Developing complex network perspectives as an alternative view on nonlinear dynamics in large multi-component mechanical structures - Towards a better understanding of engineering vibrations

该项目旨在将复杂网络领域的方法集成到大型多部件机械结构及其动力学的分析中。复杂网络分析是一个不断发展的研究领域，它应用于许多不同的学科，如医学、地球科学或流体动力学。我们提出了一种新的方法来应对当前机械系统分析中的挑战，用功能网络的观点补充了经典的几何结构观点：结构被表示为单个部件的网络，因此可以比传统方法更好地研究整个系统动力学中的动态相互作用、驱动力和部件角色。利用网络分析工具，可以用新的和更简单的方法来处理当前非线性工程动力学中的挑战。特别是，该项目的成果将有助于(I)将隐藏在系统高维中的动态现象可视化；(Ii)确定集体行为引起的紧急现象；(Iii)通过网络分析工具改进机械系统的分析和设计。基于网络的结构动力学观点将使我们能够识别和预测系统行为的质变，如分叉和涌现现象。复杂动力系统的泛函网络表示将提供对系统动力学、其支配的非线性以及部件和子组件之间的动态关系的更直观的理解。这一观点将有利于开发新的多部件机械系统，因为在设计过程中可以将资源集中在动态最相关的部件上。在整个项目中获得的方法将在定义制造公差或评估故障影响时用于制造和质量管理。基于提出的复杂网络分析，可以建立对过渡和罕见事件的早期预警方法，这在预测性维护中特别重要。因此，产品生命周期的所有阶段都可以从复杂的网络视角中获益，可以通过该项目访问系统动态。

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.