Density filtering regularization of finite element model updating problems

• Published in: Mechanical systems and signal processing 2019-08, Vol.128, p.282-294
• Main Authors: Reumers, P., Van hoorickx, C., Schevenels, M., Lombaert, G.
• Format: Article
• Language: English
• Subjects: Algorithms; Conditioning; Damage detection; Density; Density filter; Filtration; Finite element method; Finite element model updating; Mathematical models; Model updating; Nondestructive testing; Optimization; Parameter estimation; Regularization; Regularization methods; Spatial data; Spatial resolution; Stiffness; Structural damage
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2019.03.038

•A density filtering regularization method is proposed to smooth out strong local stiffness variations.•The density filter controls the length scale of the damaged zone by selecting a proper filter radius.•The method is compared with classical Tikhonov regularization in a numerical case study.•Compared with Tikhonov regularization, density filtering is found to be more successful in identifying the damaged zone. Finite element (FE) model updating is often used as a non-destructive method to detect structural damage. Stiffness parameters of an FE model of the structure are calibrated based on experimental vibration data. If the desired spatial resolution is high, the problem is likely to be ill-conditioned and requires regularization. Tikhonov regularization is frequently used for FE model updating problems, but the selection of a proper regularization parameter and a good initial estimate of the stiffness parameters is difficult. This paper proposes an alternative, density-filtering-based method where the filter radius acts as regularization parameter. Since the filter radius controls the minimal length scale of the identifiable damaged zones, it has a clear physical meaning. Furthermore, an initial estimate of the stiffness parameters is only required as a starting point for the optimization algorithm whereas in the case of Tikhonov regularization it also guides the optimization. Both regularization methods are compared in a numerical case study. The density filtering regularization method is found to be more successful in identifying the damaged zone, while Tikhonov regularization sometimes fails to do so.