Research On Optimization And Application Of Two Types Of Grey Power Model

In various prediction theory systems,grey prediction model is widely used in various fields because of its advantages such as fewer samples and simple modeling process.At present,researchers at home and abroad have done a lot of research work in the field of grey prediction system theory,and has achieved many important results,but there are still urgent problems.Therefore,it is of great significance to optimize and perfect the grey prediction model for theoretical development and practical application.Grey GM(1,1,t?)model and GM(1,1)power model are the derivative models of classical GM(1,1)model,which have attracted a large number of scholars to study them.Based on the existing research,this paper studies the applicability and modeling accuracy of GM(1,1,t?)model and GM(1,1)power model.The main contents are as follows:(1)Optimization for the GM(1,1,t?)model.To boost the accuracy of GM(1,1,t?)model and improve its application limitations,it is proposed to construct a direct discrete GM(1,1,t?)model by using the original sequence x(0),which is DDGM(1,1,t?).The initial value of iteration is x(0)(n)and x(0)(1),and extend the application range of gray forecasting model to power function and approximate non-homogeneous exponential combination sequence,power function and homogeneous exponential combination sequence,approximate power function sequence.(2)Aiming at the optimization of traditional GM(1,1)power model.First,based on the time response of the GM(1,1)power model,eliminate the parameters in the model:gray effect and development coefficient,so as to derive calculation expressions containing only power exponents,estimate the linear parameters after using the function f(x)=aarccotx transformation method on the modeling sequence.Give the optimal initial conditions of the model.Then the traditional non-equidistant GM(1,1)power model is extended to the linear time-varying parameter non-equidistant GM(1,1)power model,derive the model time response,based on the principle of integration,using the 1-? power generation sequence of the original data sequence and its corresponding one-time accumulative generation sequence to construct a gray differential equation matching the parameters of the model whitening equation,and the optimal initial conditions of the model and power exponent solution method are studied.Finally,the application analysis results verify the effectiveness and feasibility of the optimized GM(1,1)power model and the direct discrete GM(1,1,t?)model.