Development and application of chaotic attractor property analysis for vibration-based structural damage assessment

Long-term, high-level performance demands on a variety of structures and equipment have stimulated significant research in the field of structural health monitoring. The primary goals of this field are to provide information regarding structural performance capability, damage assessment, and even structural prognosis, all of which may potentially reduce the ownership costs associated with the maintenance and operation of the structure. Much of the research has largely taken a vibration-based approach, whereby the structural dynamic response to either ambient or applied loading is analyzed for changes in certain characteristic "features" that serve as appropriate damage indicators. Many of the features proposed have involved parameters derived from a modal analysis of the structure, e.g., resonant frequencies, mode shapes, damping, strain energy, flexibility, etc. In this work, we present features taken from measured attractors of the structure. System characterization (including damage detection) by means of geometric invariants, such as attractor(s), is potentially a powerful generic approach which does not rely on implicit assumptions in an underlying model, e.g., linearity. The structure is excited with a chaotic oscillator, and the combined chaotic excitation dynamics and structural response may be thought of as the "filtering" of chaotic data: the structure acts as a "filter" through which the chaotic signal is processed so that small changes to the structure (ostensibly due to damage) will serve to alter the degree to which the signal is filtered. We develop the attractor property trajectory prediction error as a candidate feature and evaluate its utility in detecting clamping force degradation on a continuous metal beam.