Research On Grey Prediction Model Reduction And Parameter Solving Method

The Grey system theory is a kind of new theory.It is a systematic engineering discipline based on mathematical theory,proposed by Professor Deng Julong for the first time in 80 s.It mainly solves some special problems that contain unknown factors.This theory is widely applied in real life.Many common and extensive models of application and research include traditional GM(1,1)model,non-homogeneous GM(1,1)model and DGM(1,1)model.As one of the most widely used models of application and research,the GM(1,1)model has been optimized by many scholars.However,the GM(1.1)model is less research work based on its application as the main theory.Therefore,the theoretical system of GM(1,1)is still not very perfect.This is the direction that the scholars are going to work on.Most of the optimization methods of GM(1,1)model affect the final accuracy of the model by indirectly optimizing parameter,so it is particularly important to identify better parameter.This paper mainly studies the two aspects of the traditional GM(1,1)model,which are the reduction method and the time selection of the simulated prediction formula,the method of determining the parameter,the development coefficient of time and the non-homogeneous GM(1,1)model,and the parameter estimation.The main work is as follows:(1)First of all,it is proved that after the response formula is reduced to the simulation formula,the initial predictive coefficient is replaced with the prediction coefficient determined directly by the corresponding formula.For a model with whitening index coincidence,the former can guarantee the coincidence of whitening coefficient whether it is determined by single initial condition or combined with all initial conditions.Then,in view of the optimization of the background value model,this paper proves the superiority of the derivation reduction.Then,we analyze and compare the different prediction methods of the prediction coefficients at different time points,the initial conditions,and the prediction results of the six kinds of different models determined by the different selection of the objective function.Finally,the feasibility and effectiveness of the proposed method are verified by an example,and the correctness of the analysis results is proved.(2)Secondly,when the application range of the research model is under the condition of approximate non homogeneous exponential sequence,a simple formula for solving the development coefficient of the simulation formula is derived.The method ofdetermining the prediction coefficient and translation constant through the two initial and the initial conditions is given.It is illustrated by examples that these two ways of determining parameters can combine themselves to form new models,and one of them can be combined with other ways of remaining parameter to get improved models.All of them can improve modeling accuracy.