Quantifying uncertainty for structural damage identification in the presence of model errors from a deterministic sensitivity-based regime

Abstract

Structural damage identification is often recast as the procedure to find the damage parameters from the measured data and the prescribed structural model. However, noises are encountered inevitably in practical tests and this essentially introduces uncertainty into damage identification. Most of the existed damage identification methods are deterministic and unable to provide the uncertainty information. In this paper, the widely-used sensitivity approach, though being deterministic, is further explored and extended for uncertainty quantification. The key lies in the equivalence between Tikhonov regularization in the sensitivity approach and the prior distribution in Bayesian inference. Motivated by this equivalence, a new uncertainty quantification approach is proposed where the uncertainty information is directly drawn from the deterministic sensitivity-based regime. As is noteworthy, the proposed approach can quickly quantify the uncertainty even when the probabilistic information of the measurement noise and the prior distribution are unknown. Furthermore, considering the model errors, a measurement-changes-correction strategy is adopted where the measured data is simply corrected by pre-post measurement changes and by this way, uncertainty is quantified in the same sensitivity-based regime. Numerical examples and an experimental case are studied to verify the effectiveness of the proposed approach for uncertainty quantification in structural damage identification.