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Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method
1. | CASA- Centre for Analysis, Scientific computing and Applications, Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands, Netherlands |
2. | CASA- Centre for Analysis, Scientific computing and Applications, ICMS - Institute for Complex Molecular Systems, Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands |
References:
[1] |
H. T. Banks and W. C. Thompson, Least Squares Estimation of Probability Measures in the Prohorov Metric Framework, Center for Research in Scientific Computation Tech Rep, CRSC-TR12-21, North Carolina State University, Raleigh, NC. |
[2] |
N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Mathematical Models and Methods in Applied Sciences, 22 (2012), 1230004, 29 pp.
doi: 10.1142/S0218202512300049. |
[3] |
M. Boltes and A. Seyfried, Collecting pedestrian trajectories, Neurocomputing, 100 (2013), 127-133.
doi: 10.1016/j.neucom.2012.01.036. |
[4] |
L. Bruno and A. Corbetta, Multiscale probabilistic evaluation of the footbridge crowding. Part 2: Crossing pedestrian position, in Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (eds. A. Cunha, E. Caetano, P. Ribeiro and G. Müller), 2014, 937-944. |
[5] |
A. Corbetta, L. Bruno, A. Muntean and F. Toschi, High statistics measurements of pedestrian dynamics, Transportation Research Procedia, 2 (2014), 96-104; The Conference on Pedestrian and Evacuation Dynamics 2014 (PED 2014), Delft, The Netherlands, October 2014, 22-24.
doi: 10.1016/j.trpro.2014.09.013. |
[6] |
A. Corbetta, A. Muntean, F. Toschi and K. Vafayi, Structural identification of interaction terms in a Langevin-like model for crowd dynamics, in preparation, 2014. |
[7] |
R. T. Cox, Probability, frequency and reasonable expectation, American Journal of Physics, 14 (1946), 1-13.
doi: 10.1119/1.1990764. |
[8] |
R. Cox, Algebra of Probable Inference, Algebra of Probable Inference, Johns Hopkins University Press, 1961. |
[9] |
C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren der mathematischen Wissenschaften, Springer, Berlin, New York, 2000.
doi: 10.1007/3-540-29089-3_14. |
[10] |
C. De Boor, A Practical Guide to Splines, Vol. 27, Springer-Verlag, New York, 1978. |
[11] |
P. Degond, C. Appert-Rolland, M. Moussaid, J. Pettre and G. Theraulaz, A hierarchy of heuristic-based models of crowd dynamics, Journal of Statistical Physics, 152 (2013), 1033-1068.
doi: 10.1007/s10955-013-0805-x. |
[12] |
R. O. Duda, P. E. Hart and D. G. Stork, Pattern Classification, John Wiley & Sons, 2012. |
[13] |
D. C. Duives, W. Daamen and S. P. Hoogendoorn, State-of-the-art crowd motion simulation models, Transportation Research Part C: Emerging Technologies, 37 (2013), 193-209.
doi: 10.1016/j.trc.2013.02.005. |
[14] |
J. Evers, S. C. Hille and A. Muntean, Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions, Comptes Rendus Mathematique, 352 (2014), 51-54.
doi: 10.1016/j.crma.2013.11.012. |
[15] |
D. Helbing and A. Johansson, On the controversy around Daganzo's requiem for an Aw-Rascle's resurrection of second-order traffic flow models, Modelling and Optimisation of Flows on Networks, Lecture Notes in Mathematics, 2062 (2013), 271-302.
doi: 10.1007/978-3-642-32160-3_4. |
[16] |
D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical Review E, 51 (1995), pp. 4282.
doi: 10.1103/PhysRevE.51.4282. |
[17] |
S. Hoogendoorn and R. Hoogendoorn, Calibration of microscopic traffic-flow models using multiple data sources, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368 (2010), 4497-4517.
doi: 10.1098/rsta.2010.0189. |
[18] |
N. Jaklin, A. Cook and R. Geraerts, Real-time path planning in heterogeneous environments, Computer Animation and Virtual Worlds, 24 (2013), 285-295.
doi: 10.1002/cav.1511. |
[19] |
E. T. Jaynes, Prior probabilities, Systems Science and Cybernetics, IEEE Transactions on, 4 (1968), 227-241.
doi: 10.1109/TSSC.1968.300117. |
[20] |
E. T. Jaynes, The well-posed problem, Foundations of Physics, 3 (1973), 477-492.
doi: 10.1007/BF00709116. |
[21] |
E. T. Jaynes, Probability Theory: the Logic of Science, Cambridge University Press, 2003.
doi: 10.1017/CBO9780511790423. |
[22] |
S. Kirkpatrick and M. Vecchi et al., Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[23] |
X. Liu, W. Song and J. Zhang, Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing, Physica A: Statistical Mechanics and its Applications, 388 (2009), 2717-2726.
