Modal analysis is the process of estimating a system’s modal parameters such as its natural frequencies and mode shapes. One application of modal analysis is in structural health monitoring (SHM), where a network of sensors may be used to collect vibration data from a physical structure such as a building or bridge. There is a growing interest in developing automated techniques for SHM based on data collected in a wireless sensor network. In this talk, Mike will survey a broad class of sampling and compression strategies that one might consider in a physical sensor network; these methods are intended to minimize power consumption by allowing the data to be sampled and/or transmitted more efficiently. He will consider two techniques for modal analysis at the central node: (1) a simple and commonly used SVD-based technique, which can give accurate approximations of a structure’s mode shapes, and (2) a formulation of modal analysis as an atomic norm minimization problem, which can be solved efficiently and in some cases recover perfectly a structure’s mode shapes and frequencies. Mike will present new theoretical bounds on sample complexity and recovery accuracy, and will discuss the trade-offs among the various sampling/compression strategies.
Michael B. Wakin is the Ben L. Fryrear Associate Professor in the Department of Electrical Engineering and Computer Science at the Colorado School of Mines (CSM). Dr. Wakin received a B.S. in electrical engineering and a B.A. in mathematics in 2000 (summa cum laude), an M.S. in electrical engineering in 2002, and a Ph.D. in electrical engineering in 2007, all from Rice University. He was an NSF Mathematical Sciences Postdoctoral Research Fellow at Caltech from 2006-2007 and an Assistant Professor at the University of Michigan from 2007-2008. His research interests include sparse, geometric, and manifold-based models for signal processing and compressive sensing. In 2007, Dr. Wakin shared the Hershel M. Rich Invention Award from Rice University for the design of a single-pixel camera based on compressive sensing; in 2008, Dr. Wakin received the DARPA Young Faculty Award for his research in compressive multi-signal processing for environments such as sensor and camera networks; in 2012, Dr. Wakin received the NSF CAREER Award for research into dimensionality reduction techniques for structured data sets; and in 2014, Dr. Wakin received the Excellence in Research Award for his research as a junior faculty member at CSM.
This talk is suitable for anyone with an interest in applied maths, signal processing and structural and civil engineering.
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