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A sensitivity‐based finite element model updating based on unconstrained optimization problem and regularized solution methods

An effective and reliable approach to updating finite element (FE) models of real structures is to utilize a sensitivity‐based strategy. A challenging issue concerning the sensitivity‐based finite element model updating (FEMU) is to create a well‐established framework for updating the inherent structural properties of FE models under incomplete noisy modal data. When noise contaminates the measured modal parameters, another challenging issue stems from the ill‐posedness of the FEMU inverse problem. This article proposes an innovative sensitivity‐based FEMU strategy based on the combination of modal kinetic energy and modal strain energy for simultaneously updating the element mass and stiffness matrices of FE models. The great novelty of this strategy is to get an idea from the unconstrained optimization problem for the establishment of a sensitivity‐based FEMU framework. The correction of the element mass and stiffness matrices in a simultaneous way is another novelty of the proposed FEMU strategy. Moreover, new iterative and hybrid regularization methods under the Krylov subspace theory and bidiagonalization process are presented to solve the ill‐posed inverse problem of FEMU. The accuracy and reliability of the proposed methods are numerically validated by a two‐story concrete frame and a two‐span continuous steel truss along with some comparative analyses. Results demonstrate that the suggested sensitivity‐based strategy and regularized solution methods are influential and successful in FEMU under incomplete noisy modal data.