Research On GM(1,1) Model Of Grey System And Its Application

Grey System Theory (GST) studies on the indeterminate system with"a few samples"and"poor"information,which is in the situation of"part of information known,part of information unknown". By generating and developing the"part of information known", GST can help us understand and recognize the real world,and help us rightly master and describe the operational behavior and evolutional law of the investigated system.His characteristic is"pattern of minority according to builds".With the other theories difference is that the object of the research"extension is clear and definite and the intension is not clear and definite"is stressed to the grey system theory. Studying the content chiefly includes:the grey system builds pattern theory and grey system control theory,interrelated analysis method of grey, grey forecasting method, grey planning method and grey policy decision method etc.The nucleus of grey system theory and method is the system model of grey, and his characteristic is comeing or bring into being function and grey differential equation.The system model of grey is comeing or bring into being the function concept with the grey serving as the foundation,and with the differential drawing up closing the pattern the building method for the nucleus.This paper puts emphases on GM (1,1) model of the grey system.It studies on data processing,modeling and solving GM (1,1) and the selection of initial value. The central contents of the paper are as follows:1.It expounds the research background and significance of GM (1,1) model,introduces the applied status of grey system and summarizes the research aim and central task of the paper.2. It studies on the data processing.After introducing the two ways of data processing (buffer operater,data transform),it uses the data transformation functions to unify the data transformation.And it judges the conditions of using which kind of data transformation by error analysis.3.It studies on the solving of parameters a and u in GM (1,1) model. By analyzing the modeling mechanism and the background Sequence Z⁽¹⁾ (t),it tells us that the key of solving parameters a and u is the solving ofλvalue. The optimization method of solvingλvalue are the genetic algorithm and the step by step optimum grey derivative. This paper solvesλvalue by optimization.This paper uses the optimization to getλvalue for the first time.Butλvalue are not same during building the background sequence Z⁽¹⁾ (t).In differentλvalue are different.This paper uses optimizationto solve the differentλvalue. This method improves the precision of the model.4.It studies the initial value.The selection of initial value affects the result of Fitting and prediction.This paper summarizes the way of the initial value selection And it combines selectingαx(0)(1)as the initial value and optimization to improve the precision of fitting and prediction.And it test the method by the example.