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.

In Bayesian model updating, probability density functions of model parameters are updated accounting both for the information contained in the data and for uncertainties present in the measurements and model predictions, requiring a probabilistic model for the error between predictions and observations. Most often, a zero-mean uncorrelated Gaussian prediction error is assumed, although in many engineering applications prediction errors will show non-negligible spatial and/or temporal correlation (e.g. when densely populated sensor grids are used). In this paper, the effect of prediction error correlation on the results of the Bayesian model updating scheme is studied, and it is investigated how the challenging task of selecting a suitable prediction error correlation structure can be addressed appropriately. In two illustrative applications, it is demonstrated that Bayesian model class selection can be effectively applied to this end, ensuring more realistic modeling and corresponding Bayesian model updating results.

In this paper, Bayesian linear finite element (FE) model updating is applied for uncertainty quantification (UQ) in the vibration-based damage assessment of a seven-story reinforced concrete building slice. This structure was built and tested at full scale on the USCD-NEES shake table : progressive damage was induced by subjecting it to a set of historical earthquake ground motion records of increasing intensity. At each damage stage, modal characteristics such as natural frequencies and mode shapes were identified through low amplitude vibration testing; these data are used in the Bayesian FE model updating scheme. In order to analyze the results of the Bayesian scheme and gain insight into the information contained in the data, a comprehensive uncertainty and resolution analysis is proposed and applied to the seven-story building test case. It is shown that the Bayesian UQ approach and subsequent resolution analysis are effective in assessing uncertainty in FE model updating. Furthermore, it is demonstrated that the Bayesian FE model updating approach provides insight into the regularization of its often ill-posed deterministic counterpart.

Bayesian finite element (FE) model updating is used for uncertainty quantification (UQ) purposes in the vibration-based damage assessment of a seven-story reinforced concrete building slice. This structure was built and tested at full scale on the USCD-NEES shake table: a progressive damage pattern was induced by subjecting the structure to a number of historical earthquake records. At each damage stage, modal characteristics (i.e. natural frequencies and mode shapes) were determined through vibration testing, these data are used in the Bayesian FE model updating schemes. In order to analyze the results of the Bayesian scheme and gain insight into what information is contained in the data, a comprehensive uncertainty and resolution analysis performed. It is shown that the Bayesian UQ approach and subsequent resolution analysis are effective in assessing uncertainty in FE model updating. Furthermore, it is demonstrated that insight into the Bayesian FE model updating approach provides a very natural way to regularize its often ill-posed deterministic counterpart.

No abstract

No abstract

No abstract

No abstract