Forecast of Energy Consumption Based on FGM(1, 1) Model

-e normal supply of energy is related to the stable development of the economy and society. Forecasting energy consumption helps prepare for the normal supply of energy. In the study of energy consumption forecasting, different scholars have used different forecasting models. -is paper uses five-year energy consumption data in the Beijing-Tianjin-Hebei region and uses the grey fractional FGM(1, 1) model to analyze the next six years. -en, the energy consumption of three places is predicted. -e advantage of the grey score FGM(1, 1) model is that it can get more accurate prediction results based on a small amount of information. In this study, relatively outdated information affects the accuracy of prediction results. However, other prediction models have great limitations on data. Choosing the grey number fractional model for prediction research can get a more reasonable prediction result. We use the FGM(1, 1) model to make predictions and get the prediction results. In Beijing, the growth rate of natural gas consumption has slowed down and will be basically stable by 2023. -e average annual deceleration of coal consumption is 32%.-e average annual deceleration of coke consumption is 10%. Crude oil consumption decreased by 6.3% annually. Gasoline consumption is slowly increasing. -e consumption of kerosene increased about 8% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 17% annually. -e average annual growth rate of power consumption exceeds 6%. In Tianjin, the annual growth rate of natural gas consumption is about 5%. Coal consumption is reduced by about 8% every year.-e average annual deceleration of coke consumption is 7%. Crude oil consumption decreased by 2.4% annually. Gasoline consumption is slowly decreasing. -e consumption of kerosene has increased by about 20% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 20% annually. Electricity consumption is slowly increasing. In Hebei Province, the annual growth rate of natural gas consumption is about 15%. Annual coal consumption is reduced by about 3%. Coke consumption remained stable. Crude oil consumption is reduced by 3% annually. Gasoline consumption is slowly increasing, and kerosene consumption has increased by about 31% annually. Diesel consumption is reduced by about 3% annually. Fuel oil consumption remained stable. Electricity consumption is slowly increasing.


Introduction
Energy is an important material basis for human progress and social and economic development. e development and utilization of energy has greatly promoted the development of the world economy and human society. And the increase in energy consumption is the inevitable result of economic and social development. e rapid development of China's economy is also inseparable from the normal supply of energy. In the year 2000, China's GDP was 10,028 trillion RMB￥ and the total national energy consumption was 1469.6 million tons of standard coal. In 2017, China's GDP was 832.35 billion RMB￥ and the total national energy consumption was 4,455.2 million tons of standard coal. It should be noted that with the rapid economic development and rapid energy consumption, economic development and environmental pollution have become the main contradictions that currently exist. It is under this background that the Chinese government has proposed the scientific development concept to accelerate the development of modern energy. Industries adhere to the basic national policy of saving resources and protecting the environment. While developing the economy, we should also pay attention to the issue of energy consumption. While improving energy supply capacity, we should pay attention to energy efficiency and energy conservation and emission reduction.
As an important part of China's economy, the Beijing-Tianjin-Hebei region is also an important issue of concern to scholars in terms of economic development, energy consumption, and environmental protection. Especially with the acceleration of the integration of Beijing-Tianjin-Hebei and the construction of Xiong'an New Area, the economic development of the Beijing-Tianjin-Hebei region has ushered in new development opportunities. And the demand for energy for economic and social development will further increase. Research on the prediction of energy consumption has become a necessary research topic. Accurate prediction will help the government and enterprises do a good job of energy planning ahead of time.
ere are many methods for data forecasting [1][2][3][4]. Different forecasting methods have different requirements for raw data. One of the characteristics of grey model is that it can forecast small data and poor information. e grey system model can be used for forecasting.
e grey system is a relatively new theory developed by Julong in the 1980s [5,6]. In this theory, information that is clearly known is defined as white information and information that is completely unknown is defined as black information. Information that falls between completely known and completely unknown is defined as grey information. In the real world, situations with incomplete information are ubiquitous. For example, agricultural yield, stock returns, and unemployment rates can be affected by uncertainties. us, problems related to these issues can be solved using grey system theory.
Many researchers use the first-order single variable grey forecasting model, GM (1,1) [7][8][9][10], to make predictions. But the model has relatively large errors in the prediction of specific problems. Under certain conditions, the fractional grey model, FGM(1, 1) [11][12][13][14], has a higher accuracy than the GM(1, 1) model. e FGM(1, 1) model performs the calculation using the time series of the predicted object itself and only needs a small amount of data to achieve a better prediction.
Many scholars have made predictions on energy consumption using other models. Electric load forecasting is done by complete ensemble empirical mode decomposition adaptive noise and support vector regression with quantum-based dragonflfly algorithm by Zhang and Hong [15]. Combining the PEM, LSSVR model, and CCPSO algorithm, a hybrid forecasting method for SMTS, PEM, and LSSVR-CCPSO, is developed by Li et al. [16]. Forecasting electric by seasonal recurrent SVR (support vector regression) with chaoticartificial bee colony algorithm was done by Hong [17].
ere are many scholars based on the improved GM (1,1) model for forecasting, or GM (1,1) model combined with other models for forecasting [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. e research draws on the related research results of predecessors. is paper uses energy consumption data from 2013 to 2017 in the Beijing-Tianjin-Hebei region [33] and uses the FGM(1, 1) model to predict energy consumption. rough prediction, the result of the research is to use less original data to obtain 6-year forecast data of energy consumption in Beijing, Tianjin, and Hebei. At the same time, compared with the traditional FM(1, 1) model, the prediction error of the fractional FGM(1, 1) model is smaller in most cases.

