Research On The Nonlinear Fractional Grey Model Of Short-term Traffic Flow Forecast

Timely forecasting to urban traffic situation is the foundation of traffic guidance and control.Using the data of traffic flow from SCATS ofChangsha,analyzing the characteristic of data,this paper establishes nonlinearity fractional grey models to forecast the short-time traffic flow.The specific contents are as follows:The fractional accumulated GM(1,1)(i.e.FAGM(1,1))is constructed.Firstly,the GM(1,1)model is established relating the flow and accumulation to forecasting the traffic flow in small sample.Considering the limits of origin GM(1,1),that the origin data must obey the exponential law or that the class ratio should be in admissible region,this paper takes the fractional accumulated generating operation into GM(1,1)to construct the FAGM(1,1)model,which could effectively improve the exponential law of data,with the generalized admissible region of class ratio FAGM(1,1)proved.Considering the leaping between parameter estimation and model prediction in FAGM(1,1),this paper proposes a discrete FAGM(1,1)model(i.e.FAGM(1,1,D)),and discussed the error analysis between FAGM(1,1,D)and FAGM(1,1).According to the oscillation of traffic flow data,the fractional differential grey model(i.e.FGM(q,1))is built.This paper expands the differential equation of FAGM(1,1)model from the first order to fractional order differential equations andconstructs the FGM(q,1)model.With the mean absolute percentage error(i.e.MAPE)as the objective function of the optimization model,the particle swarm algorithm is used as a solving tool to calculate the accumulation number and the order of the differential equation.With other model parameters estimation completed by least squares to complete,the model is settled down by the finite difference method.Based on the decomposition of the parameter estimation matrix,this paper discusses the derivation of the three kinds of grey models.Taking the regularity of traffic travel into consideration,the nonlinearity fractional grey model is assembled.As the trend of traffic flow could be described using polynomial regression analysis and residual a priori estimates based on historical big data,the history traffic flow information integration grey system model is constructed.And the model is solved using the method of variation of constants complete model.The MCMC for prior residual sampling and simulation is employed to solve the point and interval estimations of traffic flow.At the end of this paper,traffic flow data information from SCATS system of Changsha is used to test the model,traffic flow information of grey model complete for the next 15 days(contains 495 groups,each group of four predictive value)receding horizon predictive,final prediction result of reliability as high as 94.65%.