Several Kinds Of Fractional Reverse Accumulation Grey Prediction Models And Its Application

For more than forty years,the grey system theory has experienced continuous development and enrichment,and the corresponding theoretical knowledge and system have been continuously improved.Among them,the grey prediction model has always been a hot research topic and is widely used in all walks of life.However,there are still some grey prediction models that need to be improved and perfected.In this paper,firstly,starting from the generation mode of fractional reverse accumulation,the equally spaced and unequally spaced fractional reverse accumulation GOM^（p,q）（1,2）model with different accumulation orders for different sequences is proposed.Secondly,the fractional reverse accumulation Verhulst model with linear time-varying parameters and the unequal interval fractional reverse accumulation Verhulst model with linear time-varying parameters are proposed.Finally,the proposed fractional reverse cumulative grey model is applied to the prediction of air pollution in China,and the effectiveness of the proposed model is verified.The main work is as follows:Firstly,by combining fractional accumulation with reverse accumulation,the fractional reverse accumulation GOM^（p,q）（1,2）model with different accumulation orders for different sequences is proposed,and the linear correction term and grey function are added,and the expression of parameter estimation and solution of the new model is proved;In addition,a non-equidistant fractional reverse accumulation GOM^（p,q）（1,2）model with different accumulation orders for different sequences is proposed,and the expressions of parameter estimation and solution are proved.This method provides a new idea for the research and application of grey prediction model.Secondly,by taking the reciprocal of the solution of the whitening differential equation of the fractional backward accumulation Verhulst model,the solution of the whitening differential equation of the fractional backward accumulation gray Verhulst model is transformed into the solution of the whitening differential equation of the fractional backward accumulation GOM（1,1）model,and starting from the whitening differential equation of the fractional backward accumulation GOM（1,1）model,the linear time-varying parameters are increased,two new Verhulst models are proposed:fractional reverse accumulation Verhulst model with linear time-varying parameters and unequal interval fractional reverse accumulation Verhulst model with linear time-varying parameters,and the parameter estimation formula and solution expression of the models are proved.Through these improvement measures,the traditional grey Verhulst model is successfully optimized and its application scope is expanded.Finally,the proposed model is applied to the prediction of air pollution in China,and the GOM^（p,q）（1,2）model with fractional reverse accumulation is combined with the neural network model to establish the GOM^（p,q）（1,2）-BP neural network combined model,which is applied to the modeling and prediction of air quality index in China.The modeling and analysis results show that the new model has obvious advantages in accuracy and reliability compared with the traditional model.