The Optimization Of GM(1,1) Models And IT Application

Grey prediction,which includes GM(1,1) model and verhulst model, is one of theimportant contents in the grey system theory. Because it requires small sample capacity,and it’s easy to calculate, it is widely used in country economy, management science,engineer technology and many other prediction field. Though GM(1,1) model andVerhulstmodel have good prediction accuracy, GM(1,1) model can not perfectly modelapproximate non-homogeneous index sequence. It is difficult to define the initial value forVerhulst model.According to the questions of GM(1,1) model and Verhulst model, the paperproposed several kinds of extension of the grey prediction model: ANGM(1,1) model,å'ŒOANGM(1,1) model and researches the character of two model.To solve the questiongrey Verhulst model,this paper proposed optimized prediction function of grey Verhulstmodel and provide the model accuracy.Firstly, based on the definition of the GM(1,1) model background value, it launchesapproximate non-homogeneous index sequence ANGM(1,1) model.The conclusion showsthat the new model has good prediction accuracy when it is use to predict approximatenon-homogeneous index sequence.Secondly, research the ANGM(1,1) model based on matrix analysis.By analyzeaffine transformation of original sequence, it is obvious that the affine transformationsequence and original sequence have the same modeling and prediction accuracy.Thirdly, through analyzing the problems that is ineffectiveness of the first entry ofthe original sequence in ANGM(1,1)model, the paper produce a new OANGM(1,1).Thenew model get a new data sequence by accumulating constant value in front of the firstentry of original sequence. Then,the model can be construct by using the new sequence.Finally, as for the optimization of Verhulst model on initial condition. This paperproposes a new method to create the time response sequence of whiterization for Verhulstmodel. The constant c of the time response sequence of whiterrizatin equation ofverhulstmodel can be found by an optimized method. The optimized method uses square sum of difference value of the count backwards of accumulated generation sequence andsimulation value to create nonlinear unconstrained optimization model.Then,the timeresponse sequence of grey differential equation can be got. The experiment shows that theimproved verhulst model is superior in prediction and simulation.