Research And Application Of Two Types Of Improved Grey DGM(2,1) Model

As one of the important contents of the grey system theory,the grey prediction model has solved many problems with uncertain information since the birth of the grey system theory.After the continuous research and improvement by several scholars,the grey prediction model has been widely used in various fields,and has achieved remarkable results.In many grey prediction models,DGM(2,1)model is a second-order linear dynamic model,and has a higher sensitivity compared to other grey prediction models,the effect will be more significant in fitting the data with more strong trends.However,in practical problems,because the system is influenced by human factors and natural environmental factors,the data sequence often changes dynamically,even showing stochastic oscillation.Obviously,the single grey amount of the original DGM(2,1)model,and in the process of building the model,the derivative is directly replaced by difference quotient,which will lead to the model unable to adapt to this dynamically changing data sequence.And for the stochastic oscillation sequences,it is even more difficult to achieve high simulation and prediction accuracy by using the original DGM(2,1)model.Therefore,this paper mainly carries out the research work from the following two aspects:(1)In view of the problem that the grey action is constant in the DGM(2,1)model,and the large error caused by selecting grey derivative directly by difference quotient instead of derivative in this model construction process,replacing the b in the original model withbk(10)c,namely linear time-varying grey action is introduced into the DGM(2,1)model,and the first order central difference quotient of the transformation is constructed to replace the integration term,so as to optimize the grey derivative in the model,then the DGM(2,1)model optimized based on the grey action amount and grey derivative is obtained.And apply the model to the prediction of in-homogeneous exponential sequences,as well as short-term predictions of wobble sequences.(2)In view of the problem that the grey model is bad for the simulation of stochastic oscillation sequences,the accelerated translation smoothing data transformation is constructed on the basis of the existing research,transforming the stochastic oscillation sequence into a new sequence of monotonic growth suitable for modeling.At the same time,in order to avoid the defect of difference direct to differential crossing,and to achieve the purpose of describing the growth trend of data series,the quadratic time term is introduced to establish a discrete DGM(2,1,t~2)model based on the stochastic oscillation sequence,and expand the scope of application of DGM(2,1)model.In the practical application analysis in different fields,the two types of optimized DGM(2,1)models are compared with the simulation prediction effect of three types of different gray models,indicating that the two types of optimized DGM(2,1)models have good simulation prediction effect,and have important practical significance and wide application value.