Research On Construction Of A New GM（1,N） Power Model Based On Double Optimization Of Initial Value And Background Value

As an uncertain method focusing on small sample and poor information,grey system theory shows unique advantages.However,the traditional grey forecasting model usually requires a linear relationship between the research object and the modeling data,so it cannot meet the prediction needs of the nonlinear problems such as municipal solid waste(MSW).To settle this problem,this paper aims to study the nonlinear grey prediction model-GM(1,N)power model,and explores new thoughts to improve the accuracy of the model by combining theoretical research with practical application.In this paper,the defects of the traditional grey GM(1,N)power model in the initial value and background value are explored and addressed.At the same time,the modeling conditions are reduced to make a single sequence meet the conditions of non-negative and grey exponential rate,so as to expand the scope of application of the grey model.In addition,the main influencing factors of the system are mined by the grey correlation analysis method for subsequent construction of the model.GM(1,1)model based on the optimization of initial value is applied in the new model to predict the future values of the main influencing factors.Based on these,the improved nonlinear grey multivariable GM(1,N)power model is constructed.We name the new model BIGM(1,N)power model.Last,nonlinear case study,MSW generation in Shanghai is applied to verify the optimized model.The main achievements and value of this study are listed as follows.(1)In terms of initial value,we make a new assumption of the initial condition according to the new information priority principle and obtain the new time response.As for the background value,since the background value directly affects the parameters of the model,it plays a key role in the accuracy of the model.Thus,this paper starts with the error generated by the background value,then deduces the optimized background value.The original GM(1,N)power model is then modified through two dimensions of initial value and background value.(2)The prediction of Shanghai’s MSW production based on optimization model is then conducted.It is a vital measure for the government to implement waste management to forecast the future waste production scientifically,which is of great significance for environmental protection as well.Since the total amount of MSW generation is small and it actually belongs to a nonlinear system,the grey multivariable model has good adaptability to this case.Compared with four models which include GM(1,N)power model optimized only with background value,GM(1,N)power model optimized only with initial value,original GM(1,N)power model and traditional GM(1,N)model,the proposed BIGM(1,N)power model performs better than other models in our results.This suggests that the dual optimization of the background value and the initial value plays a good role.This model is an effective method to predict MSW production in Shanghai and can provide more accurate prediction for nonlinear problems.Then we use it to forecast the MSW production in Shanghai in the future.The specific values from 2021 to 2023 are 8.138 million tons,8.947 million tons and 9.816 million tons respectively,which shows that it will still be at a high level and maintain a rising trend.We put forward corresponding policy suggestions subsequently to provide reference for Shanghai municipal government to formulate forward-looking policies and measures in the treatment of MSW and planning.(3)Conduct a measure research for MSW generation in Shanghai.Grey incidence analysis method is applied in this article to extract the main influencing factors on MSW generation in Shanghai.The result shows that in the five factors(the population of permanent residents in Shanghai,Shanghai’s GDP,per capita disposable income of city households,the amount of urban infrastructure investment and the total retail sales of social consumer goods),the main influencing factors on the amount of MSW generated in Shanghai are the population of permanent residents in Shanghai and the amount of urban infrastructure investment.It can also provide ideas for the government to explore the path of MSW reduction production.