A cross-entropy method and probabilistic sensitivity analysis framework for calibrating microscopic traffic models

Abstract

ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.A cross-entropy method and probabilistic sensitivity analysis framework for calibrating microscopic traffic models AbstractCar following modeling framework seeks for a more realistic representation of car following behavior in complex driving situations to improve traffic safety and to better understand several puzzling traffic flow phenomena, such as stop-and-go oscillations. Calibration and validation techniques pave the way towards the descriptive power of car-following models and their applicability for analyzing traffic flow. However, calibrating these models is never a trivial task. This is caused by the fact that some parameters, such as reaction time, are generally not directly observable from traffic data. On the other hand, traffic data might be subject to various errors and noises. This contribution puts forward a Cross-Entropy Method (CEM) based approach to identify parameters of deterministic car-following models under noisy data by formulating it as a stochastic optimization problem. This approach allows for statistical analysis of the parameter estimations. Another challenge arising in the calibration of car following models concerns the selection of the most important parameters. This paper introduces a relative entropy based Probabilistic Sensitivity Analysis (PSA) algorithm to identify the important parameters so as to reduce the complexity, data requirement and computational effort of the calibration process. Since the CEM and the PSA are based on the Kullback-Leibler (K-L) distance, they can be simultaneously integrated into a unified framework to further reduce the computational burden. The proposed framework is applied to calibrate the intelligent driving model using vehicle trajectories data from the NGSIM project. Results confirm the great potential of this approach.

A user equilibrium-based fast-charging location model considering heterogeneous vehicles in urban networks

“…The cross-entropy method (CEM) originated from an adaptive variance minimization algorithm for estimating the probabilities of rare events on stochastic networks and could be adapted to solve static and noisy combinatorial optimization problems. For further details about CEM and its specific applications in a range of transportation problems, we refer to Maher (2011, 2012); Maher, Liu, and Ngoduy (2013); Abudayyeh, Ngoduy, and Nicholson (2018); Zhong et al (2016).…”

Strengthening the Case for a Bayesian Approach to Car-following Model Calibration and Validation using Probabilistic Programming

“…In [7], the influence of sampling from parameter distributions when generating simulation traces rather than fixing parameter values is additionally evaluated. [8] modeled the Intelligent Driver Model using Gaussian random variables as the parameters to perform a probabilistic sensitivity analysis based on the Kullback-Liebler dissimilarity measure in order to limit the number of parameters requiring value estimation to those yielding the greatest performance improvement relative to default parameter values. [3] advocated for the use of a Bayesian approach to calibration by directly comparing an MCMC-based calibration method with a deterministic optimization method, using one synthetic data set to show that the Bayesian method could recover known parameter values and one real-world data set as a case study.…”

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

“…The use of entropy instead of variance is usually justified by the need to analyze the output random variable with heavy-tail or outliers [13]. SA based on entropy was used to study, for example, traffic flow [13], limit states of load-bearing structures [14,15], the seismic demand of concrete structures [16], and groundwater level [17].…”