doi: 10.1016/j.physa.2009.03.017. |
[24] |
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equation of state calculations by fast computing machines, Journal of Chemical Physics, 21 (1953), 1087-1092.
doi: 10.1063/1.1699114. |
[25] | |
[26] |
M. Moussaid, D. Helbing and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters, Proceedings of the National Academy of Sciences, 108 (2011), 6884-6888.
doi: 10.1073/pnas.1016507108. |
[27] |
P. Romanczuk, M. Bär, W. Ebeling, B. Lindner and L. Schimansky-Geier, Active Brownian particles, The European Physical Journal Special Topics, 202 (2012), 1-162.
doi: 10.1140/epjst/e2012-01529-y. |
[28] |
C. Rudloff, T. Matyus and S. Seer, Comparison of different calibration techniques on simulated data, in Pedestrian and Evacuation Dynamics 2012, Springer International Publishing, 2014, 657-672.
doi: 10.1007/978-3-319-02447-9_55. |
[29] |
A. Schadschneider, D. Chowdhury and K. Nishinari, Stochastic Transport in Complex Systems: From Molecules to Vehicles, Elsevier, 2010. |
[30] |
S. Seer, N. Brändle and C. Ratti, Kinects and human kinetics: A new approach for studying pedestrian behavior, Transportation Research Part C: Emerging Technologies, 48 (2014), 212-228.
doi: 10.1016/j.trc.2014.08.012. |
[31] |
D. S. Sivia, Data Analysis: A Bayesian Tutorial, Oxford University Press, 1996. |
[32] |
J. Skilling, Probabilistic data analysis: An introductory guide, Journal of Microscopy, 190 (1998), 28-36.
doi: 10.1046/j.1365-2818.1998.2780835.x. |
[33] |
The OpenPTV Consortium, OpenPTV: Open source particle tracking velocimetry, 2012. |
[34] |
A. U. K. Wagoum, A. Seyfried and S. Holl, Modeling the dynamic route choice of pedestrians to assess the criticality of building evacuation, Advances in Complex Systems, 15 (2012), 1250029, 22 pp.
doi: 10.1142/S0219525912500294. |
[35] |
J. Willneff, A Spatio-Temporal Matching Algorithm for 3D Particle Tracking Velocimetry, Mitteilungen-Institut für Geodäsie und Photogrammetrie an der Eidgenossischen Technischen Hochschule Zürich, 2003. |
show all references
References:
[1] |
H. T. Banks and W. C. Thompson, Least Squares Estimation of Probability Measures in the Prohorov Metric Framework, Center for Research in Scientific Computation Tech Rep, CRSC-TR12-21, North Carolina State University, Raleigh, NC. |
[2] |
N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Mathematical Models and Methods in Applied Sciences, 22 (2012), 1230004, 29 pp.
doi: 10.1142/S0218202512300049. |
[3] |
M. Boltes and A. Seyfried, Collecting pedestrian trajectories, Neurocomputing, 100 (2013), 127-133.
doi: 10.1016/j.neucom.2012.01.036. |
[4] |
L. Bruno and A. Corbetta, Multiscale probabilistic evaluation of the footbridge crowding. Part 2: Crossing pedestrian position, in Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (eds. A. Cunha, E. Caetano, P. Ribeiro and G. Müller), 2014, 937-944. |
[5] |
A. Corbetta, L. Bruno, A. Muntean and F. Toschi, High statistics measurements of pedestrian dynamics, Transportation Research Procedia, 2 (2014), 96-104; The Conference on Pedestrian and Evacuation Dynamics 2014 (PED 2014), Delft, The Netherlands, October 2014, 22-24.
doi: 10.1016/j.trpro.2014.09.013. |
[6] |
A. Corbetta, A. Muntean, F. Toschi and K. Vafayi, Structural identification of interaction terms in a Langevin-like model for crowd dynamics, in preparation, 2014. |
[7] |
R. T. Cox, Probability, frequency and reasonable expectation, American Journal of Physics, 14 (1946), 1-13.
doi: 10.1119/1.1990764. |
[8] |
R. Cox, Algebra of Probable Inference, Algebra of Probable Inference, Johns Hopkins University Press, 1961. |
[9] |
C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren der mathematischen Wissenschaften, Springer, Berlin, New York, 2000.
doi: 10.1007/3-540-29089-3_14. |
[10] |
C. De Boor, A Practical Guide to Splines, Vol. 27, Springer-Verlag, New York, 1978. |
[11] |
P. Degond, C. Appert-Rolland, M. Moussaid, J. Pettre and G. Theraulaz, A hierarchy of heuristic-based models of crowd dynamics, Journal of Statistical Physics, 152 (2013), 1033-1068.
