Persistent Link:
http://hdl.handle.net/10150/184651
Title:
Modeling and identification of nonlinear oscillations.
Author:
Head, Kenneth Larry.
Issue Date:
1989
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The topic of this dissertation, modeling and identification of nonlinear oscillation, represents an area of mathematical systems theory that has received little attention in the past. Primarily, the types of oscillation of interest are those found in biological systems where theoretical foundations for mathematical models are insufficient. These oscillations are also observed in other systems including electrical, mechanical, and chemical. The contributions of this dissertation are a generalized class of autonomous differential equations that are found to exhibit stable limit cycles, and an investigation of a method of system identification that can be used to estimate the model parameters. Here the observed signal is modeled as the response of a nonlinear system that can be described by differential equations. Modeling the signal in this way shifts the emphasis from signal characteristics, such as spectral content, to system characteristics, such as parameter values and system structure. This shift in emphasis may provide a better method for monitoring complex systems that exhibit periodic behavior such as patients under anesthesia. A class of autonomous differential equations, called the generalized oscillator models, are presented as one nᵗʰ-order differential equations with nonlinear coefficients. The coefficients are chosen to change sign depending on the magnitude of the phase variables. The coefficients are negative near the origin and positive away from the origin. Motivated by the generalized Routh-Hurwitz criterion, this coefficient sign changing produces the desired oscillation. Properties of the generalized oscillator model are investigated using the describing function method of analysis and numerical simulation. Several descriptive examples are presented. Based on the generalized oscillator model as a set of candidate models, the system identification problem is formed as a mathematical programming problem. The method of quasilinearization is investigated as method of solving the identification problem. Two examples are presented that demonstrate the method. It is shown that in general, the method of quasilinearization as a solution to the system identification problem will not converge regardless of the initial starting point. This result indicates that although the quasilinearization method is useful for solving two-point boundary value problems, it is not useful (in its present form) for solving the system identification problem.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Nonlinear oscillations -- Mathematical models.; Anesthesia -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Schultz, Donald G.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleModeling and identification of nonlinear oscillations.en_US
dc.creatorHead, Kenneth Larry.en_US
dc.contributor.authorHead, Kenneth Larry.en_US
dc.date.issued1989en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe topic of this dissertation, modeling and identification of nonlinear oscillation, represents an area of mathematical systems theory that has received little attention in the past. Primarily, the types of oscillation of interest are those found in biological systems where theoretical foundations for mathematical models are insufficient. These oscillations are also observed in other systems including electrical, mechanical, and chemical. The contributions of this dissertation are a generalized class of autonomous differential equations that are found to exhibit stable limit cycles, and an investigation of a method of system identification that can be used to estimate the model parameters. Here the observed signal is modeled as the response of a nonlinear system that can be described by differential equations. Modeling the signal in this way shifts the emphasis from signal characteristics, such as spectral content, to system characteristics, such as parameter values and system structure. This shift in emphasis may provide a better method for monitoring complex systems that exhibit periodic behavior such as patients under anesthesia. A class of autonomous differential equations, called the generalized oscillator models, are presented as one nᵗʰ-order differential equations with nonlinear coefficients. The coefficients are chosen to change sign depending on the magnitude of the phase variables. The coefficients are negative near the origin and positive away from the origin. Motivated by the generalized Routh-Hurwitz criterion, this coefficient sign changing produces the desired oscillation. Properties of the generalized oscillator model are investigated using the describing function method of analysis and numerical simulation. Several descriptive examples are presented. Based on the generalized oscillator model as a set of candidate models, the system identification problem is formed as a mathematical programming problem. The method of quasilinearization is investigated as method of solving the identification problem. Two examples are presented that demonstrate the method. It is shown that in general, the method of quasilinearization as a solution to the system identification problem will not converge regardless of the initial starting point. This result indicates that although the quasilinearization method is useful for solving two-point boundary value problems, it is not useful (in its present form) for solving the system identification problem.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectNonlinear oscillations -- Mathematical models.en_US
dc.subjectAnesthesia -- Mathematical models.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorSchultz, Donald G.en_US
dc.contributor.committeememberSzidarovsky, Ferencen_US
dc.contributor.committeememberSen, Suvrajeeten_US
dc.identifier.proquest8915961en_US
dc.identifier.oclc702154214en_US
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