Optimization Model Based on Multivariable Grey Model and Its Application to Energy Consumption in China


 Currently, the energy development in China is in a critical period of transformation and reform, facing unprecedented opportunities and challenges. Accurate energy consumption forecast is conducive to promoting the diversification of energy development and utilization, and ensuring the healthy and rapid development of China's economy. Based on the existing multivariable grey prediction model, a nonlinear multivariable grey prediction model with parameter optimization is established in this paper, which used the genetic algorithms to find the optimal parameters, and the modelling steps are obtained. Then, the novel model takes the oil natural gas, coal and clean energy in China as the research objects, and the results are compared with the other four grey prediction models. The novel model has higher simulation and prediction accuracy, which is better than the other four grey prediction models. Finally, the novel model is used to predict those four energy consumption forecasts in China from 2020 to 2024. The results show that various energy consumption will further increase, while the fastest growing is clean energy and natural gas, which provides effective information for the Chinese government to formulate energy economic policies.


Introduction 24
At present, facing the profound adjustment of the international energy supply and demand 25 pattern a new round of energy technological transformation is under way. As a major energy 26 producer and consumer, China must seize the opportunity, implement the new development concept, 27 focus on supply-side structural reform, and actively promote energy consumption, supply, 28 technology, institutional revolution and international cooperation. Also need to optimize the energy 29 structure, strive to make up for many shortcomings in energy development, such as resource and 30 environmental constraints, low quality and efficiency, weak infrastructure, and lack of key 31 technologies, etc. Then, those efforts should be made to enhance the competitiveness of the energy 32 industry, build a clean, low-carbon, safe and efficient modern energy system, and better support the 33 sustained and stable development of Chinese economy. 34 According to the preliminary calculation by the National Bureau of Statistics (NBS), China's 35 GDP in 2019 reached 99086.5 billion yuan, and its economic aggregate approached the 100 trillion 36 yuan mark. Translated at the average annual exchange rate, it reached 14.4 trillion dollar, ranking 37 second in the world. As of 2019, The energy production of China was generally stable. In the past 38 decade, from the perspective of total energy production, the total energy production of China has 39 continued to grow. Primary energy production totaled 3.97 billion tons of standard coal, up 5.1% 40

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(1), (2), , ( )} X X X X n  L , after an accumulation, 175 the sequence is recorded as (1) ( where, r is the number of data points used for modelling,

181
And the differential equation 182 is called the whitening equation of the GMC(1,N) model, and 184 (1) (0) 11 1 where, ( 2) ut is 195 6 the unit step function, defined as 196 ( 2) 0, 2 Then the reduction formula is 198 which limits its applicability. Therefore, this section first establishes a nonlinear model, as follows: 205 ,, X X Z are defined as Definition 1, then the model can be built as This model is called the nonlinear GMC(1,N) optimization model, abbreviated as GOMC(1,N) 208 model. The following whitening equation can be obtained from Eq. (4): 209 where 216  ( 1) Set 226 ( 1) According to the above equations, the following equation can be got: 231 From Theorem 2, the following theorem can be obtained: 234 The solution of Eq. (5) is: 237 where, ( 2) ut is the unit step function, and defined as 239 ( 2) 0, 2 And the reduction formula is: 241

Optimization of nonlinear correction term in GMC(1,N) model 243
As can be seen from Section 3.2, the parameters be obtained by determining the order r , which is the nonlinear quantity. In this section, the genetic 245 algorithm is used to search this order, and the average absolute percentage error MAPE is taken as 246 the objective function, which is defined as: 247 The optimization of nonlinear terms is mainly aimed at the order  Table 1. 257 Table 1 258 Algorithm: The algorithm of GA to find the optimal r Set the objective function Input: The original series and the number of modeling data Output: The best order for Based on the definition of GOMC(1,N) model and the genetic algorithm, the whole prediction 260 process of this model is proposed as follows: 261 Step 1: Input the original series (0) x . 262 Step 2: Compute the 1-AGO series (1) x of ( 0) x , and the mean sequence (1) z of 1-AGO series. 263 Step 3: Substitute the data of step 1 into Eq. (6) and initial nonlinear order to obtain parameters 264 12 , , , , , Step 4: Substitute the coefficients obtained in the previous step into the time response equation, then 266 computing the restored value (0) () xk .

