An efficient variational Bayesian algorithm for calibrating fundamental diagrams and its probabilistic sensitivity analysis

Fundamental diagrams (FDs) are the basis of traffic flow theory. Efficient model calibration from noisy traffic data is essential to identify the parameters of FDs to describe the traffic flow characteristics. Conventional least-squares based methods fit the aggregated traffic data to certain prescribed functions to obtain the FDs without considering the traffic dynamics or data scattering. To deal with this problem, this paper proposes a probabilistic sensitivity analysis guided variational Bayesian (PSA-VB) framework with high efficiency. Firstly, we formulate the calibration problem as a rare event optimization problem. Then, we develop a mean-field variational Bayesian algorithm to infer the unknown parameters by random sampling. To reduce the computational cost, a probabilistic sensitivity analysis (PSA) procedure is introduced for identifying important parameters, and an efficient two-stage PSA-VB calibration algorithm is proposed. We apply the proposed algorithms to calibrate the modified cell transmission model (MCTM) using the traffic data collected from the M25 highway in England. Compared with the cross entropy method (CEM), the least squares (LS) method and the weighted least squares (WLS) method, the proposed PSA-VB method possesses much lower computational cost and faster convergence speed. Moreover, by explicitly considering the traffic dynamics, the PSA-VB method can capture traffic flow characteristics such as the capacity drop.