The Application Study Of Optimized Grey Prediction Models

Grey prediction model is an important research content of grey system theory,and it is an indispensable bridge to apply grey system theory to practical prediction problems.GM(1,1)model is a classical grey prediction model,which is a prediction model with requirement of a small amount of modeling samples and high prediction accuracy.Many imperfections exist in the theoretical system of grey system theory,so do defects in GM(1,1)model.The prediction error of GM(1,1)model is one of the main defects,which affects the application scope of GM(1,1)model.To find out and to analyze the key factors that contribute to the large prediction error of GM(1,1)model and to improve the algorithm of GM(1,1)model can not only improve the prediction accuarcy of GM(1,1)model,but also expand the application range of GM(1,1)model.Therefore,to improve and to optimize GM(1,1)model have great theoretical and practical significance.Based on the comprehensive analysis of the existing literatures,it is found that the improvement and optimization of the original data sequence and background value formula of GM(1,1)model can effectively reduce the prediction error and improve the prediction accuracy of GM(1,1)model.At the same time,it is also demonstrated that GM(1,1)model can be scientifically and reasonably combined with other prediction models and algorithms to build new combination forecasting models,which can not only give full play to the advantages of each of these forecasting models,but also to a certain extent improve the prediction performance and expand the practical application of GM(1,1)model.The main research contents of this paper are as follows:Firstly,two novel optimized GM(1,1)are proposed based on improvements of GM(1,1)model per se.(1)GM(1,1)model has obvious advantages in dealing with short-term prediction of limited sample data,so it can be used to predict power consumption.This paper constructs DCOGM(1,1)model,which is based on the data transformation of the original modeling data sequence and improvement and optimization of the background value constructed by using the combined interpolation method of the Simpson 3/8 formula and the Newton interpolation formula.By applying DCOGM(1,1)model to the short-term electricity consumption forecast of Asia-Pacific Economic Cooperation(APEC)countries and regions and the electricity consumption forecast of Turkey,as well as the total power consumption forecast in Shanghai from 2017 to 2021,it's indicated that DCOGM(1,1)model is superior to the traditional GM(1,1)model and other existing improved GM(1,1)models in terms of prediction performance,and Shanghai's electricity consumption will increase in a sustained and steady trend in the next five years.(2)In order to improve the prediction performance of GM(1,1)model,this study optimizes and improves the construction formula of the background value of GM(1,1)model and transforms the original modeling data series at the same time,and finally obtains the improved GM(1,1)model(TBGM(1,1)model),relevant prediction results demonstrate that compared with the traditional GM(1,1)model and other improved GM(1,1)models,TBGM(1,1)model presents less prediction error.TBGM(1,1)model is subsequently applied to forecast the energy consumption of Shanghai,and it indicates that the energy consumption of Shanghai will show a steady growing trend in the next five years.In addition,the forecast results suggest that each prediction model has its own scope of application,and the prediction accuracy of the optimized GM(1,1)models may be compromised in some specific cases;therefore,appropriate prediction models should be carefully selected in the context of different prediction backgrounds.Secondly,GM(1,1)is combined with other prediction models and algorithm to predict the energy consumption of China.Energy resources are strategically important for economic and social development,and are crucial for the healthy development of economic and social work in a country(region).The GDP of China ranks the second worldwide,but the total energy consumption ranks first;the supply and demand of energy resources in China shows a serious imbalance,the energy demand increases sharply,and there is a serious lack of the right to set energy prices,also global energy prices are rising and fluctuate violently.Therefore,scientific and accurate prediction of China's total energy consumption can not only provide the necessary theoretical basis for the relevant decision-making departments to formulate safe and reasonable energy policies,but also contribute to the healthy,sustainable and stable development of China's economy and society.(3)GM(1,1)model is combined with ARMA model,and GM(1,1)-LR-ARMA model is proposed.Based on certain combination of three forecasting models,namely,GM(1,1)model,ARMA model and LR model,GM(1,1)-LR-ARMA model is constructed,in which the error reciprocal variable weight combination forecasting method is used to solve the weight value.GM(1,1)-LR-ARMA model is subsequently employed to predict China's energy consumption,and we can find that GM(1,1)-LRARMA model not only can overcome the shortcomings of each and every single prediction model,but also bears the prediction advantages in dealing with fluctuating,linear original modeling data.However,it should be noticeable that appropriate weight value of the combination forecasting model determines the prediction effects of the model.(4)This paper discusses the combined application of grey prediction models and BP neural network model and puts forward GM(1,1)-BPNN-GA model.GM(1,1)-BPNN-GA model is based on three grey prediction models,namely,GM(1,1)model,DCOGM(1,1)model,TBGM(1,1)model and the BP neural network model.In the process of modeling,the equal-dimension and new information rolling mechanism is used to construct the three grey prediction models,and then the prediction results of GM(1,1)model,DCOGM(1,1)model and TBGM(1,1)model are employed as the input variables of BP neural network model,and the genetic algorithm(GA)is applied to solve and to optimize the initial weight and threshold of BP neural network model.Finally,GM(1,1)-BPNN-GA model is applied to predict China's energy consumption.The prediction results suggest that GM(1,1)-BPNN-GA model dramatically outperforms the traditional GM(1,1)model and the other two improved grey prediction models,DCOGM(1,1)model and TBGM(1,1)model,thus expanding the application scope of grey prediction model.