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System Augmentation and Optimal Feedback Auxiliary Signals for Interrogating Nonlinear Systems.

By Kiran X. D'Souza


System augmentation is introduced and developed as a tool for modeling nonlinear systems in the context of a variety of applications including damage detection, system identification and sensing. The idea of creating augmented models enables the construction of higher dimensional models which are characterized by a specialized/augmented forcing. This specialized forcing enforces that an augmented model exactly follows a single trajectory of the nonlinear system when projected onto the subspace of the physical structure. Within the context of damage detection, the augmentation can be combined with a generalized minimum rank perturbation theory that is specifically developed to handle augmented systems. This model-based detection method uses the fact that often damage occurs in localized regions. That results in localized changes in the corresponding (model) matrices for the structure, which leads to perturbation matrices of minimum rank. Ideally one would have sensor information at all the nodes of a finite element model used for structural health monitoring. Practically, however, due to cost, weight and accessibility issues only a limited number of locations can be instrumented. Hence, an important, current challenge for damage detection is identifying multiple damages in complex structures using few sensors. This work develops a new integrated sensor placement and reduced order health assessment approach that can be applied to nonlinear structures. This method exploits the fact that the damageable regions (hot spots) of the system are often known in advance. The central advancement is an approach to expand the partial eigenvector information obtained from few sensors into the full space (of a detailed structural model) using the knowledge that damage is limited to the hot spots. Furthermore, most current approaches used for structural health monitoring are passive, while others are active in applying an auxiliary signal (excitation) to the structure. These current methods use predefined excitation signals (e.g. pulsed-waves, frequencysweeps). Such signals are designed offline and do not adapt to the response of the structure during its interrogation. In contrast, this work develops optimal feedback auxiliary signals. The feedback nature of these signals is a key enabling technique for enhancing sensitivity/selectivity, and leads to a new structural interrogation paradigm

Topics: System Augmentation, Optimal Feedback Auxiliary Signals, Nonlinear Systems, Generalized Minimum Rank Perturbation Theory, Reduced Order Health Assessment, Nonlinear Control
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