Monitoring the Health of Structural Systems from the Geometry of Sensor Traces

由于时间的推移和暴露于大荷载事件而导致的劣化会降低结构系统的安全性。维持足够可靠性的干预措施的有效性和效率取决于现有的资料，而结构监测的目标就是提供这些资料。通过跟踪共振频率来表征劣化的尝试成功有限，因为相对于它们不可约的可变性，特征的灵敏度很小。该奖项支持一种完全不同范例的研究：在这种范例中，监测不是通过检查谐振频率，而是通过检查闭环操作中获得的测量结果构建的几何物体。在迄今为止所追求的路径上，收益来自于通过选择控制律来“调整”被监视对象的能力。本研究成果将为结构健康监测系统的开发开辟一条新的道路。这条新路径以及由此带来的进步，将通过降低检查成本、推进基于状态的维护实践，并最终通过降低结构系统的生命周期成本，使美国经济受益。这个项目的研究处于几个学科的交叉点，这方面被利用在一个教育组件中，旨在激励来自不同领域的学生和年轻研究人员。该奖项的研究将监测问题描述为跟踪由系统在非线性反馈下自主运行时所穿越的轨迹所产生的物体的几何形状。与线性反馈相反，线性反馈保留了经典的监测结构，从而从特征值推断变化，非线性反馈试图将参考状态映射到吸引子的几何形状，并关注系统变化如何影响所得流形。指导如何指定非线性控制使系统具有稳定的吸引子，并具有可预测的吸引池的理论，目前尚缺乏。模拟指导的理论研究是这项工作的核心，旨在填补这一知识空白。该研究还解决了如何选择系统“启动”状态的问题，以使对必要驱动的需求最小化；驱动的无穷范数的最小化对于所研究范式的实用性是重要的。尽管最佳传感器和执行器的放置问题并未明确包含在项目范围内，但计划对这两个问题进行探索性工作。

Deterioration from the passage of time and from exposure to large loading events can reduce the safety of structural systems. The effectiveness and efficiency of interventions to maintain adequate reliability depend on the available information, and the objective of structural monitoring is to provide it. Attempts to characterize deterioration by tracking resonant frequencies has had limited success due to small sensitivity of the features relative to their irreducible variability. This award supports research on an entirely different paradigm: one where monitoring is carried out not by inspection of resonant frequencies, but by examination of a geometric object built from measurements obtained in closed-loop operation. Gains, over the path so far pursued, come from the ability to "tune" the monitored object by selection of the control laws. The results from this research will open a new path for developing structural health monitoring systems. This new path, and the progress that will come from it, will benefit the US economy by reducing the cost of inspections, by advancing the practice of condition based maintenance, and, ultimately, by reducing the life cycle cost of structural systems. The research in this project sits at the intersection of several disciplines and this aspect is exploited in an educational component designed to inspire students and young researchers from various fields. The research in this award casts the monitoring problem as that of tracking the geometry of an object generated by trajectories that are traversed as the system operates autonomously under nonlinear feedback. In contrast with linear feedback, which retains the classical monitoring structure, and thus infers about changes from eigenvalues, nonlinear feedback attempts to map the reference state to the geometry of an attractor and focuses on how system changes affect the resulting manifold. Theory to guide how to specify the nonlinear control so the system has a stable attractor, with a predictable basin of attraction, is currently lacking. The simulation-guided, theoretical research that is central to this work is intended to contribute in filling this knowledge gap. The research tackles also the question of how to select the state from where the system is "launched" so the demands on the necessary actuation is minimized; minimization of the infinity norm of the actuation being important to the practicality of the investigated paradigm. Albeit the optimal sensor and actuator placement problems are not explicitly included in the scope of the project, exploratory work in both of these issues is planned.