doi: 10.1007/s10955-013-0805-x. |
[12] |
R. O. Duda, P. E. Hart and D. G. Stork, Pattern Classification, John Wiley & Sons, 2012. |
[13] |
D. C. Duives, W. Daamen and S. P. Hoogendoorn, State-of-the-art crowd motion simulation models, Transportation Research Part C: Emerging Technologies, 37 (2013), 193-209.
doi: 10.1016/j.trc.2013.02.005. |
[14] |
J. Evers, S. C. Hille and A. Muntean, Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions, Comptes Rendus Mathematique, 352 (2014), 51-54.
doi: 10.1016/j.crma.2013.11.012. |
[15] |
D. Helbing and A. Johansson, On the controversy around Daganzo's requiem for an Aw-Rascle's resurrection of second-order traffic flow models, Modelling and Optimisation of Flows on Networks, Lecture Notes in Mathematics, 2062 (2013), 271-302.
doi: 10.1007/978-3-642-32160-3_4. |
[16] |
D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical Review E, 51 (1995), pp. 4282.
doi: 10.1103/PhysRevE.51.4282. |
[17] |
S. Hoogendoorn and R. Hoogendoorn, Calibration of microscopic traffic-flow models using multiple data sources, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368 (2010), 4497-4517.
doi: 10.1098/rsta.2010.0189. |
[18] |
N. Jaklin, A. Cook and R. Geraerts, Real-time path planning in heterogeneous environments, Computer Animation and Virtual Worlds, 24 (2013), 285-295.
doi: 10.1002/cav.1511. |
[19] |
E. T. Jaynes, Prior probabilities, Systems Science and Cybernetics, IEEE Transactions on, 4 (1968), 227-241.
doi: 10.1109/TSSC.1968.300117. |
[20] |
E. T. Jaynes, The well-posed problem, Foundations of Physics, 3 (1973), 477-492.
doi: 10.1007/BF00709116. |
[21] |
E. T. Jaynes, Probability Theory: the Logic of Science, Cambridge University Press, 2003.
doi: 10.1017/CBO9780511790423. |
[22] |
S. Kirkpatrick and M. Vecchi et al., Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[23] |
X. Liu, W. Song and J. Zhang, Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing, Physica A: Statistical Mechanics and its Applications, 388 (2009), 2717-2726.
doi: 10.1016/j.physa.2009.03.017. |
[24] |
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equation of state calculations by fast computing machines, Journal of Chemical Physics, 21 (1953), 1087-1092.
doi: 10.1063/1.1699114. |
[25] | |
[26] |
M. Moussaid, D. Helbing and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters, Proceedings of the National Academy of Sciences, 108 (2011), 6884-6888.
doi: 10.1073/pnas.1016507108. |
[27] |
P. Romanczuk, M. Bär, W. Ebeling, B. Lindner and L. Schimansky-Geier, Active Brownian particles, The European Physical Journal Special Topics, 202 (2012), 1-162.
doi: 10.1140/epjst/e2012-01529-y. |
[28] |
C. Rudloff, T. Matyus and S. Seer, Comparison of different calibration techniques on simulated data, in Pedestrian and Evacuation Dynamics 2012, Springer International Publishing, 2014, 657-672.
doi: 10.1007/978-3-319-02447-9_55. |
[29] |
A. Schadschneider, D. Chowdhury and K. Nishinari, Stochastic Transport in Complex Systems: From Molecules to Vehicles, Elsevier, 2010. |
[30] |
S. Seer, N. Brändle and C. Ratti, Kinects and human kinetics: A new approach for studying pedestrian behavior, Transportation Research Part C: Emerging Technologies, 48 (2014), 212-228.
doi: 10.1016/j.trc.2014.08.012. |
[31] |
D. S. Sivia, Data Analysis: A Bayesian Tutorial, Oxford University Press, 1996. |
[32] |
J. Skilling, Probabilistic data analysis: An introductory guide, Journal of Microscopy, 190 (1998), 28-36.
doi: 10.1046/j.1365-2818.1998.2780835.x. |
[33] |
The OpenPTV Consortium, OpenPTV: Open source particle tracking velocimetry, 2012. |
[34] |
A. U. K. Wagoum, A. Seyfried and S. Holl, Modeling the dynamic route choice of pedestrians to assess the criticality of building evacuation, Advances in Complex Systems, 15 (2012), 1250029, 22 pp.
doi: 10.1142/S0219525912500294. |
[35] |
J. Willneff, A Spatio-Temporal Matching Algorithm for 3D Particle Tracking Velocimetry, Mitteilungen-Institut für Geodäsie und Photogrammetrie an der Eidgenossischen Technischen Hochschule Zürich, 2003. |
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