Grey Forecasting Modeling Technique Research Containing Time Delay Factor

Along with the diversification and complexity of social and economy development, practical application of existing grey model presents some limitations. During the thorough research of classical grey prediction model, researchers find that some special methods are necessary for the practical problems under certain circumstances.So a number of GM derived model were found to deal with these more complex practical problems. In this paper, the author attempt to introduce the extensively existing hysteresis effect into the theory of grey modeling, through a thorough research,including construction of GDM(1,1) model and GDM(1,2) model, analysis of the modeling mechanism,the model parameter identification method and the solution of the GDM model. Both models are applied to the prediction of the transportation problem in our country. This paper aims to further deepen the theory study of grey system and broaden the application area of grey forecasting theory. The main work is as follow:(1) As for single variable grey model, the author analyzed the connotation of hysteresis effect.Basing on classical GM(1,1) model, grey GDM(1,1)model with time-delay is built by introducing time delay parameter. Based on the data relation formula deduced from GDM(1,1) model’s transformation, grey relative model is used to estimate the time-delay parameter.Then the time response formula of the GDM(1,1)model is figured out. Finally, a numerical example illustrates the model can achieve the better simulating effect.(2) AS for the input- output system with hysteresis effect, the GDM(1,2) model is built by introducing the time delay parameter. By introducing cubic spline interpolation, the limitation that the time delay must be an integer is eliminated. Then an optimization model whose target was minimizing the average relative error is established. Finally the particle swarm optimization(PSO) is used to estimate the parameters.The model approximate time response formula is presented. Finally, a numerical example illustrated the validity of the model.(3) GDM(1,1)model is applied to predict the traffic investment of our country, including total fixed asset investment in transport and Highway construction fixed assets investment. Based on the original and prediction result, a trend analysis and explanation of traffic investment is concluded.GDM(1,2) model is applied to the volume of passenger transportation and the volume of freight traffic.finally the analysis of the prediction results is given.