Collaborative Research: Health Monitoring and System Identification of Complex Mechanical Systems Using Fractional-Order Calculus Modeling

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Inspection and maintenance are significant cost drivers to manage and preserve the quality of our nation's transportation systems and infrastructure. Current strategies are based on preventive approaches that do not consider the actual real-time status of a specific structural component. In these approaches, the systems are subject to routine inspections and replacement of components that are scheduled a priori based on a combination of empirical data and numerical predictions of the estimated life. Such approaches are sub-optimal because they may lead to replacement of fully-functional components, on the one hand, and may miss rapidly deteriorating conditions between scheduled inspections, on the other. This research will develop new methods to address both shortcomings by investigating new modeling and monitoring techniques particularly suited and applicable to modern, complex systems. To enable this condition-based monitoring approach, better theoretical and numerical models are needed to simulate the dynamic behavior of complex mechanical systems as well as to produce metrics capable of tracking their status in real-time. This award supports fundamental research to develop mathematical and computational models based on fractional calculus. The methods resulting from this research will be highly useful in application that use imaging and remote sensing in structural, geological, and biological media. The educational part of this project will feature, among its different components, the development of a new course to introduce engineering students to fractional calculus and its applications to modeling of engineering systems.This research will involve a systematic study to determine how fractional-order differential equations will enhance the state-of-the-art in system identification and monitoring. Fractional-order models are a new and useful tool for modeling of complex engineering systems, however they are not yet common in engineering. Their application to structural health monitoring will provide a substantially new approach for damage detection and diagnostics, it will introduce the system order as a new parameter for system assessment, and it will provide highly mathematically structured and concise descriptions of the dynamics of complex systems. More specifically, this work will (1) determine the effect of structural damage on the fractional order of the host system and develop methodologies to account for its impact on the underlying governing equations; (2) use fractional approaches to achieve efficient order reduction, sub-structuring, and inverse problem solutions; (3) develop fractional models for system identification based on purely experimental data; and (4) develop testbeds for experimental validation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.