Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
File(s)
OA Location
Author(s)
Gomes, Susana N
Stuart, Andrew M
Wolfram, Marie-Therese
Type
Journal Article
Abstract
In this paper we develop a framework for parameter estimation in macroscopic
pedestrian models using individual trajectories---microscopic data. We consider a unidirectional flow
of pedestrians in a corridor and assume that the velocity decreases with the average density according
to the fundamental diagram. Our model is formed from a coupling between a density dependent
stochastic differential equation and a nonlinear partial differential equation for the density, and
is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the
fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian
methods to perform the identification. We analyze the performance of the developed methodologies in
various situations, such as for different in- and outflow conditions, for varying numbers of individual
trajectories, and for differing channel geometries.
pedestrian models using individual trajectories---microscopic data. We consider a unidirectional flow
of pedestrians in a corridor and assume that the velocity decreases with the average density according
to the fundamental diagram. Our model is formed from a coupling between a density dependent
stochastic differential equation and a nonlinear partial differential equation for the density, and
is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the
fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian
methods to perform the identification. We analyze the performance of the developed methodologies in
various situations, such as for different in- and outflow conditions, for varying numbers of individual
trajectories, and for differing channel geometries.
Date Issued
2019-08-06
Date Acceptance
2019-05-23
Citation
SIAM Journal on Applied Mathematics, 2019, 79 (4), pp.1475-1500
ISSN
0036-1399
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Start Page
1475
End Page
1500
Journal / Book Title
SIAM Journal on Applied Mathematics
Volume
79
Issue
4
Copyright Statement
© 2019, Society for Industrial and Applied Mathematics.
Identifier
https://epubs.siam.org/doi/10.1137/18M1215980
Subjects
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published
Date Publish Online
2019-08-06