9
Step 5: Substitute the data of above three steps into Eq. (11) to construct the GOMC model and 268 compute the MAPE 269 Step 6: Using GA algorithm to optimize nonlinear term and computing the lowest value MAPE. 270 Step 7: Substituting the optimal r to reconstruct GOMC model and computing the simulated data    According to the results in the Table 3 The object of the second case study is the oil consumption in China, which is the same as the 314 previous case. The data of the first five years is used to build the model, and the data of the next five 315 years is used for model testing. The calculation results of each models are shown in Table 4, where 316 the optimal parameter of GOMC(1,N) is 1.3979 r  and the optimal background value parameter 317 of OBGM(1,N) is 0.6652. The data trend chart is also made, as shown in Fig. 4. 318 Table 4 319  The results in the Table 4 Table 5, where the optimal parameter of GOMC(1,N) is 5.1988 r  339 and the optimal background value parameter of OBGM(1,N) is 0.0015. Then, according to the 340 obtained data, the data trend comparison chart is made, as shown in Fig. 6. 341 Table 5 342  The results in the Table 5 N) model is the best, which is close to 0, and significantly improves the error of the 346 model before optimization, which shows that GOMC is more suitable for natural gas consumption 347 14 prediction than other models. In the Fig. 6, the NGM(1,N), GM(1,N) and OBGM(1,N) model are 348 basically overestimate the actual consumption trend, while only the GOMC(1,N) model is close to 349 the actual trend. In the comparison chart of APE value in Fig. 7, OBGM(1,N) Table 6, in which the optimal parameter of GOMC(1,N) is 2.1658 r  , and the 361 optimal parameter of OBGM(1,N) is 0.5373. The data trend chart is also made, as shown in Fig. 8. 362 Table 6 363  The results in the Table 6 show that the NGM(1,N) model has the largest error in the two 364 stages, and the OBGM(1,N) model has the smallest MAPESIM, and the MAPESIM of the GOMC(1,N) 365 model is second only to OBGM(1,N) model, with an error less than 2%, but the GOMC(1,N) model 366 has the best MAPEPRE, which is close to 0, and the error effect of the model before optimization is 367 significantly improved. Through the data comparison, it can be seen that the error in the modelling 368 stage is reduced by 0.4%, and the error effect in the prediction stage is increased by 10%, indicating 369 that GOMC(1,N) is more suitable for the clean energy consumption prediction than other models. The validity of the novel model proposed in this paper is verified through the above four cases, 381 and it can be seen that the GOMC(1,N) model always shows a high precision in the process of model 382 comparison. As described in the introduction, energy consumption is affected by various factors. 383 Therefore, the energy consumption trend and various related factors are considered to 384 comprehensively model, and the nonlinear term is optimized by the genetic algorithm, which can 385 make the overall performance of the model better than other models, which also explains the 386 rationality of the novel model. 387

Energy consumption forecast for the next five years 388
The population and GDP factors are predicted by the GM(1,1) model, which used the data form  Table 7. In order 391 to directly represent the consumption trends of the four types of energy in the next five years, the 392 trend charts of different energy data are shown in Fig. 10. Combined with the chart, it can be seen 393 that the consumption of all kinds of energy in China will continue to rise and will not reach its peak 394 within five years, at the same time, the consumption of the clean energy and natural gas are growing 395 fastest, which is good news for China. 396 According to Table 7 and Figure 10, it can be observed that the energy consumption in the 400 future will still be dominated by coal, while the consumption of natural gas and other clean energy 401 will show an upward trend. The national energy structure has changed. The national energy structure 402 has changed, and the natural gas as a kind of low-carbon and clean energy, which was clearly 403 proposed by the Chinese management in 2004 to vigorously develop natural gas and increase the 404 proportion of natural gas in primary energy. The promotion and use of natural gas play a beneficial 405 role in environmental governance. At the same time, the "Natural Gas Utilization Policy" 406 promulgated by the Chinese government also reflects the emphasis of Chinese government on the 407 use of natural gas and the attitude of giving priority to the development of urban natural gas. With 408 the support and promotion of the country, the utilization rate of other clean energy will also show 409 an upward trend. Therefore, it is an inevitable trend that the usage rate of natural gas and other 410 clean energy will gradually increase under the current policy circumstances. 411

5.Conclusion 412
Based on the complexity of the energy consumption system, this paper adds nonlinear terms to 413 the classic GMC(1,N) model, and uses the genetic algorithms to optimize the nonlinear terms, 414 therefore, a nonlinear grey multivariate prediction model GOMC(1,N) was proposed. Through the 415 case analysis, it can be seen that the GOMC(1,N) model has better effect than GM(1,N), NGM(1,N), 416 OBGM(1,N) and GMC(1,N) models, which proves that the GOMC(1,N) model obtained by adding 417 nonlinear terms and optimizing the nonlinear terms can effectively predict the energy consumption. 418 In addition, by predicting several energy consumption in the next five years, the predicted trend is 419 consistent with the actual situation according to the characteristics of the energy structure in China. 420 Therefore, the novel model proposed in this paper can effectively predict the energy consumption. 421 Based on the data trends of different energy sources predicted by the model in the next five 422 years, the following policy recommendations are made: 423