Designing complex behaviour: novel pathways for assisting design based on dynamics-informed machine learning in structural mechanics

机械系统是许多迫切的社会进步需求领域的核心，如可持续性、脱碳、运输、医药等。最先进的系统设计范例大多基于一些关于负载和系统复杂性的关键简化和理想化假设，其中非平稳性构成了对稳态操作的扰动。事实上，在真实系统中，静态负载情况实际上很少发生：飞机发动机、风力涡轮机和车辆部件在非平稳、非周期、多尺度和总的复杂负载下持续运行。在数值上，时间分辨模拟的计算量大得令人望而却步，但由于固有的建模和参数化的不准确性，时间分辨模拟并不是特别准确。在实验上，只能从原型系统中获得很小的数据。因此，设计工程师缺乏一个工具集来使早期设计服从真实的加载场景和形式化的标准，从而使设计符合实际的操作动态。该项目旨在开发新的机器学习方法，以从小数据中获取结构在复杂瞬时载荷下的非线性动力学行为的设计辅助工具。为了给工程师提供一个形式化的目标来设计结构在数百个时间分辨场景下的动力行为，提出了一种新型的动态信息水库计算机(DIRC)。这种新的系统设计策略致力于使预测模型的结构和复杂性适应单个系统的动态，从而获得数据需求小、实时能力强的高精度代理模型。它们的模块化使DIRC具有高度的灵活性，因此很容易集成到现有的工具集中，同时与数据密集型和计算密集型深度学习技术相比，具有最小的生态足迹。这个有远见的项目旨在加强动态行为领域的模拟驱动设计研究，超越数值和实验最先进的技术。将非线性振动、复杂网络理论和尖端机器学习方法相结合，开发了新型的设计辅助工具。由于动力学本质上与序列数据相关，因此一类新的动力学信息机器学习方法是为预测任务量身定制的。所提出的方法将a)能够以最小的计算成本针对运行中的瞬变和复杂加载场景进行早期设计，b)灵活和模块化以直接与已有的数值和实验工具对接，以及c)开发和验证跨越(准)周期、不规则、瞬变、多尺度和时空动力学水平的机械振动的一系列基准案例。

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.