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In structural engineering, model updating is often used for non-destructive damage assessment: by calibrating stiffness parameters of finite element models based on experimentally obtained (modal) data, structural damage can be identified, quantified and located. However, the model updating problem is an inverse problem prone to ill-posedness and ill-conditioning. This means the problem is extremely sensitive to small errors, which may potentially detract from the method's robustness and reliability. As many errors or uncertainties are present in model updating, both regarding the measurements as well as the employed numerical model, it is important to take these uncertainties suitably into account. This paper aims to provide an overview of the available approaches to this end, where two methods are treated in detail: a non-probabilistic fuzzy approach and a probabilistic Bayesian approach. These methods are both elaborated for the specific case of vibration-based finite element model updating for damage assessment purposes.

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A new probabilistic finite element(FE) model updating technique based on Hierarchical Bayesian modeling is proposed for identification of civil structural systems under changing ambient/environmental conditions. The performance of the proposed technique is investigated for (1) uncertainty quantification of model updating parameters, and (2) probabilistic damage identification of the structural systems. Accurate estimation of the uncertainty in modeling parameters such as mass or stiffness is a challenging task. Several Bayesian model updating frameworks have been proposed in the literature that can successfully provide the "parameter estimation uncertainty" of model parameters with the assumption that there is no underlying inherent variability in the updating parameters. However, this assumption may not be valid for civil structures where structural mass and stiffness have inherent variability due to different sources of uncertainty such as changing ambient temperature, temperature gradient, wind speed, and traffic loads. Hierarchical Bayesian model updating is capable of predicting the overall uncertainty/variability of updating parameters by assuming time-variability of the underlying linear system. A general solution based on Gibbs Sampler is proposed to estimate the joint probability distributions of the updating parameters. The performance of the proposed Hierarchical approach is evaluated numerically for uncertainty quantification and damage identification of a 3-story shear building model. Effects of modeling errors and incomplete modal data are considered in the numerical study.