Regularization in Structural Model Updating in the Presence of Noisy Data

This article addresses the presence of noise when solving the inverse problem of determining the material properties of an elastic engineering structure from measured vibration data. After identifying the frequencies, material properties are determined by solving an optimization problem. However, if the experimental frequencies are affected by noise (as often happens in practice), this can lead to inaccuracy due to the ill-conditioning of the problem. A regularization strategy based on Tikhonov regularization is discussed, and an automatic regularization parameter choice is introduced to deal with cases where the noise level is not known beforehand. The algorithm is tested on three examples, including artificial models where the exact solution is known and a case study from the Matilde donjon in Livorno, with experimental data measured by seismic stations during ambient vibration tests. The proposed method consistently performs well across all tests, validating the reliability of the approach.