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Conference Papers Year : 2014

Identification of time varying parameters using numerical differentiation by integration.


The present contribution is dedicated to the identification of mechanical parameters, especially time varying parameters for vibrating structures. The approach is experimentally illustrated with vertical beam having a time varying torsional stiffness (1-DOF mechanical system). In many identification techniques, space/time derivatives and noise sensitivity are recurring problems. Displacements (angle) and accelerations are necessary in the differential equation governing the mechanical behaviour of the structure. In rotating systems, angular sensors are commonly used and the angle is directly measured but the acceleration has to be estimated. The time derivatives of the recorded signals are computed using the Lanczos' generalized derivatives for higher orders. This kind of differentiation by integration methods allows an accurate and robust estimation of the acceleration of the measured input. Thanks to these estimated derivatives, the differential equation of motion of the structure can be partially reconstructed at each time step. Then, using short sliding windows where the unknown parameter is fit by a polynomial function, the coefficients defining these functions are computed using a weighted least square estimate. The unknown parameter and its time variation are then estimated by association of these polynomial expansions. The method is then applied to experimental data obtained from an equilateral beam excited in torsion while one beam support location is changed over time, creating a time varying torsional stiffness. Approach and results are analyzed and compared to another method based on the derivative formulation of the Chebyshev polynomial basis. This general method can be extended to system identification, structure identification, damage detection, etc. 1. Introduction
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hal-01059007 , version 1 (29-08-2014)


  • HAL Id : hal-01059007 , version 1


Simon Chesné, Catherine Chochol, Didier Rémond, F. Martel, Denis Rancourt. Identification of time varying parameters using numerical differentiation by integration.. 21st International Congress on Sound and Vibration, Jul 2014, Beijing, China. pp.1-8. ⟨hal-01059007⟩
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