Research On The Improvement Of Power Exponent Of Traditional Power Model And The Solution Method Of Inhomogeneous Power Model

Grey prediction model is the main conponent of grey system theory,which is widely used in ordinary life.Grey prediction model mainly studies a series of problems such as less data and less information in life.For the problems existing in the grey power model,this paper explores the power model from two different perspectives,namely the new power index calculation method and the grey action term,so as to achieve the purpose of improving the modeling accuracy.The main contents of the research are as follows:1?Improve the calculation method of power exponent(1)Aiming at the power exponent problem of traditional power model,this paper mainly starts from the time response formula of the model,and gets the specific calculation formula of the background value through processing,so as to reduce the influence of the background value on the power exponent,and the formula is much simpler.(2)When the power index is known,the problem is solved for the other parameters in the power model,this paper first through data transform the traditional power model albino differential equation into a familiar and simple GM(1,1)model of albinism differential equation,then integrate new bleaching differential equation to get the background value,the solution of the power model parameters were converted to the parameters of GM(1,1)model to solve.Finally,the parameters in the new model are solved,and the correlation model is established through an example to verify the practicability and feasibility of the model in this paper.Moreover,the model is simple and convenient.2?Improved ash action term(1)Based on the non-homogeneous GM(1,1)model and the non-homogeneous Verhulst model,a non-homogeneous GM(1,1)power model is obtained by improving the grey action term in the whitening differential equation of the traditional power model and solving the parameters.Finally,the model is established by using columns to verify the practicability of the model.(2)To further improve the modeling accuracy,based on the inhomogeneous which has more extensively applicable scope is on the basis of GM(1,1)model of power in the case of the bleaching equation is not involved in the discretization process of the model,and according to the discrete model is derived for an arbitrary time response of the initial value,then the time response type processing,get the discrete model under different conditions of general term formula.And,all parameters were optimized at the same time with Matlab,Lingo and other software under the objective function with the minimum average relative error.Finally,the feasibility and superiority of the model in this paper are verified by setting up different models and comparing the prediction accuracy of simulation.