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Research Papers

Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

[+] Author and Article Information
Chandrika P. Vyasarayani1

 Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canadacpvyasar@engmail.uwaterloo.ca

Thomas Uchida, John McPhee

 Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

For the problems considered in this work, δλ=0.1 was found to provide good results.

1

Corresponding author.

J. Comput. Nonlinear Dynam 7(1), 011012 (Oct 05, 2011) (8 pages) doi:10.1115/1.4004885 History: Received April 23, 2011; Revised August 12, 2011; Published October 05, 2011; Online October 05, 2011

The identification of parameters in multibody systems governed by ordinary differential equations, given noisy experimental data for only a subset of the system states, is considered in this work. The underlying optimization problem is solved using a combination of the Gauss–Newton and single-shooting methods. A homotopy transformation motivated by the theory of state observers is proposed to avoid the well-known issue of converging to a local minimum. By ensuring that the response predicted by the mathematical model is very close to the experimental data at every stage of the optimization procedure, the homotopy transformation guides the algorithm toward the global minimum. To demonstrate the efficacy of the algorithm, parameters are identified for pendulum-cart and double-pendulum systems using only one noisy state measurement in each case. The proposed approach is also compared with the linear regression method.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Evolution of parameter estimates for the Lorenz system

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Figure 2

Schematic of pendulum-cart system

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Figure 3

Evolution of parameter estimates for the pendulum-cart system

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Figure 4

Experimental and simulated responses for the pendulum-cart system

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Figure 5

Schematic of double-pendulum system

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Figure 6

Evolution of parameter estimates and objective function for the double-pendulum system (γ1=γ2=10)

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Figure 7

Evolution of parameter estimates and objective function for the double-pendulum system (γ1=γ2=20)

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