Research Papers

Parameters Identification for Nonlinear Dynamic Systems Via Genetic Algorithm Optimization

[+] Author and Article Information
A. C. Gondhalekar, E. P. Petrov, M. Imregun

Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

J. Comput. Nonlinear Dynam 4(4), 041002 (Aug 24, 2009) (9 pages) doi:10.1115/1.3187213 History: Received December 05, 2007; Revised November 24, 2008; Published August 24, 2009

This paper presents a frequency domain method for the location, characterization, and identification of localized nonlinearities in mechanical systems. The nonlinearities are determined by recovering nonlinear restoring forces, computed at each degree-of-freedom (DOF). Nonzero values of the nonlinear force indicate nonlinearity at the corresponding DOFs and the variation in the nonlinear force with frequency (force footprint) characterizes the type of nonlinearity. A library of nonlinear force footprints is obtained for various types of individual and combined nonlinearities. Once the location and the type of nonlinearity are determined, a genetic algorithm based optimization is used to extract the actual values of the nonlinear parameters. The method developed allows simultaneous identification of one or more types of nonlinearity at any given DOF. Parametric identification is possible even if the type of nonlinearity is not known in advance, a very useful feature when the type characterization is difficult. The proposed method is tested on simulated response data. Different combinations of localized cubic stiffness nonlinearity, clearance nonlinearity, and frictional nonlinearity are considered to explore the method’s capabilities. Finally, the response data are polluted with random noise to examine the performance of the method in the presence of measurement noise.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Footprint library for various nonlinearity types

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Figure 2

Comparison of cubic stiffness and clearance away from the resonance

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Figure 3

Flowchart for the genetic algorithm

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Figure 4

Representative 2DOF system

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Figure 5

Response with cubic stiffness (a) and clearance (b) nonlinearity

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Figure 6

Nonlinear force variation for cubic stiffness nonlinearity

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Figure 7

Effect of binary multipliers on the performance of GAs

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Figure 8

Response with 7.5% noise (cubic stiffness nonlinearity)

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Figure 9

Error in parameter estimation-cubic stiffness nonlinearity

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Figure 10

Error in parameter estimation (cubic stiffness+clearance)

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Figure 11

Selection of points for the three cases

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Figure 12

Nonlinear beam with cubic stiffness nonlinearity

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Figure 13

Comparison of linear and nonlinear response

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Figure 14

Comparison of nonlinear force for case B



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