Finite element model updating for structural applications

Abstract

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.

Nonlinear Fe Model Updating for Masonry Constructions via Linear Perturbation and Modal Analysis

“…The model updating algorithm allows for minimizing the discrepancy between the experimental and numerical frequencies, as the materials' constants vary within a given set. As in the case of linear elastic materials addressed in [18,19] the minimum problem to be solved is a nonlinear least squares problem. In the presence of masonry materials a further nonlinearity, due to the dependence of the tangent stiffness matrix on the solution to the equilibrium problem, affects the objective function and makes it impossible to resort to the efficient model reduction techniques adopted in [18,19].…”

“…with f the vector of the measured frequencies, f (x) the vector of numerical frequencies obtained from (1) and w i suitable weights. A numerical method for FE model updating of structures made of linear elastic materials has been described in [18,19]. The minimum problem addressed in [18,19] is a nonlinear least squares problem: the objective function, having the form (2), is nonlinear as the frequencies f (x) depend nonlinearly on the vector x of material properties.…”

“…A numerical method for FE model updating of structures made of linear elastic materials has been described in [18,19]. The minimum problem addressed in [18,19] is a nonlinear least squares problem: the objective function, having the form (2), is nonlinear as the frequencies f (x) depend nonlinearly on the vector x of material properties. In this paper, another source of nonlinearity of Φ(x) is the dependence of K T (x), and then of f (x), on the solution of the equilibrium problem in step (1).…”

“…The algorithms implemented in NOSA-ITACA are based on those described in [20,21], and allow to manage a generic number of variables, as well as to get approximations at different levels of precisions. The details of the implementation are given in [22]. In the next sections the building blocks of our method are briefly explained, and then the approach is summarized in section 2.3.…”

“…Greater details on how to build such an approximation of Φ and on the effectiveness of the approach are given in [22].…”