Sensitivity Analysis for Microscopic Crowd Simulation

Microscopic crowd simulation can help to enhance the safety of pedestrians in situations that range from museum visits to music festivals. To obtain a useful prediction, the input parameters must be chosen carefully. In many cases, a lack of knowledge or limited measurement accuracy add uncertainty to the input. In addition, for meaningful parameter studies, we first need to identify the most influential parameters of our parametric computer models. The field of uncertainty quantification offers standardized and fully automatized methods that we believe to be beneficial for pedestrian dynamics. In addition, many methods come at a comparatively low cost, even for computationally expensive problems. This allows for their application to larger scenarios. We aim to identify and adapt fitting methods to microscopic crowd simulation in order to explore their potential in pedestrian dynamics. In this work, we first perform a variance-based sensitivity analysis using Sobol’ indices and then crosscheck the results by a derivative-based measure, the activity scores. We apply both methods to a typical scenario in crowd simulation, a bottleneck. Because constrictions can lead to high crowd densities and delays in evacuations, several experiments and simulation studies have been conducted for this setting. We show qualitative agreement between the results of both methods. Additionally, we identify a one-dimensional subspace in the input parameter space and discuss its impact on the simulation. Moreover, we analyze and interpret the sensitivity indices with respect to the bottleneck scenario.

[1]  A. Seyfried,et al.  Methods for measuring pedestrian density, flow, speed and direction with minimal scatter , 2009, 0911.2165.

[2]  B. Iooss,et al.  A Review on Global Sensitivity Analysis Methods , 2014, 1404.2405.

[3]  Catherine Beaulieu,et al.  Intercultural Study of Personal Space: A Case Study , 2004 .

[4]  Jia Yu,et al.  Pre-evacuation Time Estimation Based Emergency Evacuation Simulation in Urban Residential Communities , 2019, International journal of environmental research and public health.

[5]  William Becker,et al.  Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices , 2017, Environ. Model. Softw..

[6]  Ziyou Gao,et al.  Simulating the Dynamic Escape Process in Large Public Places , 2014, Oper. Res..

[7]  Isabella von Sivers,et al.  How Stride Adaptation in Pedestrian Models Improves Navigation , 2014, ArXiv.

[8]  Bernhard Steffen,et al.  New Insights into Pedestrian Flow Through Bottlenecks , 2009, Transp. Sci..

[9]  Emanuele Borgonovo,et al.  A new uncertainty importance measure , 2007, Reliab. Eng. Syst. Saf..

[10]  Stefano Tarantola,et al.  Uncertainty in Industrial Practice , 2008 .

[11]  Andreas Schadschneider,et al.  Empirical results for pedestrian dynamics and their implications for modeling , 2011, Networks Heterog. Media.

[12]  J. Drury,et al.  Come together: two studies concerning the impact of group relations on personal space. , 2010, The British journal of social psychology.

[13]  Serge P. Hoogendoorn,et al.  Pedestrian route-choice and activity scheduling theory and models , 2004 .

[14]  Armin Seyfried,et al.  Collision-free nonuniform dynamics within continuous optimal velocity models. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Sergei S. Kucherenko,et al.  Derivative based global sensitivity measures and their link with global sensitivity indices , 2009, Math. Comput. Simul..

[16]  Armin Seyfried,et al.  Influence of Geometry Parameters on Pedestrian Flow through Bottleneck , 2011 .

[17]  Abbas Rajabifard,et al.  Simulating Indoor Evacuation of Pedestrians: The Sensitivity of Predictions to Directional-Choice Calibration Parameters , 2018 .

[18]  Constantinos C. Pantelides,et al.  Monte Carlo evaluation of derivative-based global sensitivity measures , 2009, Reliab. Eng. Syst. Saf..

[19]  P G Gipps,et al.  A micro simulation model for pedestrian flows , 1985 .

[20]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Gerta Köster,et al.  Natural discretization of pedestrian movement in continuous space. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Felix Dietrich,et al.  The effect of stepping on pedestrian trajectories , 2015 .

[23]  Qiqi Wang,et al.  Erratum: Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces , 2013, SIAM J. Sci. Comput..

[24]  Marcello Montanino,et al.  Do We Really Need to Calibrate All the Parameters? Variance-Based Sensitivity Analysis to Simplify Microscopic Traffic Flow Models , 2015, IEEE Transactions on Intelligent Transportation Systems.

[25]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[26]  Serge P. Hoogendoorn,et al.  Continuum modelling of pedestrian flows - Part 2: Sensitivity analysis featuring crowd movement phenomena , 2016 .

[27]  M. Jansen Analysis of variance designs for model output , 1999 .

[28]  M. Schreckenberg,et al.  Experimental study of pedestrian flow through a bottleneck , 2006, physics/0610077.

[29]  Constantinos Antoniou,et al.  Simulation-based evacuation planning using state-of-the-art sensitivity analysis techniques , 2018, Simul. Model. Pract. Theory.

[30]  Matieyendou Lamboni,et al.  Derivative-based global sensitivity measures: General links with Sobol' indices and numerical tests , 2012, Math. Comput. Simul..

[31]  Emanuele Borgonovo,et al.  Sensitivity analysis: A review of recent advances , 2016, Eur. J. Oper. Res..

[32]  Hans-Joachim Bungartz,et al.  Modelling social identification and helping in evacuation simulation , 2016, ArXiv.

[33]  Fernando Fernández,et al.  Emergent behaviors and scalability for multi-agent reinforcement learning-based pedestrian models , 2017, Simul. Model. Pract. Theory.

[34]  Armin Seyfried,et al.  Collective phenomena in crowds—Where pedestrian dynamics need social psychology , 2017, PloS one.

[35]  Armin Seyfried,et al.  Experimental Study on Pedestrian Flow through Wide Bottleneck , 2014 .

[36]  Paul G. Constantine,et al.  Global sensitivity metrics from active subspaces , 2015, Reliab. Eng. Syst. Saf..

[37]  A. Saltelli,et al.  On the Relative Importance of Input Factors in Mathematical Models , 2002 .

[38]  Felix Dietrich,et al.  Gradient navigation model for pedestrian dynamics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Majid Sarvi,et al.  Crowd behaviour and motion: Empirical methods , 2018 .

[40]  T. Ishigami,et al.  An importance quantification technique in uncertainty analysis for computer models , 1990, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis.

[41]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[42]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

[43]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[44]  Fernando Fernández,et al.  Strategies for simulating pedestrian navigation with multiple reinforcement learning agents , 2014, Autonomous Agents and Multi-Agent Systems.

[45]  Benedikt Zönnchen,et al.  Vadere: An open-source simulation framework to promote interdisciplinary understanding , 2019, Collective Dynamics.

[46]  Enrico Ronchi,et al.  A Method for the Analysis of Behavioural Uncertainty in Evacuation Modelling , 2014 .

[47]  B. Iooss,et al.  Derivative based global sensitivity measures , 2014, 1412.2619.