Model Introduction of FGM(1, 1)
e execution of GM (1, 1) model is done through data accumulation, grey model, and inverse accumulation of data.
e advantage is that it can process grey information and sparse data. However, the model has disadvantages. Namely, the errors are large for certain problems. FGM(1, 1) addresses this deficiency of the GM(1, 1) and reduces the errors by judiciously selecting the accumulation order number. With this approach, better prediction results can often be achieved. e basic process of FGM(1, 1) is given by the following equations.
For a non-negative sequence, . , x (0) (n)}, the FGM(1, 1) model is constructed as follows: Step 1: by the accumulation generation operator, Note that a superscript (0) indicates an original sequence and a superscript (r) indicates an rth-order accumulation sequence.
Step 2: establish the differential equation as where a is the development grey number and b is the endogenous control grey number. e solution of the equation is an exponential function: Using the least-squares method, a and b are solved by Step 3: obtain the corresponding time function as where x (r) (k + 1) is the value at time k + 1.
Step 4: for sequence X (r) � x (r) (1), x (r) (2), . . . , where α (1) . en, the predicted value is Step 5: there are many testing methods for grey forecasting models. And the average absolute percentage is a commonly used testing method in grey forecasting. is paper uses this method for model testing. Grey systems are often evaluated by using the mean absolute percentage error (MAPE � 100% × 1/n n k�1 |x (0) (k) − x (0) (k)/x (0) (k)|). e evaluation criteria of the model MAPE are shown in Table 1. When MAPE < 10%, it means that the model fitting effect is better and the prediction result is more reliable. When 10% < MAPE < 20%, the model fit has a certain degree of credibility. When MAPE > 20%, the fitting effect of the model is average and the prediction result has little reference value.
In particular, for the fractional FGM(1, 1) model, at that time r � 1, the FGM(1, 1) model is the GM(1, 1) model. e traditional grey GM(1, 1) model can be regarded as a special case of the fractional model.

