"Uncertainty quantification in finite element model updating"
Ellen Simoen(Department of Civil Engineering, K.U.Leuven)
Abstract
Finite element (FE) model updating is a technique where parameters of a FE model are calibrated such that the model output corresponds better with experimental observations of structural behaviour. In a structural mechanics context, the experimental data often consists of vibration data, i.e. time histories obtained from forced, ambient or hybrid vibration testing, as well as modal characteristics (i.e.eigenfrequencies, mode shapes ...) identified from these vibration tests. The actual determination of the FE model parameters based on observed data involves solving an inverse problem, which is usually formulated as a constrained optimization problem. The optimal model parameters are determined by minimizing a cost function that measures the discrepancy between the observed and predicted data. In many cases, however, the inverse problem is ill-posed, meaning that uniqueness, stability and even existence of the solution of the inverse problem cannot be guaranteed. Therefore, the quantification of uncertainties poses an important issue in FE model updating. There are always uncertainties associated with the FE model updating process: the presence of a measurement error causes uncertainty on the experimental data, whereas the modelling error results in uncertainty in the model predictions.
In this seminar, two complementary methods for uncertainty quantification in FE model updating are explored. A first method is based on Bayesian inference, where a prior probability density function (PDF) is updated to a posterior PDF that takes into account model and data uncertainties. In this approach, uncertainty is expressed by describing measurement and modelling error in a probabilistic manner. A second approach consists of an interval-based method for uncertainty quantification based on fuzzy set theory, where uncertainty is represented by a range on uncertain parameters. For both approaches, the description and quantification of uncertainty is based on stimates of the errors, engineering judgement or a combination of both.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
