Research On Expansion And Application Of Grey Prediction Model With Approximate Non-homogeneous Exponential Sequence

The grey system theory,which takes "small data" and "poor information" uncertain systems as research objects,has been widely used in agriculture,industry,engineering technology,medical health,economic management and other fields.After more than 30 years of in-depth research by scholars,the grey prediction model has achieved many promising results,but in the theoretical research of the grey prediction model,there are still urgent problems.So further research on the grey prediction model is promoting,the development and expansion of grey system theory have important practical significance.Based on the research on the grey prediction model of approximate non-homogeneous exponential sequences,this dissertation conducts research on the problem that the data sequence with approximate non-homogeneous exponential law are not suitable for the grey model.The main contents are as follows:(1)Construction of IANGM(1,1,k)model of approximate non-homogeneous exponential sequence.In order to make the approximate non-homogeneous exponential sequence in the modeling process directly predictable without deductive reduction process,this dissertation considers the model of the grey differential equation and the whitened differential equation matching under the integral theory,the IANGM(1,1,k)model based on the original sequence and its corresponding 1-IAGO is proposed.The solution of the model whitening differential equation is exactly the time response function of the original sequence,and the model can be directly simulated and predicted.(2)Construction of non-equidistant IANGM(1,1,k)model of approximately non-homogeneous exponential sequence.Aiming at the large number of non-equidistant approximately non-homogeneous exponential sequences in practical applications,making full use of the approximate non-homogeneous exponential sequence in the IANGM(1,1,k)model that grey differential equation matches the whitened differential equation.The solution of the whitened differential equation is exactly about the expression of the original sequence and the model does not need to reduce the reduction process advantages,based on the modeling mechanism of non-equidistant model,a non-equidistant IANGM(1,1,k)model is constructed to approximate non-homogeneous exponential sequences.,and then the parameters of the model are estimated based on the least squares,and the simulation of the model is given predictive expression.(3)Parameter estimation and application scope of IANGM(1,1,k)model withapproximate non-homogeneous exponential sequence.For the proposed IANGM(1,1,k)model with approximately non-homogeneous exponential sequence parameters,there is a jump problem from discrete to continuous.Inspired by the discrete grey model,the parameters of the model are estimated using a whitened differential equation.First of all,starting from the expression of the IANGM(1,1,k)model whitening differential equation solution,the relationship between adjacent terms of the original sequence is deduced,and then the Least squares idea and Cramer's Rule are combined to estimate the parameters in the relationship.Using the estimated relational parameters to inverse the model parameters,the expressions that are finally substituted into the solution of the whitened differential equation can be directly simulated and predicted without deductive reduction process.