Validation Study and Analysis Results
is article predicts the energy consumption of Beijing, Tianjin, and Hebei in China. e energy consumption data come from the National Statistical Yearbook of China, including the consumption data of coal, coke, crude oil, fuel oil, gasoline, kerosene, diesel, natural gas, and electricity (data source website: http://www.stats.gov.cn/tjsj/ ndsj/). By querying the five-year data of the Statistical Yearbook, the trend of energy consumption in the three places is obtained.
Regarding energy consumption in Beijing, natural gas consumption is on the rise. Coal consumption is showing a decreasing trend. Coke consumption is showing a decreasing trend. e consumption of crude oil fluctuates. Gasoline consumption shows an increasing trend. e consumption of kerosene is showing an increasing trend. Beijing's diesel consumption is showing a decreasing trend. Fuel oil consumption shows a decreasing trend. Electricity shows an increasing trend.
Regarding energy consumption in Tianjin, natural gas consumption is on the rise. Coal consumption is showing a decreasing trend. Coke consumption is showing a decreasing trend. e consumption of crude oil fluctuates. Gasoline consumption shows an increasing trend. e consumption of kerosene is showing an increasing trend. Tianjin's diesel consumption is relatively stable. Fuel oil consumption shows a decreasing trend. Electricity shows an increasing trend.
Regarding energy consumption in Hebei Province, natural gas consumption is on the rise. Coal consumption is showing a decreasing trend. Coke consumption is showing a decreasing trend. Crude oil consumption shows an increasing trend. Gasoline consumption shows an increasing trend.
e consumption of kerosene is showing an increasing trend. Consumption in Hebei Province is showing a decreasing trend. Fuel oil presents a fluctuating trend. Electricity shows an increasing trend.
is paper firstly models and predicts natural gas in Tianjin. Other energy sources use the same process to obtain fitting and prediction results.

Natural Gas Consumption Forecast.
is paper establishes an FGM(1, 1) model for natural gas consumption in Tianjin. In particular, it is the traditional grey GM(1, 1) model when r � 1. e original columns are obtained from the original data: e cumulative sequence of order 0.1 is Establish a whitening differential equation： Solve the unknown parameters by the least-squares method： Here, the two unknown parameters a and b are solved by using the following equation: Mathematical Problems in Engineering We obtain the 0.1-order accumulation sequence as en, perform 0.9-order accumulation on the 0.1-order accumulation sequence to obtain the first-order accumulation sequence.
en, the predicted value is When r � 1 in FGM(1, 1), the fitting and prediction results of the GM(1, 1) model can be obtained. e fitting results of the two models are shown in Table 2. Generally, the MAPE of the fractional FGM(1, 1) model is smaller, and the fractional FGM(1, 1) model is selected for prediction. Otherwise, when the MAPE of GM(1, 1) is less than FGM(1, 1), select the GM(1, 1) model where r � 1 in the fractional model to predict.
Comparing the results in Table 2, it can be found that the MAPE of the fractional FGM(1, 1) model and the MAPE of the traditional GM(1, 1) model both meet the requirements. e order of FGM(1, 1) is calculated by the particle swarm algorithm. As the fitting effect is the best at 0.1, the prediction is more accurate. e MAPE of FGM(1, 1) is 2.4 which is less than 4.8 of the traditional grey GM(1, 1) model. From the comparison of the fitted values, we can also find the fitted value of the FGM(1, 1) model is closer to the true value than the fitted value of the GM(1, 1) model, which also shows that the FGM(1, 1) model is more accurate than the traditional GM(1, 1) model.
Using the data from 2013 to 2017 and using the FGM(1, 1) model, the fitted values of natural gas consumption in Beijing, Tianjin, and Hebei from 2013 to 2017 are shown in Table 3.
It can be seen from Table 3 that for natural gas consumption in Beijing, when r � 0.3, the MAPE of FGM(1, 1) is 3.25. For natural gas consumption in Hebei Province, when r � 0.9, the MAPE of FGM(1, 1) is 4.9. And the model's MAPE is less than 10%, indicating that the model prediction is relatively accurate. e model can be used to predict the natural gas consumption of the three places. e prediction results are shown in Table 4. e forecast results show that in the next few years, natural gas consumption in the three places will continue to increase rapidly. By 2023, natural gas consumption in Beijing will reach 19.1 billion cubic meters, that in Tianjin City will reach 11.9 billion cubic meters, and that in Hebei Province will reach 23.1 billion cubic meters. It also reflects the preference for clean energy.
rough the same process, select the optimal order and use the FGM(1, 1) model to fit and predict other energy consumption; we can get the fitting value of other energy, and judge whether the prediction result based on the value of MAPE is credible.

