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vol. 6, nr. 3 (2005)
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Aapproximation of the retardation spectrum of viscoelastic plant materials using Lagendre functions
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Anna Stankiewicz
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Department of Technical Science, University of Agriculture, ul. Doświadczalna 50A, 20-280 Lublin |
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vol. 6 (2005), nr. 3,
pp. 794-813
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abstract:
The paper deals with the problem of direct recovery of continuous retardation spectrum of linear viscoelastic materials from discrete-time noise measurements of creep compliance obtained in a standard creep experiment. An optimal orthogonal scheme of the spectrum approximation by the finite series of Legendre functions is presented. Since the problem of retardation spectrum identification is practically an ill-posed problem of reconstructing solution of Fredholm integral equation of the first kind from measured data, Tikhonov regularization with generalized cross validation (GCV) is used to guarantee the stability of the scheme. It is proved that the accuracy of the spectrum approximation depends both on measurement noises and regularization parameter as well as on the proper selection of the basic orthogonal functions. Numerical calculations on model data are enclosed.
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keywords:
viscoelasticity, retardation spectrum, identification algorithm, regularization, Legendre functions
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original in:
Polish
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