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

随着时间的推移和暴露在大型加载事件中的劣化，可能会降低结构系统的安全性。维持足够可靠性的干预措施的效力和效率取决于可获得的信息，而结构监测的目标是提供这些信息。通过跟踪共振频率来表征恶化的尝试取得了有限的成功，这是因为特征相对于它们的不可减少的变异性的敏感性很小。该奖项支持对一种完全不同的范式的研究：在这种范式中，监测不是通过检查谐振频率，而是通过检查由闭环系统操作中获得的测量结果构建的几何对象来进行的。在迄今所追求的道路上，收益来自于通过选择控制律来“调整”被监测对象的能力。这一研究成果将为结构健康监测系统的开发开辟一条新的途径。这条新的道路以及由此带来的进展，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。该项目的研究位于几个学科的交叉点上，这一方面被用在一个旨在激励来自不同领域的学生和年轻研究人员的教育组成部分中。该奖项的研究将监控问题归结为跟踪对象的几何形状，该对象由系统在非线性反馈下自主运行时经过的轨迹生成。与线性反馈不同的是，线性反馈保留了经典的监测结构，从而从特征值的变化中推断出变化，而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得到的流形。如何具体说明非线性控制使系统具有稳定的吸引子，具有可预测的吸引域，目前尚缺乏理论指导。这项工作的核心是以模拟为指导的理论研究，旨在为填补这一知识空白做出贡献。这项研究还解决了如何选择系统从哪里“启动”的状态的问题，从而使对必要驱动的要求最小化；最小化驱动的无穷范数对于所研究范例的实用性是重要的。虽然最优传感器和执行器的位置问题没有明确地包括在项目的范围内，但在这两个问题上的探索性工作是计划的。

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.