Coal Consumption Forecast.
As a traditional energy source in production and life, coal consumption in Beijing, Tianjin, and Hebei still accounts for a large proportion of energy consumption. According to data in recent years, it has been found that coal consumption has shown a downward trend year by year. We use FGM(1, 1) model to build models, and the fitting results are shown in Table 5.
It can be seen from Table 5 that for coal consumption in Beijing, when r � 1, the MAPE of FGM(1, 1) is 3.46. For coal consumption in Tianjin, when r � 1, the MAPE of FGM(1, 1) is 0.47. For coal consumption in Hebei Province, when r � 1, the MAPE of FGM(1, 1) is 0.08. And the model prediction accuracy is less than 10%. e FGM(1, 1)model prediction is relatively accurate. e model can be used to predict coal consumption in the three places. In these three cases, the order r is equal to 1, and then the FGM(1, 1) model is the GM(1, 1) model. Table 6 shows the predicted value of coal consumption in the three places from 2018 to 2023. From the forecast results, the coal consumption in the three places has shown a decreasing trend. Specific to the three places, Beijing's coal consumption will decrease rapidly and it will be reduced to 530,000 tons by 2023. Tianjin's coal consumption will be at a moderate rate and will be reduced to 23.13 million tons by 2023. Hebei's coal consumption the decline is the smallest. And 234.14 million tons will still be consumed by 2023.

Coke Consumption Forecast.
As an important industrial raw material, Tianjin City and Hebei Province consume more coke while Beijing consumes less coke. is also reflects the characteristics of the industrial structure of the three places. Hebei Province and Tianjin City have a higher industrial share. Using the same process as above, the fitting results are shown in Table 7.
It can be seen from Table 7 that for coke consumption in Beijing, when r � 0.8, the MAPE of FGM(1, 1) is 6.89. For coke consumption in Tianjin, when r � 0.9, the MAPE of FGM(1, 1) is 0.93. For coke consumption in Hebei Province, when r � 0.1, the MAPE of FGM(1, 1) is 1.18. And the model prediction accuracy is less than 10%. e model prediction is  Table 8 shows the coke consumption in the three places from 2018 to 2023. From the forecast results, the coke consumption in the three places shows a decreasing trend. Specific to the three places, the base of coke consumption in Beijing is relatively small, showing a decreasing trend. e coke consumption in Tianjin has fallen by a large margin, and by 2023, the coke consumption in Tianjin will be     Mathematical Problems in Engineering reduced to 5.36 million tons. At the same time, it can be seen that coke consumption in Hebei Province will remain relatively stable in the next few years.

Crude Oil Consumption Forecast.
As a raw material for petroleum fuels, the consumption of crude oil in Beijing, Tianjin, and Hebei is very large. Observing the crude oil consumption data of the three places from 2013 to 2017, it is found that the change in crude oil consumption is relatively small. Using the same modeling process as above, the fitting results are shown in Table 9. It can be seen from Table 9 that for crude oil consumption in Beijing, when r � 1, the MAPE of FGM(1, 1) is 3.74. For crude oil consumption in Tianjin, when r � 1, the MAPE of FGM(1, 1) is 3.42. For crude oil consumption in Hebei Province, when r � 0.5, the MAPE of FGM(1, 1) is 5.6. e model whose prediction accuracy is less than 10% is more accurate. By comparing the fitted value and the actual value, it can also be observed that the fitting effect is better. Table 10 shows the crude oil consumption in the three places from 2018 to 2023. From the forecast results, the crude oil consumption in the three places is showing a decreasing trend. Among them, the rate of decrease in Beijing is relatively fast, and the crude oil consumption will be 5.71 million tons by 2023. Tianjin's crude oil consumption has declined slowly and will be 13.44 million tons by 2023. Hebei's crude oil consumption has remained stable and shows a slight decrease.

