Improvement Of GM(1,1) Model And Its Application

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 one 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 in practice that the fitting or predictive effect of this model sometimes is good, sometimes the deviation is big, and even invalidate completely. Through analyzing the modeling principle of GM(1,1) model, we found two problems: (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;(2) The disperse fitting equation built by grey differential fitting method is an approximate difference equation. So 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.In this thesis some mathematical processing methods are tried to solve the two problems above, improve GM(1,1) model from modeling mechanism and reduce the inherited error caused by the defect of modeling method. The main work is: (1) To pre-process the primary sequence in order to improve its smoothness, and then to build the model; (2) To use the numerical solution of difference equation to build GM(1,1) model, and enhance the degree of approximation of fitting equation and the differential equation of fitting system.The improved model is more flexible and more precise than the traditional model, thus the coverage of the GM(1,1) predictive model is widened. In this thesis, the application of improved GM(1,1) model in mechanical engineering is discussed by examples and the results prove the validity and practicability of improved method.