Antoulas, Athanasios C.2018-12-032018-12-032009Ionita, Antonio Cosmin. "Recursive identification and model reduction from time domain data." (2009) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/103741">https://hdl.handle.net/1911/103741</a>.https://hdl.handle.net/1911/103741In a system theoretic setting, identification from time domain data can be viewed as interpolating derivatives of a rational function. Typically, rational interpolation of derivatives requires computing the singular value decomposition (SVD) of large Loewner matrices constructed directly from the data. As a result, significant computational overhead is introduced through the SVD. The main result of the present thesis is simple—we construct interpolants efficiently without forming large Loewner matrices. A previously known recursive procedure is revisited with new insights, then further developed in a state-space setting. The key is to construct an interpolant recursively from ground up, by using the minimum amount of data. The resulting recursive interpolant is minimal and given in a state space form with rich structure. An important special case is the interpolation of impulse response measurements. This case is addressed separately and an efficient implementation requiring only matrix-vector multiplications is put forward. Furthermore, we extend the method to data corrupted by noise, where an additional model order reduction step is used to identify a low order model from the data. The newly developed recursive procedure is then tested on two examples involving actual noisy time-domain responses of a beaded elastic string and a cantilever beam.113 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Applied MathematicsElectrical engineeringSystems scienceApplied sciencesThesis751020081THESIS E.E. 2010 IONITA