Distributed Parameter Model Updating using the Karhunen-Loeve Expansion
S Adhikari & MI Friswell (Swansea University)
Mechanical Systems and Signal Processing, Vol. 24, No. 2, February 2010, pp. 326-339
Discrepancies between experimentally measured data and computational predictions are unavoidable for complex engineering dynamical systems. To reduce this gap, model updating methods have been developed over the past three decades. Current methods for model updating often use discrete parameters, such as thickness or joint stiffness, for model updating. However there are many parameters in a numerical model which are spatially distributed in nature. Such parameters include, but are not limited to, thickness, Poisson's ratio, Young's modulus, density and damping. In this paper a novel approach is proposed which takes account of the distributed nature of the parameters to be updated, by expressing the parameters as spatially correlated random fields. Based on this assumption, the random fields corresponding to the parameters to be updated have been expanded in a spectral decomposition known as the Karhunen-Loeve (KL) expansion. Using the KL expansion, the mass and stiffness matrices are expanded in series in terms of discrete parameters. These parameters in turn are obtained using a sensitivity based optimisation approach. A numerical example involving a beam with distributed updating parameters is used to illustrate this new idea.
This material has been published in the Mechanical Systems and Signal Processing, Vol. 24, No. 2, February 2010, pp. 326-339, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the Elsevier.
Link to paper using doi: 10.1016/j.ymssp.2009.08.007
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