Title page for ETD etd-11012007-141208


Type of Document Dissertation
Author Allison, Timothy Charles
Author's Email Address talliso@vt.edu
URN etd-11012007-141208
Title System Identification via the Proper Orthogonal Decomposition
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Inman, Daniel J. Committee Chair
Beattie, Christopher A. Committee Member
Goulbourne, Nakhiah C. Committee Member
Kurdila, Andrew J. Committee Member
Miller, A. Keith Committee Member
Keywords
  • Deconvolution
  • Nonlinear Dynamics
  • Linear Time-Varying Systems
  • System Identification
  • Proper Orthogonal Decomposition
Date of Defense 2007-10-26
Availability unrestricted
Abstract
Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed.
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