant companies should be encouraged to compete. Replacing fossil fuels with new sources of energy is cheaper to develop and less polluting in certain industries. Energy conservation and emission reduction awareness should be increased, green travel should be vigorously promoted, and urban residents should be encouraged to adopt public transportation or low-carbon travel modes. Moreover, transportation departments should formulate stricter number limit measures, promote a lifestyle that is less dependent on coal and more on gas among rural residents, reduce the use of domestic coal, and lower the emission of pollutants due to energy consumption through the above measures.

As mentioned in this article, the irrational use of coal will cause serious pollution, which will restrict the healthy development of the energy economy. Reasonable prediction of carbon emissions will provide benefits to energy trade. China is a major coal consumer and carbon dioxide emitter worldwide, and it is of a certain significance to predict coal consumption. Corresponding policy measures should be predicted and formulated to save energy and reduce emissions. In the future, according to the characteristics of structural development and changes, we should establish relevant and suitable prediction models. This is also a future research direction. At present, we are considering energy consumption under general circumstances, mainly accounting for the impact of the consumption of other energy sources. In real life, energy consumption is related not only to the consumption of other energy sources but also to economic development and international events, such as financial crises and large outbreaks of infectious diseases. When faced with these notable impacts, improvement of the model structure to generate more effective energy consumption predictions so that China can formulate corresponding decisions in response to the above events will be investigated in the future.

Footnotes

Acknowledgments

The authors are grateful to the editors and the reviewers for their insightful comments and suggestions.

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