Gasoline Consumption Forecast.
With the rapid growth of the number of motor vehicles, the gasoline consumption in the Beijing-Tianjin-Hebei region from 2013 to 2017 also showed a trend of increasing year by year, especially in Hebei Province. Using the same process as above, the fitting results are shown in Table 11.
It can be seen from Table 11 that for gasoline consumption in Beijing, when r � 0.9, the MAPE of FGM(1, 1) is 0.44. For gasoline consumption in Tianjin, when r � 0.5, the MAPE of FGM(1, 1) is 1.82. For gasoline consumption in Hebei Province, when r � 0.5, the MAPE of FGM(1, 1) is 7.53. e model prediction accuracy is less than 10%. e FGM(1, 1) model prediction is more accurate. Table 12 shows the gasoline consumption in the three places from 2018 to 2023. From the forecast results, the gasoline consumption in Beijing and Hebei Province is showing an increasing trend. But the growth rate is gradually slowing down. e gasoline consumption in Tianjin is relatively stable and showing a slight decrease. According to the trend, by 2023, gasoline consumption in Beijing, Tianjin, and Hebei will reach 5.27 million tons, 2.62 million tons, and 6.83 million tons, respectively.

Forecast of Kerosene Consumption.
As an important lighting fuel, the consumption of kerosene in Beijing is relatively large, while the consumption of kerosene in Tianjin and Hebei Province is relatively small. Using the same modeling process as above, the fitting results are shown in Table 13.
It can be seen from Table 13 that for kerosene consumption in Beijing, when r � 1, the MAPE of FGM(1, 1) is 0.27. For kerosene consumption in Tianjin, when r � 0.4, the MAPE of FGM(1, 1) is 2. For kerosene consumption in Hebei Province, when r � 0.5, the MAPE of FGM(1, 1) is 31.68. e MAPE of Beijing and Tianjin is relatively small, and the fitting prediction effect is better. Because of the large fluctuation of the original data, the fitting effect of Hebei Province is relatively poor. Table 14 shows the consumption of kerosene in the three places from 2018 to 2023. From the forecast results, the consumption of kerosene in the three places is showing an increasing trend. e rate of decrease in Beijing is relatively slow. e growth rate of Tianjin is relatively fast. And the consumption of kerosene in Hebei Province also shows a rapid growth trend. Due to the large fluctuation of the original data, the reliability of the forecast results is low.

Diesel Consumption Forecast.
As an important engine fuel, diesel consumption is relatively large in Beijing, Tianjin, and Hebei. But the original data of kerosene are obvious. Using the same process as above, the fitting results are shown in Table 15.        Table 16 shows the diesel consumption in Beijing, Tianjin, and Hebei from 2018 to 2023. From the forecast results, the diesel consumption in the three places is showing a decreasing trend. e diesel consumption in Beijing is relatively stable. And the diesel consumption in Tianjin and Hebei is relatively stable. e drop is comparable.

Fuel Oil Consumption Forecast.
e main use of fuel oil is in industrial production. e consumption of fuel oil in Tianjin and Hebei Province is relatively high. Using the same process, the fitting results are shown in Table 17.
It can be seen from Table 17 that for coal consumption in Beijing, when r � 0.9, the MAPE of FGM(1, 1) is 7.27. For fuel oil consumption in Tianjin, when r � 0.9, the MAPE of FGM(1, 1) is 13.91. For fuel oil consumption in Hebei Province, when r � 0.2, the MAPE of FGM(1, 1) is 12.9. e MAPE of Tianjin and Hebei Province exceeds 10%. And the prediction effect of the model is relatively poor. Table 18 shows the fuel oil consumption in the three places from 2018 to 2023. From the forecast results, the fuel oil consumption in the three places has shown a decreasing trend. Specifically, Tianjin's fuel oil consumption has fallen the fastest while fuel oil consumption of Beijing and Hebei has slowed down relatively. However, it should be noted that the forecast results of Tianjin and Hebei's fuel oil are less reliable.

Power Consumption Forecast.
As an important secondary energy source, electricity is indispensable in today's social production and life. Observing the electricity consumption data of Beijing, Tianjin, and Hebei from 2015 to 2019, it can be found that the electricity consumption of the three places has shown a slight upward trend. Using the same process, the fitting results are shown in Table 19.
It can be seen from Table 19 that for the power consumption of Beijing, when r � 0.9, the MAPE of FGM(1, 1) is 0.62. For the power consumption of Tianjin, when r � 0.1, the MAPE of FGM(1, 1) is 0.79. For power consumption in Hebei Province, when r � 0.1, the MAPE of FGM(1, 1) is 0.14.
e FGM(1, 1) model whose prediction accuracy is less than 10% is more accurate. Table 20 shows the power consumption of the three places from 2018 to 2023. From the forecast results, the power consumption of the three places is showing an increasing trend. e power growth reflects the expansion of the scale of production of enterprises and the improvement of people's living standards. And the slower increase in power consumption means that the efficiency of electricity consumption is continuously improving.

