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Finite element model updating for structural applications. (English) Zbl 07169492
Summary: A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown material parameters (such as mass density and Young’s modulus) of the materials and/or the boundary conditions, which are often known only approximately. In particular, this is the case when considering historical buildings.
The straightforward application of a general-purpose optimizer can be impractical, given the large size of the model involved. In the paper, we show that, by slightly modifying the projection scheme used to compute the eigenvalues at the lowest end of the spectrum one can obtain local parametric reduced order models that, embedded in a trust-region scheme, form the basis for a reliable and efficient specialized algorithm.
We describe an optimization strategy based on this approach, and we provide numerical experiments that confirm its effectiveness and accuracy.
MSC:
65F18 Numerical solutions to inverse eigenvalue problems
15A22 Matrix pencils
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
70J10 Modal analysis in linear vibration theory
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