Uncertainty Quantification in Finite Element Model Updating (Het begroten van onzekerheden in eindige-elementenmodelupdating)
Uncertainty Quantification in Finite Element Model Updating
Simoen, Ellen; S0104678
The validity and accuracy of numerical models is crucial in all science and engineering fields, as these models are typically used to analyze and design structures and to predict future structural behavior. For existing structures, model updating techniques allow for the calibration of uncertain or unknown characteristics of the model, based on experimentally observed data. In a civil engineering context, vibration data such as natural frequencies and mode shapes are often used to update model parameters characterizing a finite element (FE) model. The deterministic model updating process consists in solving an inverse problem where the model parameters are searched so that the observed system behavior is predicted in the best possible way. In many cases, however, this inverse problem is ill-posed, meaning that uniqueness, stability and even existence of the solution of the inverse problem cannot be guaranteed. This is a non-negligible issue in model updating, as modeling errors and measurement errors are unavoidably present. In this work, two alternative methods are explored to account for uncertainty in model updating: a non-probabilistic interval-based method founded on fuzzy set theory, and a probabilistic method based on Bayesian inference. The workings behind both uncertainty quantification (UQ) approaches are investigated in detail, and benefits and shortcomings are discussed and addressed where possible. The fuzzy approach is very well-suited to compute worst-case scenarios at several uncertainty levels, but its straightforward application to the inverse model updating problem proves particularly challenging as it entails solving an involved nested optimization problem. This is partly resolved by proposing an alternative formulation which only requires forward computations. The Bayesian inference approach is commonly applied for UQ purposes in inverse problems such as model updating; it allows for detailed insight into parameter resolution and interactions. In this thesis, particular attention is paid to the development of effective methods for exploring the posterior results, and to the construction of the likelihood function.