Transportation systems need more accurate predictions to further optimize traffic network design with the development and application of autonomous driving technology. In this article, we focus on highway traffic flow systems that are often simulated by the modified Greenshields model. However, this model can not perfectly match the true traffic flow due to its underlying simplifications and assumptions, implying that it is inexact. Specifically, some parameters affect the simulation accuracy of the modified Greenshields model, while tuning these parameters to improve the model’s accuracy is called model calibration. The parameters obtained using the L2 calibration have the advantages of high accuracy and small variance for an inexact model. However, the method is calculation intensive, requiring optimization of the integral loss function. Since traffic flow data are often massive, this paper proposes a fast L2 calibration framework to calibrate the modified Greenshields model. Specifically, the suggested method selects a sub-design containing more information on the calibration parameters, and then the empirical loss function obtained from the optimal sub-design is utilized to approximate the integral loss function. A case study highlights that the proposed method preserves the advantages of L2 calibration and significantly reduces the running time.
The problem with computer model calibration by tuning the parameters associated with computer models is significant in many engineering and scientific applications. Although several methods have been established to estimate the calibration parameters, research focusing on the design of calibration parameters remains limited. Therefore, this paper proposes a sequential computer experiment design based on the D-optimal criterion, which can efficiently tune the calibration parameters while improving the prediction ability of the calibrated computer model. Numerical comparisons of the simulated and real data demonstrate the efficiency of the proposed technique.
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