In this thesis we investigate the dynamics of pedestrian crowds in a fundamental and applied perspective. Envisioning a quantitative understanding we employ ad hoc large-scale experimental measurements as well as analytic and numerical models. Moreover, we analyze current regulations in matter of pedestrians structural actions (structural loads), in view of the need of guaranteeing pedestrian safety in serviceable built environments. This work comes in three complementary parts, in which we adopt distinct perspectives and conceptually different tools, respectively from statistical physics, mathematical modeling and structural engineering. Chapter 1 introduces these perspectives and gives an outline of the thesis. The statistical dynamics of individual pedestrians is the subject of Part I. Although individual trajectories may appear random, once we analyze them in large ensembles we expect ``preferred'' behaviors to emerge. Thus, we envisage individual paths as fluctuations around such established routes. To investigate this aspect, we perform year-long 24/7 measurements of pedestrian trajectories in real-life conditions, which we analyze statistically and via Langevin-like models. Two measurement locations have been considered: a corridor-shaped landing in the Metaforum building at Eindhoven University of Technology and the main walkway within Eindhoven Train Station. The measurement technique we employ, based on overhead Microsoft \Kinect\ 3D-range sensors and on ad hoc tracking algorithms, is introduced in Chapter 2. In Chapter 3 we describe the low density pedestrian flows in the Metaforum landing. In this location hundreds of thousands of high-resolution trajectories have been collected. First, we discuss standard crowd-traffic descriptions based on average quantities such as fundamental diagrams. Then, thanks to our large dataset, we address the dynamics beyond average values via probability distributions of pedestrian positions and velocities. Chapter 4 focuses on the dynamics of pedestrians crossing the landing alone, i.e. undisturbed by peers. The simple crossing dynamics is affected by stochastic fluctuations due to the variability of individuals' behavior as well as external factors. In the chapter we propose a quantitative Langevin-like model for these stochastic fluctuations, that we compare with the experimental data in terms of stationary velocity distributions and time correlation functions. The avoidance regime which takes place when two pedestrians walk simultaneously in the landing and in opposite directions is addressed in Chapter 5. In this regime, the statistical features of pedestrian motion change from the undisturbed case (Chapter 4). Here, we study the avoidance dynamics as a linear superposition of the undisturbed motion and an interaction force. First, we estimate average interaction force fields from the data. Then, we extend the Langevin model of Chapter 4 to reproduce statistics of the pair-wise interactions. Finally, in Chapter 6, we discuss in brief the measurements collected at Eindhoven Train Station in view of future dense crowd analyses. In Part II we zoom out from the perspective of individual pedestrians and we look at crowds, adopting a genuine mathematical modeling point of view. In this context a microscopic, i.e. particle-like, or a macroscopic, i.e. fluid-like, observation scale can be employed. In Chapter 7, we establish a general background of crowd dynamics modeling, which includes an introduction of the modeling framework by Cristiani, Piccoli and Tosin (CPT framework, in use in Chapters 8,9,11 and 12. This framework is suitable to model systems governed by social interactions and stands on a first order measure-valued evolution equation. The use of measures is crucial in the following, as it enables a unified treatment of crowd flows at the microscopic and macroscopic scales. Chapter 8 comprises a comparison of microscopic and macroscopic dynamics given via the CPT framework. In a Wasserstein space context, we wonder when these two dynamics are consistent as the number of agents involved grows. In this comparison we consider agents whose mass (in a measure sense) is independent on the size of the crowd. In Chapter 9 we focus on the modeling of crowds moving across elongated geometries resembling footbridges. We address pedestrians' motion in a macroscopic perspective via the CPT framework. According to the framework, dynamics are prescribed as a linear superposition of two components: a desired velocity (that encodes the motion of pedestrians walking alone) and a social velocity (that weights the crowd mass via an interaction kernel to assess individual reactions to mutual presence). Footbridge-like geometries are simple scenarios in which, from phenomenological considerations, we are able to give these components a reasonable form and thus perform simulations. In Part III we consider crowd flows on footbridges in relation to the way the safety of pedestrians is ensured by the current building practice and in terms of crowd-structure dynamics interaction. Chapter 10 addresses crowd-footbridge systems in terms of featured uncertainties. We provide a categorized review of the literature giving a synthetic comparison of uncertainties involved. In general, beside the uncertainties affecting the mechanical properties of the structure, the status of the crowd is itself uncertain. Taking inspiration from wind engineering, we approach the crowd dynamics through a separation of the approaching and the crossing traffic. Within the review, we consider how building regulations address the crowd load. On one hand, no uncertainty, nor variability, is considered on the crowd state, therefore the roughest possible model (constant load) is typically retained. On the other hand, we notice how a large dissent is present in the prescribed load values, suggesting a possible inadequacy in regulations. Chapter 11 rises from the point made in Chapter 10. We propose a framework to deal with uncertainties related to the crowd traffic on footbridges. The framework addresses the pedestrian density, a major player in the determination of live loads. Following the previous categorization, the framework is a composition of different modeling blocks and it considers approaching and crossing traffic at different scales, respectively macroscopic and microscopic. The output is a probabilistic description of the spatial density of the crossing crowd. In Chapter 12 we consider the dynamics of the human-structure system as a whole, targeting the vertical vibrations of slender footbridges excited by crowds of walking pedestrians. We combine the microscopic counterpart of the CPT modeling framework for the pedestrian dynamics with a simple single degree of freedom structural model to provide a modeling framework for the crowd-structure interaction. We realize the coupling modeling the dynamical forces exchanged by the structure and each pedestrian via per-pedestrian single degree of freedom vertical oscillators. We study how the active presence of pedestrians influences the structure dynamics in terms of vertical accelerations and varied effective damping. A discussion chapter addressing independently the content of the parts and then commenting on them as a whole closes the thesis.

