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Academic Lectures / Courses
Computational STEM Seminar Series — Thursday 2/23/17, 11:00AM, CH 156
Department / Organization: AMS
Dr. Jeffrey Hokanson (CSM) will present “Projected Nonlinear Least Squares for Modal Analysis”
Abstract: With the increasing power of data acquisition technology, the sheer quantity of data collected poses a challenge for parameter estimation. Here we consider the case where measurements represent the sum of an underlying parameterized model plus Gaussian noise; this yields a nonlinear least squares problem to recover the maximum likelihood parameter estimates. Here we reduce the dimension of this nonlinear least squares problem by projecting both the model and the measurements onto a low dimensional subspace. Although a general approach, there are five constraints that apply both the model and subspace that must be satisfied for this projection approach to be practical. Here we consider the modal analysis problem and use a subspace spanned by a Vandermonde matrix. For this pair of model and subspace we are able to satisfy all five constraints, allowing us to rapidly solve the modal analysis problem. Even though modal analysis has been an active area of research for decades, we are able to improve on existing techniques, obtaining estimates fourteen times faster than state of the art methods in the limit of large data.
Bio: Jeffrey Hokanson did his PhD work at Rice University with Mark Embree and Steve Cox and now works with Paul Constantine on Active Subspaces.