Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.

[1]  Dirk Helbing,et al.  Pedestrian, Crowd and Evacuation Dynamics , 2013, Encyclopedia of Complexity and Systems Science.

[2]  P. Degond,et al.  A Hierarchy of Heuristic-Based Models of Crowd Dynamics , 2013, 1304.1927.

[3]  J. Skilling,et al.  Probabilistic data analysis: an introductory guide , 1998 .

[4]  R. T. Cox The Algebra of Probable Inference , 1962 .

[5]  Doreen Eichel,et al.  Data Analysis A Bayesian Tutorial , 2016 .

[6]  E. Jaynes The well-posed problem , 1973 .

[7]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[8]  Sander C. Hille,et al.  Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions , 2013 .

[9]  D. Helbing,et al.  On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models , 2008, 0805.3402.

[10]  Jochen Willneff,et al.  A spatio-temporal matching algorithm for 3D particle tracking velocimetry , 2002 .

[11]  Carlo Ratti,et al.  Kinects and human kinetics: a new approach for studying pedestrian behavior , 2014 .

[12]  Serge P. Hoogendoorn,et al.  State-of-the-art crowd motion simulation models , 2013 .

[13]  Dirk Helbing,et al.  How simple rules determine pedestrian behavior and crowd disasters , 2011, Proceedings of the National Academy of Sciences.

[14]  Luca Bruno,et al.  Multiscale probabilistic evaluation of the footbridge crowding. Part 2: Crossing Pedestrian position , 2014 .

[15]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[16]  Shigeo Abe DrEng Pattern Classification , 2001, Springer London.

[17]  R. T. Cox Probability, frequency and reasonable expectation , 1990 .

[18]  R. T. Cox,et al.  The Algebra of Probable Inference , 1962 .

[19]  Edwin T. Jaynes Prior Probabilities , 2010, Encyclopedia of Machine Learning.

[20]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[21]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[22]  C. Dafermos Hyberbolic Conservation Laws in Continuum Physics , 2000 .

[23]  Debashish Chowdhury,et al.  Stochastic Transport in Complex Systems: From Molecules to Vehicles , 2010 .

[24]  Roland Geraerts,et al.  Real‐time path planning in heterogeneous environments , 2013, Comput. Animat. Virtual Worlds.

[25]  Stefan Seer,et al.  Comparison of Different Calibration Techniques on Simulated Data , 2014 .

[26]  Stefan Holl,et al.  Modeling the Dynamic Route Choice of Pedestrians to Assess the Criticality of Building Evacuation , 2011, Adv. Complex Syst..

[27]  Helbing,et al.  Social force model for pedestrian dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[29]  Nicola Bellomo,et al.  Modeling crowd dynamics from a complex system viewpoint , 2012 .

[30]  Jun Zhang,et al.  Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing , 2009 .

[31]  Carlo Ratti,et al.  Kinects and Human Kinetics: A New Approach for Studying Crowd Behavior , 2012, ArXiv.

[32]  Serge Hoogendoorn,et al.  Calibration of microscopic traffic-flow models using multiple data sources , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[33]  Luca Bruno,et al.  High statistics measurements of pedestrian dynamics , 2014, 1407.1254.

[34]  Harvey Thomas Banks,et al.  Least Squares Estimation of Probability Measures in the Prohorov Metric Framework , 2012 .

[35]  W. Ebeling,et al.  Active Brownian particles , 2012, The European Physical Journal Special Topics.

[36]  Dirk Helbing,et al.  Modelling and Optimisation of Flows on Networks , 2013 .

[37]  Armin Seyfried,et al.  Collecting pedestrian trajectories , 2013, Neurocomputing.

[38]  David G. Stork,et al.  Pattern Classification , 1973 .