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Journal Articles Mechanical Systems and Signal Processing Year : 2008

On the improved use of Chebyshev expansion for mechanical system identification


Differential equations, and particularly those governing mechanical system behavior, can be transformed into algebraic equations by using the well-known properties of polynomial functions. In this paper, by using Chebyshev polynomials, improvements of classical methods are proposed for the identification and inverse formulation of mechanical systems. The drawbacks of these polynomials compel us to propose alternative formulations by dissociating signal expansions and parameter estimation. Before any identification, excitation and response signals have to be correctly expanded in the polynomial basis. With Chebyshev polynomials, this requires the signals to be in the same narrow frequency bandwidth. In the presence of noisy signals, correct parameter identification can be performed with a new formulation by taking only central points within the time interval. This methodology can be generalized by defining any other point selection criterion with any other polynomials. This new formulation is first tested on a linear 3-DOF mechanical system and then extended to the parameter identification of a nonlinear mechanical component by using the product property of Chebyshev polynomials. The identification carried out on the hysteretic behavior measured and exhibited by a tape-spring actuator gives relevant parameter estimation. The proposed methodologies and formulations can be easily extended to other orthogonal functions in association with differential or integral transformations of differential equations.
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hal-00381480 , version 1 (29-05-2019)





Didier Remond, Julien Neyrand, Gwenaelle Aridon, Régis Dufour. On the improved use of Chebyshev expansion for mechanical system identification. Mechanical Systems and Signal Processing, 2008, 22 (2), pp.390-407. ⟨10.1016/j.ymssp.2007.07.011⟩. ⟨hal-00381480⟩
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