(5)The combined application of grey prediction model and least square support vector machine regression model is discussed,and GM(1,1)-LSSVMR-PSO model is constructed.GM(1,1)-LSSVMR-PSO model is a novel improved grey prediction model.In this model,the prediction results of three grey prediction models,namely,GM(1,1)model,DCOGM(1,1)model and TBGM(1,1)model,are input values of the least square support vector machine regression model,and the particle swarm optimization(PSO)algorithm is used to solve the parameters ? and for the least squares support vector machine regression model.At the same time,in order to evaluate the optimization effects of particle swarm optimization algorithm,the intelligent optimization algorithms including genetic algorithm(GA)and simulated annealing(SA)algorithm are also considered and employed to solve the parameters ? and parameter ? for the least squares support vector machine regression model,and then GM(1,1)-LSSVMR-GA model and GM(1,1)-LSSVMR-SA model are obtained correspondingly.And the prediction results indicate that GM(1,1)-LSSVMR-PSO model produces the least prediction error.GM(1,1)-LSSVMR-PSO model makes full use of the advantages of the grey prediction models and least square support vector machine regression model,and overcomes the shortcomings and defects of these prediction models to some extent.GM(1,1)-LSSVMR-PSO model demonstrates favorable advantages in dealing with fluctuating and nonlinear original modeling data sequence,thus effectively expands the practical application field and scope of the grey prediction model.Finally,based on the comprehensive analysis of the combined prediction models we proposed above,GM(1,1)-LSSVMR-PSO model significantly outperforms each individual prediction model as well as other combined prediction models we proposed here,so it's employed to predict China's energy consumption,which indicates that the energy consumption in China will increase slowly and steadily from 2019 to 2023.The main innovations of this paper are summarized as follows:(1)Based on the basic theoretical principle and mechanism of grey prediction model,some improvement and optimization work focusing on GM(1,1)model are made,and two optimized GM(1,1)models are put forward.Data transformation for the original modeling data sequence and optimization and improvement for the construction of the background value of GM(1,1)model are two important research areas for the optimization of GM(1,1)model.Then,in accord with both aspects,two novel improved GM(1,1)models,DCOGM(1,1)model and TBGM(1,1)model,are proposed and successfully applied to solve the practical forecasting issues.Compared with the existing GM(1,1)models,DCOGM(1,1)model and TBGM(1,1)model both show significantly reduced prediction error,improving the prediction performance of GM(1,1)model and extending the practical application range of GM(1,1)model.(2)By combining GM(1,1)model with statistical analysis model and machine learning models,corresponding grey combinatorial forecasting models are proposed.Combination of the statistical analysis model and machine learning models with GM(1,1)model takes full advantages of ARMA model,BP neural network model and least square support vector machine regression model in prediction,and establishes GM-LR-ARMA model,GM(1,1)-BPNN model and GM(1,1)-LSSVMR model.The prediction results from real case studies verify that these grey combinatorial forecasting models can effectively improve the prediction accuracy of GM(1,1)model.(3)By constructing the grey combinatorial forecasting models,and the intelligence optimization algorithms of machine learning are successfully applied to optimization of grey combinatorial forecasting models.Because the convergence speed of BP neural network model is relatively slow and there is a high probability that the value of the solution is the local optimal solution,the genetic algorithm(GA)is employed to construct GM(1,1)-BPNN-GA model,which significantly increases the convergence speed and convergence performance and greatly reduces the prediction error of the model.The two parameters,which are parameter ? and parameter ?,exerts significant effects on the prediction performance of the least square support vector machine regression model,so the particle swarm optimization(PSO)algorithm is used to select and solve the values of the parameters ? and ? for the least square support vector machine regression model,and the GM(1,1)-LSSVMR-PSO model is constructed accordingly.The experimental results demonstrate that the particle swarm optimization algorithm dramatically outperforms the genetic algorithm and simulated annealing algorithm in terms of optimizing and solving the parameters for the least square support vector machine regression model.To sum up,this paper makes innovative research progresses in the optimization and application of grey prediction model.On one hand,improvement and optimization of GM(1,1)model per se is put forward;on the other hand,combination forecasting models are proposed by combining GM(1,1)model with the statistical analysis model and machine learning models,and the intelligent optimization algorithms including particle swarm optimization algorithm,genetic algorithm and simulated annealing algorithm are further introduced to optimize the combination forecasting models.In order to improve and optimize GM(1,1)model,not only improvements and optimization of GM(1,1)model itself should be emphasized,but the dynamic combination of GM(1,1)model with other prediction models should be considered to make full use of the advantages of other prediction models as well.And moreover,both aspects can promote mutually and develop in parallel with each other when scientific and effective improvements on the prediction performances of GM(1,1)model is the central task that needs solving.In all,our research work promotes the integration of the grey prediction model with other prediction models and algorithms,expands the practical application range of the grey prediction model,and provides valueable references for the follow-up optimization work of the grey prediction model.