Several Kinds Of Discrete Grey Prediction Models And Their Properties Are Studied

In 1982,professor Deng Julong established the Grey Systems Theory,which is a new method to study the problem of "small sample,poor information".It mainly mines some known information and extracts valuable information to realize correct description and effective monitoring of system operation behavior and evolution law.As one of the core contents of grey system theory,grey prediction model has been widely used in many fields such as society,economy,industry,agriculture,science and technology,and its application value is gradually known by people.Based on the existing researches of many scholars,this paper mainly studies the following three aspects:(1)Based on the analysis of the current research status of the existing discrete grey prediction model,considering that the existing discrete grey prediction model only considers the linear relationship between the two adjacent items of a single accumulation,the generalized discrete grey prediction model is proposed:this model considers the linear and nonlinear relationship between the two adjacent items of a single accumulation.Secondly,the properties of the model are studied and it is found that the model has perfect coincidence for four kinds of special sequences.The variation law of model parameters and simulation values and the invariance of relative error under multiplicative variation;The modeling steps and methods of the model are given,and an example is given to show that the model can greatly improve the modeling accuracy.(2)Studied the properties of the comprehensive time-varying grey Verhulst model.First,combining the characteristics of Verhulst model and the model of approximate inhomogeneous exponential sequence:The comprehensive time-varying Verhulst model is constructed:and the corresponding whitening differential equation of the model is Because of the particularity of this whitening differential equation,the discrete values satisfying the comprehensive time-varying Verhulst model are solved by numerical method,which is why the comprehensive time-varying Verhulst model is classified as the discrete grey model.Secondly,this paper studies the properties of the model and compares it with other models through case analysis.(3)A new discrete grey Verhulst model was constructed and its properties were studied.Firstly,through the albino differential equation of Verhulst model:the idea of dividing both sides of the equation by(x(1)(t))2 was used to construct a new discrete grey prediction model:y(1)(k)=?y(1)(k-1)+?,the time response formula that can take any term in the sequence as the initial value was derived,and the feasible selection method was given.The method of solving model parameters by using the least one method and the mean relative error is given.In this paper,the solution method and modeling steps of the new discrete Verhulst model are summarized.The unbiasedness of the new model is proved.Finally,the simulation prediction accuracy of the new model is compared with that of several existing models through example analysis.The results show that the new discrete Verhulst model proposed in this paper can effectively improve the simulation prediction accuracy,and the calculation process is more simple.