Dynamic demand estimation on large scale networks using Principal Component Analysis: The case of non-existent or irrelevant historical estimates

Calibrating DTA models is complex due to the involved indeterminacy, non-linearity, and dimensionality, restricting the application of conventional calibration approaches, especially for larger networks. For this, Principal Component Analysis (PCA) is slowly establishing itself as the new state of the art because it can greatly tackle two well known challenges—i.e. problem dimensionality and non-linearity. PCA application limits the optimization search space in a lower dimension space, defined by orthogonal Principal Components, evaluated upon a set of historical estimates. In this paper, we solve practical implementation problems for PCA-based calibration techniques. Specifically, we formulate a data-assimilation framework to propose multiple OD historical data-set generation methods which allows the use of PC-based algorithms in case the historical data is irrelevant or unavailable, often the case for large-scale DTA models. Furthermore, we propose a simplified problem formulation that leverages properties of the novel data-set generation framework and helps for faster and more efficient calibration. The methodology is implemented using the PC-SPSA algorithm, which combines PCA with the popular Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, commonly used to calibrate smaller networks. The approach is tested on a large-scale case study of the Munich metropolitan urban network, with encouraging calibration results. The proposed data-assimilation framework can account for spatial, temporal, and day-to-day variations in the demand. Different methods and combinations are tested and compared. The results suggest that all these correlations should be used in order to avoid over-fitting issues. Furthermore, the implementation properties of PCA and PC-SPSA are also explored using different sensitivity analyses to assess the toll and benefits of using PCA i.e., ease in SPSA hyper-parameter, role of historical data-set generation parameters and the algorithm's performance against different target demand fluctuations. The analysis shows encouraging results for PC-SPSA robustness and helps establishing simplified guidelines for implementing such PCA-methods practically on large-scale DTA models.