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Conference Papers Year : 2014

Identification of time varying stiffness using derivative estimator and polynomial basis


The identification of time varying parameters of mechanical systems is a typical case of inverse problem treated in engineering. Parameter variations have various origins (crack apparition/propagation, temperature variation, ice deposit, etc…) and can be sources of serious problems as well as good indicators for system monitoring. The detection and quantification of these variations is essential before any analysis is performed on the system. The present contribution is then dedicated to the identification of time varying mechanical parameters for vibrating structures (illustrated by a time varying rotational stiffness). 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 behavior of the structure. In rotating systems, angular sensors are commonly used and the angle is directly measured but the acceleration has to be estimated. In the proposed approach, the time derivatives of the recorded signals are computed using the Lanczos’ generalized derivatives for higher orders. This kind of differentiation byintegration 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. First, the approach is presented and tuned in simulation. Many parameters, including the length of the integration domain and the size of the polynomial expansion, have to be optimized through the analysis of simulated results. Then, the method is 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 (1-DOF mechanical system). Finally, approach and results areanalyzed and compared to another method based on the derivative formulation of the Chebyshev polynomial basis. This general method can as well be extended to system identification, structure identification, damage detection, etc
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hal-01074979 , version 1 (16-10-2014)


  • HAL Id : hal-01074979 , version 1


Simon Chesné, F. Martel, Catherine Chochol, Denis Rancourt, Didier Rémond. Identification of time varying stiffness using derivative estimator and polynomial basis. ISMA International conference on Noise and Vibration Engineering, Sep 2014, LEUVEN, Belgium. ⟨hal-01074979⟩
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