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Shock and Vibration
Volume 10, Issue 1, Pages 15-25

How Can Spatially Distributed Uncertainties Be Included in FEA and in Parameter Estimation for Model Updating?

M.W. Zehn and A. Saitov

Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Germany

Received 1 October 2001; Revised 24 May 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Owing to manufacturing composite materials and others show considerable uncertainties in wall-thickness, fluctuations in material properties and other parameter, which are spatially distributed over the structure. These uncertainties have a random character and can therefore not being reduced by some kind of mesh refinement within the FE model. What we need is a suitable statistical approach to describe the parameter changing that holds for the statistics of the process and the correlation between the parameter spatially distributed over the structure. The paper presents a solution for a spatial correlated simulation of parameter distribution owing to the manufacturing process or other causes that is suitable to be included in the FEA. The parameter estimation methods used in updating algorithms for FE-models, depend on the choice of a priori to be determined weighting matrices. The weighting matrices are in most cases assumed by engineering judgement of the analyst carrying out the updating procedure and his assessment of uncertainty of parameters chosen and measured and calculated results. With the statistical description of the spatial distribution at hand, we can calculate a parameter weighting matrix for a Baysian estimator. Furthermore, it can be shown in principle that with model updating it is possible to improve the probabilistic parameter distribution itself.