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    Developing complex network perspectives as an alternative view on nonlinear dynamics in large multi-component mechanical structures - Towards a better understanding of engineering vibrations
    This project aims at integrating methods from the field of complex networks into the analysis of large multi-component mechanical structures and their dynamics. Complex network analysis is a growing field of research that is applied throughout many different disciplines such as medicine, earth sciences or fluid dynamics. We propose a novel way of approaching current challenges in mechanical systems analysis by complementing the classical view of a geometric structure with a functional network perspective: The structure is represented as a network of individual components, and hence one can study the dynamic interplay, driving agents and component roles in the overall system dynamics better than with traditional methods. With the tools of network analysis, current challenges in nonlinear engineering dynamics can be handled in new and simpler ways. Particularly, the outcome of this project will allow for (i) visualization of dynamical phenomena hidden in the high dimensionality of the system; (ii) identification of emergent phenomena arising from collective behavior; (iii) analysis and design of mechanical system improved by network analysis tools. A network-based view on structural dynamics will enable us to identify and predict qualitative changes in the systems behavior, such as bifurcations, and emergent phenomena. Functional network representations of the complex dynamical system will provide a more intuitive understanding of the system dynamics, its governing nonlinearities and dynamic relationships between the components and sub-assemblies. This viewpoint will be expedient in the development of new multi-component mechanical systems, as resources can be focused on the dynamically most relevant parts during the design process. The methods obtained throughout this project will be of use for manufacturing and and quality management, when defining manufacturing tolerances or assessing fault impacts. Early warning methods for transitions and rare events can be established based on the proposed complex network analysis, which are of special interest in predictive maintenance. Thus, all phases of a products life cycle can profit from a complex network perspective on the systems dynamics rendered accessible through this project.
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    Designing complex behaviour: novel pathways for assisting design based on dynamics-informed machine learning in structural mechanics
    Mechanical systems are central to many areas of pressing societal demand for progress, such as sustainability, decarbonization, transportation, medicine, and many more. The state-of-the-art system design paradigms are mostly based on a number of crucially simplifying and idealizing assumptions on load and system complexity, with nonstationarity forming perturbations to steady-state operations. In fact, static load cases actually occur only rarely in real-life systems: aircraft engines, wind turbines, and vehicle components consistently operate under non-stationary, non-periodic, multi-scale, and in total complex loads. Numerically, time-resolved simulations are prohibitively compute-intensive, and yet not particularly accurate owing to inherent modeling and parameterization inaccuracies. Experimentally, only small data can be acquired from prototypical systems. As a result, design engineers lack a toolset for subjecting early-stage designs to realistic loading scenarios and formalized criteria, and thereby tailoring designs towards the actual operation dynamics. This project aims at developing new machine learning approaches to derive design assistants for the nonlinear dynamical behavior of structures under complex transient loads from small data. To provide the engineer with a formalized objective for designing a structure’s dynamical behavior under hundreds of time-resolved scenarios, novel Dynamics-Informed Reservoir Computers (DIRCs) are proposed. This new systematic design strategy strives at adapting the prediction model structure and complexity to the individual system dynamics, thereby arriving at highly accurate surrogate models with small data requirements and real-time capabilities. Their modularity makes DIRCs are highly flexible and thus easy to integrate into existing toolsets, while having a minimal ecological footprint compared to data-hungry and compute-intense deep learning techniques. This visionary project aims at enhancing simulation-driven design studies in the field of dynamical behavior beyond numerical and experimental state-of-the-art techniques. Novel design assistants are developed by combining nonlinear vibrations, complex network theory, and cutting-edge machine learning approaches. Since dynamics are inherently related to sequential data, a novel class of dynamics-informed machine learning approaches is tailored towards the prediction task. The proposed methods will a) enable early-stage design towards transient and complex loading scenarios under operation with minimal computational cost, b) be flexible and modular for direct interfacing with established numerical and experimental tools, and c) be developed and validated for a series of benchmark cases in mechanical vibrations spanning the horizon of (quasi-) periodic, irregular, transient, multi-scale, and spatio-temporal dynamics both numerically and experimentally.
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