Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge

TL;DR

This paper reduces a high-dimensional model of pedestrian-bridge oscillations to a low-dimensional system using Ott and Antonsen's method, providing insights into the global dynamics of pedestrian-induced bridge oscillations.

Contribution

It applies a low-dimensional reduction technique to a complex pedestrian-bridge interaction model, enabling easier analysis of the system's global behavior.

Findings

Successful reduction of the high-dimensional model to a low-dimensional system

Demonstration of low-dimensional macroscopic behavior in coupled oscillators

Enhanced understanding of pedestrian-bridge synchronization phenomena

Abstract

When it opened to pedestrian traffic in the year 2000, London's Millennium Bridge exhibited an unwanted, large, side-to-side oscillation which was apparently due to a resonance between the stepping frequency of walkers and one of the bridge modes. Models for this event, and similar events on other bridges, have been proposed. The model most directly addressing the synchronization mechanism of individual walkers and the resulting global response of the bridge-pedestrian system is one developed by Eckhardt et al. This model treats individual walkers with a phase oscillator description and is inherently high dimensional with system dimensionality (N+2), where N is the number of walkers. In the present work we use a method proposed by Ott and Antonsen to reduce the model of Eckhardt et al. to a low dimensional dynamical system, and we employ this reduced description to study the global dynamics of the bridge/pedestrian interaction. More generally, this treatment serves as an interesting example of the possibility of low dimensional macroscopic behavior in large systems of coupled oscillators.