Research On Traffic Flow Fractional Prediction Model Based On Viscoelastic Characteristics

The increasingly serious traffic congestion leads to a series of serious urban management problems,such as the deterioration of traffic order,the increase of traffic accident rate year by year and the continuous deterioration of urban environment.Exploring the evolution mechanism of traffic flow and realizing accurate short-term prediction of traffic flow are the key to alleviate traffic congestion.The existing traffic flow prediction models usually regard traffic flow as an ideal fluid and ignore its viscoelastic characteristics,resulting in the existing models can not accurately explain the self-organization and self-adaptive characteristics of traffic flow.In this paper,traffic flow is regarded as viscoelastic fluid,the memory characteristics of viscoelastic fluid are well described by fractional derivative,and the fractional prediction model of viscoelastic macro traffic flow is studied based on the internal characteristics and formation mechanism of different traffic flow states.The research result is a new attempt of hydrodynamics viscoelastic theory in the field of traffic flow,which can more accurately describe the development law of traffic flow,reproduce the formation process of different traffic flow scenes,and provide theoretical reference for intelligent traffic dredging.The main work is as follows:According to the viscoelasticity of traffic flow,the internal mechanism of fractional order modeling of traffic flow is studied.Considering that the existing viscoelastic traffic flow model is complex and difficult to solve,the spatiotemporal viscoelastic traffic flow model is transformed into the temporal viscoelastic traffic flow model.It is found that the temporal viscoelastic traffic flow model is formally similar to the grey differential equation.Further,according to the characteristics of poor information and uncertainty of short-term traffic flow system,it is found that the traffic flow system has significant grey characteristics.Combined with the characteristics of viscoelastic fluid of traffic flow,the good application of fractional derivative in viscoelastic fluid constitutive model is used to find the internal mechanism of fractional modeling of traffic flow,and a unified fractional grey prediction model of time viscoelastic traffic flow is established.This model overcomes the limitation that the original traffic flow prediction theory does not deeply study the internal mechanism of the traffic system,and lays a foundation for the study of the fractional grey prediction model of viscoelastic traffic flow in the scenarios of free flow,congested flow and mixed flow.According to the weak viscoelastic characteristics of free flow in road sections,a viscoelastic univariate fractional order grey prediction model with fixed order and fixed coefficient is established.Combined with the specific conditions satisfied by the operation mechanism of free flow,based on the influence of kernel function on the singularity of fractional derivative,the viscoelastic fractional grey prediction models of road free flow under the condition of power function kernel and exponential function kernel are established respectively.Through the comparative analysis of the two models from the perspective of singularity and calculation efficiency,it is found that the viscoelastic fractional grey prediction model of road free flow based on exponential function kernel is more efficient and accurate to predict the development trend of road free flow.The empirical analysis shows that the proportional relationship between relaxation time and traffic flow viscosity and elasticity can be used to describe the evolution law of free flow.Some parameters of the new model can well explain the development law of free flow and better describe the self-organization ability of free flow.According to the spatiotemporal correlation and weak viscoelastic characteristics of free flow in road network,a multivariable grey prediction model of spatiotemporal viscoelastic free flow with fixed order and fixed coefficient is established.According to the objective fact that there is time-space correlation between the traffic flow of adjacent intersections,combined with the weak viscoelastic characteristics of free flow road network,the traffic flow of adjacent intersections is regarded as an influencing factor by using the modeling method of grey multivariable prediction model,and the single variable fractional grey prediction model of road section free flow is extended to the multivariable fractional grey prediction model of road network free flow.The results show that this method can accurately describe the impact of traffic flow at adjacent intersections without accurately quantifying spatial factors,which provides a new idea for the research of spatio-temporal viscoelastic traffic flow prediction model.According to the time-varying characteristics and strong viscoelasticity of congested flow,a fractional grey prediction model of viscoelastic congested flow with variable coefficient is established.Taking advantage of the similarity between the modeling principle of crowded flow diffusion process and bass diffusion model,combined with the properties of conformable fractional derivative,the model coefficient is transformed from constant to power function of time,and a crowded flow prediction model with coefficient varying with time is established.The change of diffusion coefficient with time in the new traffic flow model.The results show that the more congested the traffic is,the more prominent the viscoelastic characteristics are,and the longer it takes to recover to free flow.When the road is in a state of traffic paralysis,the viscoelasticity reaches a maximum.This model provides a new idea for describing the time-varying characteristics and diffusion process of congested flow.According to the stage characteristics and mixed viscoelastic characteristics of mixed flow,a variable order fractional prediction model of viscoelastic mixed flow is established.Based on the formation mechanism of mixed flow,combined with the idea of variable order fractional derivative describing the creep process,the derivative order and cumulative generation order of traffic flow prediction model are transformed from constants to functions,the determination methods of independent variables of variable order function and model expression are studied,and a variable order viscoelastic mixed flow fractional grey prediction model with variable order fractional cumulative generation and variable order fractional derivative is established.The results show that the new model can adjust the model parameters according to the stage characteristics of congested flow,and has good generalization ability.The new method promotes the development of variable order fractional derivative theory and application,and provides a new method to describe the phased characteristics of mixed flow.