Two general linear time-varying system identification methods for multiple-input multiple-output systems are proposed based on the proper orthogonal decomposition (POD). The method applies the POD to express response data for linear or nonlinear systems as a modal sum of proper orthogonal modes and proper orthogonal coordinates (POCs). Drawing upon mode summation theory, an analytical expression for the POCs is developed, and two deconvolution-based methods are devised for modifying them to predict the response of the system to new loads. The first method accomplishes the identification with a single-load-response data set, but its applicability is limited to lightly damped systems with a mass matrix proportional to the identity matrix. The second method uses multiple-load-response data sets to overcome these limitations. The methods are applied to construct predictive models for linear and nonlinear beam examples without using prior knowledge of a system model. The method is also applied to a linear experiment to demonstrate a potential experimental setup and the method’s feasibility in the presence of noise. The results demonstrate that while the first method only requires a single set of load-response data, it is less accurate than the multiple-load method for most systems. Although the methods are able to reconstruct the original data sets accurately even for nonlinear systems, the results also demonstrate that a linear time-varying method cannot predict nonlinear phenomena that are not present in the original signals.
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June 2008
Research Papers
A Deconvolution-Based Approach to Structural Dynamics System Identification and Response Prediction
Timothy C. Allison,
e-mail: talliso@vt.edu
Timothy C. Allison
Ph.D. Candidate
Virginia Polytechnic Institute and State University
, 310 Durham Hall, Mail Code 0261, Blacksburg, VA 24061
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A. Keith Miller,
A. Keith Miller
Principal Member of Technical Staff
Sandia National Laboratories
, P.O. Box 5800, Albuquerque, NM 87185-0847
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Daniel J. Inman
Daniel J. Inman
George R. Goodson Professor
Virginia Polytechnic Institute and State University
, 310 Durham Hall, Mail Code 0261, Blacksburg, VA 24061
Search for other works by this author on:
Timothy C. Allison
Ph.D. Candidate
Virginia Polytechnic Institute and State University
, 310 Durham Hall, Mail Code 0261, Blacksburg, VA 24061e-mail: talliso@vt.edu
A. Keith Miller
Principal Member of Technical Staff
Sandia National Laboratories
, P.O. Box 5800, Albuquerque, NM 87185-0847
Daniel J. Inman
George R. Goodson Professor
Virginia Polytechnic Institute and State University
, 310 Durham Hall, Mail Code 0261, Blacksburg, VA 24061J. Vib. Acoust. Jun 2008, 130(3): 031010 (8 pages)
Published Online: April 8, 2008
Article history
Received:
June 29, 2007
Revised:
October 9, 2007
Published:
April 8, 2008
Citation
Allison, T. C., Miller, A. K., and Inman, D. J. (April 8, 2008). "A Deconvolution-Based Approach to Structural Dynamics System Identification and Response Prediction." ASME. J. Vib. Acoust. June 2008; 130(3): 031010. https://doi.org/10.1115/1.2890387
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