Algorithm Study On The Multivariate Grey Control Model

Based on the classical grey theory, grey multivariable control model solves the problem which is extended from single variable, accurate sequence and single grey model to multivariable input-output situation, interval sequence and the group of grey model composed by several grey models. At present, some very important problems for grey prediction are solved clearly, such as grey relational analysis, grey generation, the parameter space of GM(1,1),the precision of GM(1,1),ill-conditioned problem of GM(1,1).But there exist many problems especially the prediction of the multivariable input-output model as well. The research on multivariable input-output grey model is not very popular and the precision of multivariable input-output model is not very satisfied. Furthermore, many scholars study on the interval prediction that the original sequence and forecasting sequence are accurate number and interval number respectively. They usually used envelope forecasting but the precision is not very high. The interval prediction problem that original sequences and the prediction result are both interval number is rarely referred.In order to improve the precision of prediction and solve the practical multivariable input-output problem, this paper analyzes the principium of classical GM (1, N),and the multivariable input-output GM(1,N) and GM(2,N) with integral transform model ,grey single variable linear regression mode, grey multivariable linear regression model ,interval grey model with grey algebra are established. Finally, the prediction of Wuhan traffic is solved by using multivariable grey control model above. The full text is divided into six chapters as follows:Chapter 1 introduces the background, motivation and some of the current research status at home and abroad, and reviews the theorem of classical grey system.The second chapter mainly studies the multivariable grey control input-output model. Firstly, multivariable input-output GM (1, N) model with integral transform is established by reviewing the classical GM (1, N) model. In the solution structure of the model, solution form with higher precision is proposed. Considering the prediction problem for the non- monotonous system, multivariable input-output GM (1, N) model with integral transform model is developed to two steps situation. The model parameter recognition and the solution formula of multivariable input-output GM (2, N) model with integral transform model are solved. Then, the property of the above model is discussed in detail. Based on the sampling theorem and the differential equation theory, the discrete model of grey state space is established by analyzing the solution structure of multivariable input-output GM (1, N) with integral transform model. For complex system prediction problem, we introduce the grey system prediction to solve the prediction of Wuhan transportation traffic.In chapter 3, we mainly study and solve the interval prediction problem. First, several kinds of common interval prediction models are reviewed, such as curve envelope forecasting, grouping modeling interval prediction. By analyzing the simplest interval prediction and on the basis of single variable grey linear regression model, multivariable grey linear regression model with multiple input single output situations is proposed. Regarding the perdition problem that original sequence and forecast result are both grey interval number, the grey interval model with single variable (IGM (1, 1)) is proposed on the basis of grey algebra system theory. Furthermore, the grey interval model with single variable IGM (1, 1) is extended to multivariable input-output situation which is called as multiple input and output grey interval model (MIOIGM(1,N)) .In chapter 4, we use the multivariable grey control model to solve actual problem. Combined grey model with the neural network model, the optimal model is established. Finally, the prediction problem of Wuhan transportation traffic is solved by using this optimal model.