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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e-mail: cpvyasar@engmail.uwaterloo.ca
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January 2012
Research Papers
Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation
Chandrika P. Vyasarayani,
e-mail: cpvyasar@engmail.uwaterloo.ca
Chandrika P. Vyasarayani
Systems Design Engineering, University of Waterloo
, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
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Thomas Uchida,
Thomas Uchida
Systems Design Engineering, University of Waterloo
, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
Search for other works by this author on:
John McPhee
John McPhee
Systems Design Engineering, University of Waterloo
, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
Search for other works by this author on:
Chandrika P. Vyasarayani
Systems Design Engineering, University of Waterloo
, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
e-mail: cpvyasar@engmail.uwaterloo.ca
Thomas Uchida
Systems Design Engineering, University of Waterloo
, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
John McPhee
Systems Design Engineering, University of Waterloo
, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
J. Comput. Nonlinear Dynam. Jan 2012, 7(1): 011012 (8 pages)
Published Online: October 5, 2011
Article history
Received:
April 23, 2011
Revised:
August 12, 2011
Online:
October 5, 2011
Published:
October 5, 2011
Citation
Vyasarayani, C. P., Uchida, T., and McPhee, J. (October 5, 2011). "Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation." ASME. J. Comput. Nonlinear Dynam. January 2012; 7(1): 011012. https://doi.org/10.1115/1.4004885
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