Modal Analysis with Compressive Measurements

Structural Health Monitoring (SHM) systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Such systems typically involve collections of battery-operated wireless sensors that sample vibration data over time. After the data is transmitted to a central node, modal analysis can be used to detect damage in the structure. In this talk, we propose and study three frameworks for Compressive Sensing (CS) in SHM systems; these methods are intended to minimize power consumption by allowing the data to be sampled and/or transmitted more efficiently.
At the central node, all of these frameworks involve a very simple technique for estimating the structure's mode shapes without requiring a traditional CS reconstruction of the vibration signals; all that is needed is to compute a simple Singular Value Decomposition.

We provide theoretical justification (including measurement bounds) for each of these techniques based on the equations of motion describing a simplified Multiple-Degree-Of-Freedom (MDOF) system, and we support our proposed techniques using simulations based on synthetic and real data.

Joint work with Jae Young Park and Michael Wakin.

Anna Gilbert received an S.B. degree from the University of Chicago and a Ph.D. from Princeton University, both in mathematics. In 1997, she was a postdoctoral fellow at Yale University and AT&T Labs-Research. From 1998 to 2004, she was a member of technical staff at AT&T Labs-Research in Florham Park, NJ. Since then Anna has been with the Department of Mathematics at the University of Michigan, where she is now a Professor. Anna has received several awards, including a Sloan Research Fellowship (2006), an NSF CAREER award (2006), the National Academy of Sciences Award for Initiatives in Research (2008), the Association of Computing Machinery (ACM) Douglas Engelbart Best Paper award (2008), the EURASIP Signal Processing Best Paper award (2010), and the SIAM Ralph E. Kleinman Prize (2013). Her research interests include analysis, probability, networking, and algorithms. I am especially interested in randomized algorithms with applications to harmonic analysis, signal and image processing, networking, and massive datasets.