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On the Use of Regularisation Techniques for Finite Element Model Updating

Ziaei Rad, S. and Imregun, M.

Inverse Problems in Engineering, Vol. 7, pp 471-503, 1999



The first part of this paper is a review of existing regularisation techniques with emphasis on the updating of finite element models for structural dynamics. Tikhonov regularisation, truncated singular value decomposition, total least-squares method and maximum entropy method are examined in some detail for their applicability to a set of noise-polluted linear equations arising from the use of measured vibration test data. Several comparative studies were conducted for three simulated examples: a 10-DOF mass-spring system, a 3D frame and a plate structure. A frequency response function based updating technique, that yields an over-determined set of equations by selecting data from a number of frequency points, was used throughout the numerical investigation. For most methods, the correct choice of the controlling regularisation parameter, such as the SVD truncation level, was found to be of primary importance for improving the quality of the solution. Possible parameter selection strategies were identified and discussed in some detail. The total least-squares method was observed to be particularly useful for dealing with noise and its accuracy was seen to increase with the increasing number of measurements. Using an L-curve technique, the determination of an optimum regularisation parameter was relatively straightforward for the maximum entropy method. However, the method was also found to be computationally very expensive. For all three cases considered, the improvement in the solution accuracy did not appear to warrant the additional computational effort required.



FE model updating, vibration analysis, regularisation parameter selection


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