DMS-EPSRC: Predictive modelling for instability avoidance under human-structure interaction

Modern civil engineering structures are designed using industry-standard packages, backed by stringent design codes. Yet, there remain frequent, costly failures caused by the unexplained dynamic interaction of crowds, notably in the lateral instability of pedestrian bridges. This project aims to provide bridge engineers with practical tools for better predicting the nonlinear effects associated with human interactions and oscillating mechanical structures. It will develop new mathematical paradigms of model reduction and data-driven dynamical systems and translate these insights into practical, quantitative design principles to avoid harmful oscillations or catastrophic bridge failures. The project will also train students in cutting-edge mathematical modeling and promote synergistic interactions with international groups of applied mathematicians and engineers in the United States and the United Kingdom. This project will contribute to the development of a new mathematical theory in a largely unexplored area of collective dynamics involving highly nonlinear agents whose individual motions can be non-smooth, with hybrid discrete-time and continuous-time elements. The project is comprised of three main objectives: (i) to understand how heterogeneity and agent-to-agent interactions influence instability thresholds in multi-agent systems coupled to a global mode; (ii) to develop and implement data-driven reduced-order modeling techniques for dynamic processes using invariance principles, such as invariant foliations and invariant manifolds; and (iii) to demonstrate the efficacy of a broader mathematical theory of emergent instability in agent-based systems due to coupling to a global environmental variable, through the development of enhanced guidelines for safe behavior in pedestrian bridges and related structures. This award by the Applied Mathematics program in the Division of Mathematical Sciences is jointly supported by the Operations Engineering as well as the Engineering Design and Systems Engineering program in the Division of Civil, Mechanical and Manufacturing Innovation, as well as the Office of International Science and Engineering. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.