Lucas Hermann, M.Sc.
Schleinitzstraße 20
38106 Braunschweig
Telephone: 0531/391-62123
Research project:
Data Fusion with the statistical Finite Element Method
A problem with Finite Element Method (FEM) simulations is that they often do not reflect reality close enough in order to properly match given measurement data of a real system. The statFEM, i.e. statistical FEM, approach can be used to fuse sensor data with an FEM model.
Thereby, the FEM model is considered as a Bayesian prior and the uncertainty is quantified in form of a Gaussian Process (GP). The advantage of using a GP instead of another surrogate model is the closed algebraic form for the posterior which can be derived if all uncertainties are Gaussian. By conditioning the prior on given data, which can be measurement data from an experiment or created synthetically, it is shown that a posterior Gaussian Process can be generated for the behavior of the model solution in the domain. The Also, the measured data is decomposed into three parts: Model, misspecification and noise. The misspecification term is also based on a GP and the hyperparameters are learned according to the data.
This combination makes it possible to describe the posterior much better in terms of an estimated mean and also the variance for each point in the domain.
The core reasearch topic is to establish a statFEM approach for linear dynamic systems in frequency domain. This could for instance, in context of the RTG, be used for a more efficient monitoring of structures equipped with sensors (structural health monitoring), for structural design involving error margins which properly reflect reality and for research on novel methods to model errors and damage in materials.
Another topic is the combination of reduced order models with statFEM. This could lead to an overall improved model both in terms of accuracy and cost, especially for frequency sweeps.