The Optimization And Improvement Of Grey Model

Grey System is a subject of applied mathematics , Grey System can be used to study the system that uncertain and some information is known and some information is unknown. Its a result of the view and methods of control theory extend to the social, economic areas. Its also a result of control science and operations research with mathematical method combined.One of the important contents of study Grey system is how to building a Model from not very clear and poor information system. GM (1,1) Model is mathematical model building on grey system .It can provide a basis for find more information from grey system. GM (1,1) Model is a similar difference Equations and differential equation models. It has difference, differential, compatibility index features. The structure and parameters of GM (1,1) Model change with time and it also not required lot of data . It is a innovative methods of model building .GM (1,1) model is the basis of grey prediction theory, it can be used to forecast the disaster , the series and topology.At present, GM (1,1) model has been widely used in industry, agriculture, social, economic and other fields, its value has been gradually recognized by the people. At the same time in the practical applications and theoretical course of the study , also found that many of the model's limitations and inadequacies. Through the learning and research of GM (1,1) Model, for the inadequate of GM (1,1) model , this paper presents some of the attempt to improve methods with a view to better simulate and predict the effects and further meet the needs of practical applications .In the main text three aspects were studied, GM (1,1) model background value optimization; the solution of GM (1,1) model parameters a and u ; the original data grey regression.1 We take the value of the background forλx¹ (t) + (1 -λ)x¹ (t - 1)(λwas background parameter). Through study the relationship of background value parametersA and fitting result of GM (1,1) model,found the function of the relationshipbetween background parameter lambda and square error sum is a under summit function near the optimal values ofλ,Λand the average relative error of model has a similar relationship . Under this article by solving a single peak to function extremum , to find the optimal parameters A of the background value. Verified by examples in this paper use the background value optimized GM (1,1) compared to the traditional model of GM (1,1) model is better fitted, and the development of the original data and the original data coefficient fluctuations in the less affected.2 Traditional GM (1,1) model in the determination of background values, using the least-squares method solving model parameters of a, u. To avoid the selection of the background value. Usex¹(t)=(x⁰(1)-u/a)e^-a(t-1)+u/aas the time response function. For the average relative errors and squared error sum minimum as standards. By solving the extreme of a single under peak function to solution parametersa, u. Examples indicate that the method is better than the traditional model of GM (1,1) model and others GM (1,1) model of background value optimization.3 In this paper using grey regression method to the raw data which have exponential trend. Obtain the grey regression model function of the original data:x⁰(t)=ce^-a(t-1)+bThrough examples in this paper verified use grey regression method, have a good fitting and prediction. In most cases better than GM (1,1) model and the improvedGM (1,1) model results.