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Research Papers

Parameter Identification in Multibody Systems Using Lie Series Solutions and Symbolic Computation

[+] Author and Article Information
Chandrika P. Vyasarayani1

Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadacpvyasar@engmail.uwaterloo.ca

Thomas Uchida, John McPhee

Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

DYNAFLEXPRO is now part of the Multibody package in MAPLESIM , a multidomain physical modeling tool developed by Maplesoft.

MAPLE is a trademark of Waterloo Maple, Inc.

MATLAB is a trademark of The MathWorks, Inc.

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(4), 041011 (Apr 28, 2011) (9 pages) doi:10.1115/1.4003686 History: Received June 29, 2010; Revised February 14, 2011; Published April 28, 2011; Online April 28, 2011

This paper studies the application of the Lie series to the problem of parameter identification in multibody systems. Symbolic computing is used to generate the equations of motion and the associated Lie series solutions automatically. The symbolic Lie series solutions are used to define a procedure for computing the sum of the squared Euclidean distances between the true generalized coordinates and those obtained from a simulation using approximate system parameters. This procedure is then used as an objective function in a numerical optimization routine to estimate the unknown parameters in a multibody system. The effectiveness of this technique is demonstrated by estimating the parameters of a structural system, a spatial slider-crank mechanism, and an eight-degree- of-freedom vehicle model.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Comparison of local and global Taylor series expansions

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Figure 2

Time integration using three-term Lie series with local expansion

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Figure 3

Block diagram illustrating the parameter estimation process

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Figure 4

Schematic of the spatial slider-crank mechanism (1)

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Figure 5

Mechanism response with actual and estimated parameters

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Figure 6

Schematic of the vehicle model

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Figure 7

Road profile used for vehicle simulation

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Figure 8

Identification of suspension stiffnesses using the Lie series technique: (a) ksf1, (b) ksf2, (c) ksr1, and (d) ksr2

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Figure 9

Value of objective function at each instant of time

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Figure 10

Vehicle response with actual and estimated parameters

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