Multiscale Crowd Dynamics: Physical Analysis, Modeling and Applications / Corbetta, Alessandro. - (2016).

### Multiscale Crowd Dynamics: Physical Analysis, Modeling and Applications

#####
*CORBETTA, ALESSANDRO*

##### 2016

#### Abstract

In this thesis we investigate the dynamics of pedestrian crowds in a fundamental and applied perspective. Envisioning a quantitative understanding we employ ad hoc large-scale experimental measurements as well as analytic and numerical models. Moreover, we analyze current regulations in matter of pedestrians structural actions (structural loads), in view of the need of guaranteeing pedestrian safety in serviceable built environments. This work comes in three complementary parts, in which we adopt distinct perspectives and conceptually different tools, respectively from statistical physics, mathematical modeling and structural engineering. Chapter 1 introduces these perspectives and gives an outline of the thesis. The statistical dynamics of individual pedestrians is the subject of Part I. Although individual trajectories may appear random, once we analyze them in large ensembles we expect ``preferred'' behaviors to emerge. Thus, we envisage individual paths as fluctuations around such established routes. To investigate this aspect, we perform year-long 24/7 measurements of pedestrian trajectories in real-life conditions, which we analyze statistically and via Langevin-like models. Two measurement locations have been considered: a corridor-shaped landing in the Metaforum building at Eindhoven University of Technology and the main walkway within Eindhoven Train Station. The measurement technique we employ, based on overhead Microsoft \Kinect\ 3D-range sensors and on ad hoc tracking algorithms, is introduced in Chapter 2. In Chapter 3 we describe the low density pedestrian flows in the Metaforum landing. In this location hundreds of thousands of high-resolution trajectories have been collected. First, we discuss standard crowd-traffic descriptions based on average quantities such as fundamental diagrams. Then, thanks to our large dataset, we address the dynamics beyond average values via probability distributions of pedestrian positions and velocities. Chapter 4 focuses on the dynamics of pedestrians crossing the landing alone, i.e. undisturbed by peers. The simple crossing dynamics is affected by stochastic fluctuations due to the variability of individuals' behavior as well as external factors. In the chapter we propose a quantitative Langevin-like model for these stochastic fluctuations, that we compare with the experimental data in terms of stationary velocity distributions and time correlation functions. The avoidance regime which takes place when two pedestrians walk simultaneously in the landing and in opposite directions is addressed in Chapter 5. In this regime, the statistical features of pedestrian motion change from the undisturbed case (Chapter 4). Here, we study the avoidance dynamics as a linear superposition of the undisturbed motion and an interaction force. First, we estimate average interaction force fields from the data. Then, we extend the Langevin model of Chapter 4 to reproduce statistics of the pair-wise interactions. Finally, in Chapter 6, we discuss in brief the measurements collected at Eindhoven Train Station in view of future dense crowd analyses. In Part II we zoom out from the perspective of individual pedestrians and we look at crowds, adopting a genuine mathematical modeling point of view. In this context a microscopic, i.e. particle-like, or a macroscopic, i.e. fluid-like, observation scale can be employed. In Chapter 7, we establish a general background of crowd dynamics modeling, which includes an introduction of the modeling framework by Cristiani, Piccoli and Tosin (CPT framework, in use in Chapters 8,9,11 and 12. This framework is