A novel partial grey prediction model based on traffic flow wave equation and its application

Due to the spatiotemporal, periodic, and wave characteristics of traffic flow, this paper considers the continuous traffic flow on the road as a special kind of fluid, and uses the wave equation in fluid mechanics to describe the fluctuation and undulation characteristics of the traffic flow data. From the traffic flow wave equation, using the partial grey prediction model can effectively reflect the time correlation of traffic flow, and establish the secondorder partial grey prediction model of the traffic flow wave equation. In solving the time response equation of the model, the modeling steps of the model were obtained by discretizing the grey differential equations and using iterative recursion. Finally, the validity of the model is verified by three case studies, in which the fitted mean absolute percentage error reaches a minimum of 5.1242%, which is better than the other three algorithms and two partial grey prediction models. Meanwhile, the new model was used to predict the short-term traffic flow for the three cases, and the situation when the traffic flow exhibits different periodicity is discussed separately, and the results show that the predicted data have great similarity with the original data trend. Therefore, the model proposed in this paper is very effective in solving the short-time traffic flow prediction problem. By using this model for real-time traffic flow prediction, the control of traffic signals can be optimized to support traffic planning decisions and enhance traffic safety and environmental protection.