Vahab Baghadam Narouie, M.Sc.
Pockelsstraße 3
38102 Braunschweig
Telefon: 0531/391-94525
Forschungsvorhaben:
Polynomial-chaos-based Statistical Finite Element Method (PC-statFEM) in Linear and Nonlinear Material Models
The study of physical systems based on models has been essential to science, engineering, and industry. Models are mathematically described using partial differential equations (PDEs). The Finite Element Method (FEM) and Isogeometric Analysis (IGA) schemes approximate their solution by solving a discretized problem on a finite mesh of the PDE domain.
Even if we could specify all parameters of a specific physical model, this would not necessarily prevent systematic measurement errors, and therefore, it does not guarantee satisfactory predictions. The investigation of different sources and levels of inaccuracy, errors in numerical analysis, and the model itself is the objective of uncertainty quantification (UQ). Uncertainty quantification generally requires an enormous number of model evaluations, which may not be attainable. Therefore, surrogate modelling has been increasingly investigated in the last decade. Polynomial Chaos Expansions (PCE) is a technique that surrogates the computational model with a series of orthonormal polynomials in the input variables.
Recently, there has been an expanding interest in adopting emerging sensing technologies for instrumentation within various structural systems. Wireless sensors, digital video cameras, and sensor networks are emerging as sensing paradigms that collect data for their in situ monitoring. Assimilating these observed data with the solution of surrogate models empowers to inspect the uncertain behavior of the true physical system.
The newly suggested statistical finite element method (statFEM) in [1] allows us to infer the behavior of the true physical system by incorporating observed data with the mismatched finite element model. In fact, by adopting a Bayesian formalism, all uncertainties, e.g., physical parameters of the model, measurement errors, and imprecision of the computer model, are considered random variables.
For this purpose, the research topic will develop the intrusive and non-intrusive Polynomial chaos expansion for statFEM. The uncertainties in material parameters will be implemented with linear elastic, hyperelastic and elastoplastic material models. In light of observation data obtained from sensors, the hyperparameters are being estimated. The hyperparameters reflect the model-reality mismatch and the measurement errors. With this framework, the true system behavior based on Bayesian formalism can be predicted.
Additional Literature:
[1] Girolami, Mark, et al. "The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions." Computer Methods in Applied Mechanics and Engineering 375 (2021): 113533.