suitable to model systems governed by social interactions and stands on a first order measure-valued evolution equation. The use of measures is crucial in the following, as it enables a unified treatment of crowd flows at the microscopic and macroscopic scales. Chapter 8 comprises a comparison of microscopic and macroscopic dynamics given via the CPT framework. In a Wasserstein space context, we wonder when these two dynamics are consistent as the number of agents involved grows. In this comparison we consider agents whose mass (in a measure sense) is independent on the size of the crowd. In Chapter 9 we focus on the modeling of crowds moving across elongated geometries resembling footbridges. We address pedestrians' motion in a macroscopic perspective via the CPT framework. According to the framework, dynamics are prescribed as a linear superposition of two components: a desired velocity (that encodes the motion of pedestrians walking alone) and a social velocity (that weights the crowd mass via an interaction kernel to assess individual reactions to mutual presence). Footbridge-like geometries are simple scenarios in which, from phenomenological considerations, we are able to give these components a reasonable form and thus perform simulations. In Part III we consider crowd flows on footbridges in relation to the way the safety of pedestrians is ensured by the current building practice and in terms of crowd-structure dynamics interaction. Chapter 10 addresses crowd-footbridge systems in terms of featured uncertainties. We provide a categorized review of the literature giving a synthetic comparison of uncertainties involved. In general, beside the uncertainties affecting the mechanical properties of the structure, the status of the crowd is itself uncertain. Taking inspiration from wind engineering, we approach the crowd dynamics through a separation of the approaching and the crossing traffic. Within the review, we consider how building regulations address the crowd load. On one hand, no uncertainty, nor variability, is considered on the crowd state, therefore the roughest possible model (constant load) is typically retained. On the other hand, we notice how a large dissent is present in the prescribed load values, suggesting a possible inadequacy in regulations. Chapter 11 rises from the point made in Chapter 10. We propose a framework to deal with uncertainties related to the crowd traffic on footbridges. The framework addresses the pedestrian density, a major player in the determination of live loads. Following the previous categorization, the framework is a composition of different modeling blocks and it considers approaching and crossing traffic at different scales, respectively macroscopic and microscopic. The output is a probabilistic description of the spatial density of the crossing crowd. In Chapter 12 we consider the dynamics of the human-structure system as a whole, targeting the vertical vibrations of slender footbridges excited by crowds of walking pedestrians. We combine the microscopic counterpart of the CPT modeling framework for the pedestrian dynamics with a simple single degree of freedom structural model to provide a modeling framework for the crowd-structure interaction. We realize the coupling modeling the dynamical forces exchanged by the structure and each pedestrian via per-pedestrian single degree of freedom vertical oscillators. We study how the active presence of pedestrians influences the structure dynamics in terms of vertical accelerations and varied effective damping. A discussion chapter addressing independently the content of the parts and then commenting on them as a whole closes the thesis.##### Pubblicazioni consigliate

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`https://hdl.handle.net/11583/2659720`

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