Research On Optimization Method And Application Scope Of Two Kinds Of Grey Forecasting Model

Grey forecasting model,as the main branch of the grey system, has achieved good results in many fields, and made a great contribution to the development and progress of society. Since there are some corresponding requirements for the grey forecasting model to select data in the modeling process, hence the application scope of the model in the practical application is limited. In this paper, we use the direct modeling method, the grey derivative optimization, the discretization method and other methods to improve and optimize of the approximation non-homogeneous GM model and the Verhulst model, thus we can break through the application scope of the model and build a better model. Specific work as follows:(1)In the first place,according to the form of the solution of the nearly non-homogeneous GM model, the coefficient of x(1)(k) is coalesced and sorted out as the form, x(1)(k)=BeAk+Ck+D. Then taking K as a continuous variable, calculating the derivative function for x(1)(k) , and replacing the grey derivative of approximation non-homogeneous GM (1,1) model with the obtained derivative function ABeAk+C, we can work out A,B,C value via simultaneous equations.Secondly, the prediction coefficient c can be determined by using the objective function J(c) =(?).Finally, an experiment shows the optimal grey derivative method that makes the background value and the grey derivative closer to the relationship between the original function and the derivative function, which achieved the original intention of the optimization model.(2) For the optimization problem of approximation non-homogeneous GM model,this paper presents a new optimization model, which combines a direct modeling thought, optimizing the grey derivative with the ahead-back difference quotient, and the comprehensive utilization of all known n data to optimize the initial value. At the same time, this paper proves that the model has the whitening index and coefficient coincidence, and analyzes the reasons why the modeling effect is better.(3) Based on direct modeling of the approximation non-homogeneous GM model,the direct GM model of the approximation non-homogeneous discrete form is obtained.This model not only improves the approximation non-homogenous exponential sequence modeling accuracy, but also the scope is extended to approximation non-homogenous exponential increase or decrease sequence and linear increase or decrease sequence's combination sequence, or parabolic increase or decrease sequence,and calculating formula of undetermined coefficients is derived. It is proved that the new model has the whitening index and the coefficient coincidence for the combination of the strictly non-homogeneous exponential increasing and decreasing sequence and the combination sequence of the linear increasing or decreasing sequence and the strict parabolic increasing and decreasing sequence. Therefore, the accuracy of the model is higher than that of the sequence like those. Secondly, the model's accuracy is also improved by optimizing the initial value.(4) For the original data with "S" type process and small sample capacity, the grey Verhulst direct model is established for reciprocal sequence. This method converts the grey Verhulst model into GM (1,1) model to solve the corresponding problem. In this paper, the least square method is applied two times to optimize the model parameters,which plays the to re-optimization role. At the same time, it is proved by the time that optimizing the background value and the parameter makes the model more consistent with the original data model with the basis of direct modeling.