"Fast Automatic System Identification Using Optimization"
Jeffrey Hokanson
(Rice university)
In our lab, we are interested in solving inverse eigenvalue problems
with data from real experiments, but determining eigenvalues from our
data is difficult. Our approach has been to solve the system
identification problem -- determining the state space representation of
a linear time invariant system from measurements of its inputs and
outputs -- and then compute the spectrum of the resulting system.
Current subspace algorithms utilize dense matrix factorizations that
scale cubically with the number of measured points. These methods are
intractable (both in storage and CPU time) when millions of
measurements must be considered. Instead, we propose a new algorithm
whose most expensive step is the Fast Fourier Transform. By
transforming the measured data by the discrete Fourier transform,
eigenvalues (poles) of the system correspond to peaks in the resulting
vector. The algorithm iteratively picks the largest peak as an estimate
of an eigenvalue; an optimization routine based on Variable Projection
then refines this estimate only using a few adjacent entries in the
transformed measurement vector; then the contribution of the estimate
eigenvalue is removed, and the process repeated on the modified data.
Unlike existing optimization approaches, no estimates of eigenvalues
need to be provided; nor does the number of eigenvalues need to be
known a priori, as required by subspace algorithms. At the conclusion
of the talk, I will discuss our attempts to determine the eigenvalues
of a damped string using this method, as well as its application to NMR
data.
Host: WG2 - Sabine Van Huffel, K.U. Leuven, ESAT-SCD
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
