Improvement And Application Of Gm(1,1) Model

GM(1,1) model is the most popular grey dynamic predictive model in the grey system theory, which is made up of first order differential equation about variable. It is used to fit and predict the characteristic function of one main factor in the complex system. So the transformation law and the develop trend of the main factor can be shown. However, we found that in practice the fitting or predictive effect of this model is not good, and even invalidate completely. In this thesis some mathematical processing methods are tried to solve the problems, improve GM(1,1) model from modeling mechanism and reduce the inherited error caused by the defect of modeling method. The main works are:(1)Grey predictive model can be regarded as index predictive model naturally. So its predictive precision is related to transformative law of the predicted object and the smoothness of date sequence; this paper pre-processes the primary sequence in order to improve its smoothness, and then to build the model.(2) The discrete fitting equation, which background value is the average of x⁽¹⁾( k ) and x⁽¹⁾( k + 1), is an approximate difference equation. When the data sequence change fast, it can not ensure fitting equation is extremely approximate to the differential equation of fitting system, also it can not ensure that the inherited error of the grey model built is infinite small amount; From the geometric meaning of z⁽¹⁾( k ), this paper proposes a method about constructing background value, making the precision of prediction and simulation significantly increased.(3) Estimation method of parameter a,b almost use Criteriaofleastsquares, but its robustness is poor, and sometimes the fitting precision of regression equation is not very ideal; Based on anglicizing deeply on modeling mechanism of GM(1,1), this paper proposes a method solving parameters of model, making the precision of prediction and simulation increased.(4) Study on improved model's application in tourism in Nanjing, the results show effectiveness and practicability of the improved method.