Optimized locating of sensors for approximating the macroscopic fundamental diagram: A PCA-based approach

The macroscopic fundamental diagram (MFD) describes the traffic state of a relatively large urban network by relating aggregated traffic variables. More research effort needs to be carried out to determine the set of links whose traffic data optimize the MFD estimation. This research approaches the MFD estimation problem as a network sensor location problem (NSLP). The link flow and density data acquired from loop detectors are first reduced into a smaller set of data with fewer dimensions using principal component analysis (PCA), an unsupervised machine learning tool for feature reduction. Based on PCA results, criticality coefficient (CC) is introduced as a novel measure to quantify the total variation in traffic variables that each link captures. Thereafter, a combined criticality coefficient (CCC) is calculated as a weighted average of criticality of flow and density and is used as a measure for selecting the links to be equipped with traffic sensors. Finally, using spectral clustering technique, the network is divided into several homogeneously congested clusters for which regional MFDs are recalibrated. Performance of the proposed approach is evaluated using simulated traffic data from the City of Edmonton based on a DYNAMEQ simulation. The results indicate that the CC-based selection approach consistently outperforms the benchmark method by reducing the error between 35 and 45% when a reasonable number of sensors is selected. Likewise, the CCC-based approach produces promising results in reconstructing regional MFDs with low errors. Further, the post-clustering recalibration reduces the resulting errors by an additional 50–90%, depending on the cluster. Results also affirm that the MFDs constructed based on the flow data produce more accurate and stable results compared to those constructed based on the density data, but MFDs constructed based on both are the most accurate.