Sensitivity-based model updating for structural damage identification using total variation regularization

Abstract Sensitivity-based Finite Element Model Updating (FEMU) is one of the widely accepted techniques used for damage identification in structures. FEMU can be formulated as a numerical optimization problem and solved iteratively making automatic updating of the unknown model parameters by minimizing the difference between measured and analytical structural properties. However, in the presence of noise in the measurements, the updating results are usually prone to errors. This is mathematically described as instability of the damage identification as an inverse problem. One way to resolve this problem is by using regularization. In this paper, we compare a well established interpolation-based regularization method against methods based on the minimization of the total variation of the unknown model parameters. These are new regularization methods for structural damage identification. We investigate how using Huber and pseudo Huber functions in the definition of total variation affects important properties of the methods. For instance, for well-localized damages the results show a clear advantage of the total variation based regularization in terms of the identified location and severity of damage compared with the interpolation-based solution. For a practical test of the proposed method we use a reinforced concrete plate. Measurements and analysis were performed first on an undamaged plate, and then repeated after applying four different degrees of damage.

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