Research On Extentions And Properties Of Discrete Grey Model

Take discrete grey model reasearch of grey modeling theory as the main, the core of whichconsisits of three parts, namely discrete grey model of approximate polynomial sequence, theexpansion of discrete grey model based on multi-factor information aggregation and characteristics ofdiscrete grey models. Combined with discrete grey models’ application in the prediction of passengerflow volume along Shanghai-nanjing railway, the practical applicability of the discrete grey modeland its extension models are analyzed. The contents include the following aspects:(1) To study the grey system modeling of small-sample and non-monotonic sequence, thediscrete grey model of approximate polynomial sequence containing dynamic grey action quantity isintroduced based on grey information principles summaries of present discrete grey models.Comparison is made on the fitting and prediction results between the new model with the m of2andother non-linear grey models. Results show that under certain circumstances the new model couldachieve unbiased curve fitting as well as high prediction accuracy.(2) Based on the GM(1,h)model, a new extention model is proposed. Solow complementarymethod is adopted in this paper to aggregate the development situation of system influence factorsequence, then dynamic aggregation information is uesd as feedback of system development situationfor behavior variable, so as to effectively solve the issue of low variable identification precisioncaused by multi-factor input collinear as well as the issue of low model precision caused byunreasonable feedback model. A real case is used to verify the effectiveness of the model.(3) Characteristic of Parameters are analyzed and the completely fitting expression of genenalexponential non-honogenous discrete grey model. Research is also made on the unbiased fittingcharacteristics of polynomial sequences and certain length sequences by the DGM(1,1,m). In addition,multiple transformations’ effect on FDGM(1,h) model is discussed.(4) Passenger flow volumes along Shanghai-nanjing railway since2000are analyzed and NDGMmodel and DGM(1,1,m) model are applied in the total volume prediciton. The prediciton results arecompared to the real data from2006-2009and the accuracy of discrete grey models are discussed.Furthermore, the optimization model is adopted in the prediction in2010-2014. Meanwhile, based onthe analysis of related factors of city passenger flow volumes along Shanghai-nanjing railway, themodel discrete grey model are adopted in the prediction of city passenger flow volumes in2010-2014.