Modeling Systems from Measurements of their Frequency Response

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dc.contributor.advisorAntoulas, Athanasios C.en_US
dc.creatorLefteriu, Sandaen_US
dc.date.accessioned2013-03-08T00:35:40Zen_US
dc.date.available2013-03-08T00:35:40Zen_US
dc.date.issued2012en_US
dc.description.abstractThe problem of modeling systems from frequency response measurements is of interest to many engineers. In electronics, we wish to construct a macromodel from tabulated impedance, admittance or scattering parameters to incorporate it into a circuit simulator for performing circuit analyses. Structural engineers employ frequency response functions to determine the natural frequencies and damping coefficients of the underlying structure. Subspace identification, popular among control engineers, and vector fitting, used by electronics engineers, are examples of algorithms developed for this problem. This thesis has three goals. 1. For multi-port devices, currently available algorithms arc expensive. This thesis therefore proposes an approach based on the Loewner matrix pencil constructed in the context of tangential interpolation with several possible implementations. They are fast, accurate, build low dimensional models, and are especially designed for a large number of terminals. For noise-free data, they identify the underlying system, rather than merely fitting the measurements. For noisy data, their performance is analyzed for different noise levels introduced in the measurements and an improved version, which identifies an approximation of the original system even for large noise values, is proposed. 2. This thesis addresses the problem of generating parametric models from measurements performed with respect to the frequency, but also with respect to one or more design parameters, which could relate to geometry or material properties. These models are suited for performing optimization over the design variables. The proposed approach generalizes the Loewner matrix to data depending on two variables. 3. This thesis analyzes the convergence properties of vector fitting, an iterative algorithm that relocates the poles of the model, given some "starting poles" chosen heuristically. It was recognized as a reformulation of the Sanathanan-Koerner iteration and several authors attempted to improve its convergence properties, but a thorough convergence analysis has been missing. Numerical examples show that for high signal to noise ratios, the iteration is convergent, while for low ones, it may diverge. Hence, incorporating a Newton step aims at making the iteration always convergent for "starting poles" chosen close to the solution. A connection between vector fitting and the Loewner framework is exhibited, which resolves the issue of choosing the starting poles.en_US
dc.format.extent213 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 2012 LEFTERIUen_US
dc.identifier.citationLefteriu, Sanda. "Modeling Systems from Measurements of their Frequency Response." (2012) Diss., Rice University. <a href="https://hdl.handle.net/1911/70311">https://hdl.handle.net/1911/70311</a>.en_US
dc.identifier.digitalLefteriuSen_US
dc.identifier.urihttps://hdl.handle.net/1911/70311en_US
dc.language.isoengen_US
dc.rightsCopyright 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.en_US
dc.subjectApplied sciencesen_US
dc.subjectFrequency responseen_US
dc.subjectFrequency domain measurementen_US
dc.subjectCircuit simulatorsen_US
dc.subjectDamping coefficientsen_US
dc.subjectApplied mathematicsen_US
dc.subjectElectrical engineeringen_US
dc.titleModeling Systems from Measurements of their Frequency Responseen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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