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Research Papers

A Deconvolution-Based Approach to Structural Dynamics System Identification and Response Prediction

[+] Author and Article Information
Timothy C. Allison

 Virginia Polytechnic Institute and State University, 310 Durham Hall, Mail Code 0261, Blacksburg, VA 24061talliso@vt.edu

A. Keith Miller

 Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0847

Daniel J. Inman

 Virginia Polytechnic Institute and State University, 310 Durham Hall, Mail Code 0261, Blacksburg, VA 24061

J. Vib. Acoust 130(3), 031010 (Apr 08, 2008) (8 pages) doi:10.1115/1.2890387 History: Received June 29, 2007; Revised October 09, 2007; Published April 08, 2008

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.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

LTI (top), LTV (middle), and NL (bottom) beam models

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Figure 2

Cubic spring force for the NL beam model

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Figure 3

Time variation of tip mass for the LTI beam model

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Figure 4

Pulse loads applied at five locations along beams

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Figure 5

First three POMs for the linear beam model

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Figure 6

Displacement norms for the LTI beam response to load 5

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Figure 7

Percentage error of displacement norms for the LTI beam response to load 5

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Figure 8

Displacement norms for the LTV beam response to load 5

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Figure 9

Percentage error of displacement norms for the LTV beam response to load 5

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Figure 10

Displacement norms for the NL beam response to load 5

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Figure 11

Percentage error of displacement norms for the NL beam response to load 5

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Figure 12

Experimental setup

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Figure 13

Application of impulsive load via shaker strike

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Figure 14

Load cell output with and without beam impact

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Figure 15

Forces applied to various beam locations

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Figure 16

Displacement norms for experimental beam response to load at 4in. location

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Figure 17

Percentage error of displacement norms for experimental beam response

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