Complex network perspectives on nonlinear dynamics

Integrating tools and methods from complex network analysis with the study of mechanical structures and their dynamics in order to better understand the underlying mechanisms is the aim of this interdisciplinary research project.

The dynamical behavior of large-multi-component structures such as wind turbines, manufacturing machines, robots, or vehicles, is often governed by phenomena which are difficult to grasp with conventional analysis tools. As these methods are mostly rooted in time and frequency domain and or based on analytical equations, they are inherently limited to only resolving specific characteristics of the dynamics. The multiplicity of components and degrees of freedom, friction, nonlinearities, emergent behavior, rare events and multi-scale dynamics pose a challenge to the linear and weakly nonlinear methods which govern the design process today. At the same time, these phenomena need to be better understood in order to improve upon current designs and to avoid catastrophic events.

To approach the current challenges in mechanical systems analysis, this projects aims at integrating solutions from complex network analysis.  The growing field of complex network analysis already provides useful tools in many disciplines, for example medicine, earth sciences and fluid dynamics. A functional network perspective onto the dynamics of multi-component structures will provide a more intuitive approach to the system at hand. By representing a structure as a network of individual components, this novel perspective provides innovative methods of studying the dynamic interplay between the agents and sub-structures, fostering deeper understanding of the underlying dynamics. Thus, phenomena hidden in the high-dimensionality of the system can be discovered and qualitative changes in the dynamics, such as bifurcations, can be identified and predicted.

Expanding the classical system analysis techniques in time and frequency domain with a complex network perspective yields a multitude of useful tools for the design and analysis of large multi-component structures. For example, development efforts can be focused pointedly onto dynamically relevant components identified with the help of the novel methods, and early warning methods for transitions and rare events are of interest for predictive maintenance. Ultimately, every step of a products life cycle can be improved upon using the methods developed throughout this project.