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Research Papers

A Methodology for the Modeling of Forced Dynamical Systems From Time Series Measurements Using Time-Delay Neural Networks

[+] Author and Article Information
John Zolock

 Exponent Failure Analysis Associates, Natick, MA 01760

Robert Greif

Department of Mechanical Engineering, Tufts University, Medford, MA 02155

J. Vib. Acoust 131(1), 011003 (Dec 29, 2008) (10 pages) doi:10.1115/1.2981096 History: Received February 01, 2006; Revised May 30, 2008; Published December 29, 2008

The main goal of this research was to develop and present a general, efficient, mathematical, and theoretical based methodology to model nonlinear forced-vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on a dynamic system theory and a nonlinear time series analysis that employ phase space reconstruction (delay vector embedding) in modeling dynamical systems from time series data using time-delay neural networks. The first part of this work details the modeling methodology, including background on dynamic systems, phase space reconstruction, and neural networks. In the second part of this work, the methodology is evaluated based on its ability to model selected analytical lumped-parameter forced-vibrating dynamic systems, including an example of a linear system predicting lumped mass displacement subjected to a displacement forcing function. The work discusses the application to nonlinear systems, multiple degree of freedom systems, and multiple input systems. The methodology is further evaluated on its ability to model an analytical passenger rail car predicting vertical wheel∕rail force using a measured vertical rail profile as the input function. Studying the neural modeling methodology using analytical systems shows the clearest observations from results, providing prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

General architecture for a time-delay neural network (TDNN)

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Figure 2

Examples of the analytical systems studied

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Figure 3

Vertical rail track geometry

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Figure 4

Example segment of input-output data

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Figure 5

(a) Mutual information and (b) percentage of false nearest neighbors

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Figure 6

Performance measure for training and validation

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Figure 7

TDNN validation output over (a) actual measured system response and (b) residual.

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Figure 8

Exploded and sectioned side front views of an equalizer beam truck

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Figure 9

Segment of input-output data

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Figure 10

(a) Mutual information and (b) percentage of false nearest neighbors

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Figure 11

Mean absolute error performance measure

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Figure 12

Comparison of (a) predicted and actual and (b) residual from validation

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Figure 13

Analytically generated white noise dataset

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Figure 14

(a) Plots of mutual information and (b) false nearest neighbors

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