Results and Discussion
rough the prediction of energy consumption in Beijing, Tianjin, and Hebei, the flexible trend of energy consumption in the three places is obtained.
In Beijing, the growth rate of natural gas consumption has slowed down and will be basically stable by 2023. e average annual deceleration of coal consumption is 32%. e average annual deceleration of coke consumption is 10%. Crude oil consumption decreased by 6.3% annually. Gasoline consumption is slowly increasing. e consumption of kerosene increased about 8% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 17% annually.
e average annual growth rate of power consumption exceeds 6%.
In Tianjin, the annual growth rate of natural gas consumption is about 5%. Coal consumption is reduced by about 8% every year. e average annual deceleration of coke consumption is 7%. Crude oil consumption decreased by 2.4% annually. Gasoline consumption is slowly decreasing.
e consumption of kerosene has increased by  In Hebei Province, the annual growth rate of natural gas consumption is about 15%. Annual coal consumption is reduced by about 3%. Coke consumption remained stable. Crude oil consumption is reduced by 3% annually. Gasoline consumption is slowly increasing, and kerosene consumption has increased by about 31% annually. Diesel consumption is reduced by about 3% annually. Fuel oil consumption remained stable. Electricity consumption is slowly increasing.
Of course, in terms of judging the usability of the model, when the MAPE is greater than 20, the prediction accuracy of the model is low, and the reliability of the prediction is relatively low. e reason for this is that the original data     have a relatively large disturbance, and the larger the model, the better the forecast. According to energy consumption data and forecast results, it can be found that as the country promotes environmental protection policies, the consumption of highpolluting energy is showing a decreasing trend, and the proportion of clean energy consumption such as natural gas and electricity is increasing. For government and enterprises, environmental protection policies should be adjusted accordingly. On the one hand, the government should limit the use of high polluting energy. On the other hand, the government should encourage the use of clean energy.

Conclusion
Energy supply directly affects the normal economic and social development and the normal work and life of residents. Analysis of energy consumption can help us not only to understand the economic and social development status but also to make plans for the supply of energy for government departments through prediction. We study the energy consumption situation in the Beijing-Tianjin-Hebei region and use the fractional FGM(1, 1) model to predict the energy consumption of the three places; compared with the traditional grey GM(1, 1) model, the prediction accuracy of fractional FGM(1, 1) model is higher. Compared with other prediction models, the fractional FGM(1, 1) model has obvious advantages and lower model requirements. It only needs a small amount of data in recent years to make predictions. At the same time, the prediction accuracy of the submodels is higher and the amount of calculation is relatively high.
rough the forecast research in this article, it can be found that in the next few years, the consumption of highly polluting energy sources such as coal and coke will show a decreasing trend. e consumption of clean energy such as natural gas and electricity is showing an increasing trend.
is is inseparable from the government's environmental protection policy.
e Beijing-Tianjin-Hebei region is a region with a large population and relatively insufficient resources. To achieve sustainable economic and social development, we must first take the path of saving resources. We should strengthen industrial energy conservation by advancing structural adjustments. Secondly, we should improve energy supply capacity, rationally use coal, actively promote power development, accelerate the popularization of low-pollution energy such as natural gas, and vigorously develop renewable energy such as wind, geothermal, and solar energy.
At the enterprise level, it is necessary to strengthen guidance, increase the enthusiasm of enterprise R&D and technological innovation, vigorously organize the research and development, promotion, and application of advanced energy technologies, and guide enterprises to accelerate technological progress and improve energy efficiency through market mechanisms. Local governments should strengthen the training and introduction of energy technology talents through policies and regulations to create a good atmosphere for the development of energy technology.
Finally, from a national perspective, China has a large population and low energy per capita. It should actively expand international energy trade and actively promote energy imports to fill the current situation of domestic energy shortages.

Data Availability
e data used to support the finding of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.