Stochastic inverse problems
Principal investigator: Joseph Nagel
Description
Bayesian inference establishes a convenient framework for uncertainty quantification and data analysis of engineering systems. It allows one to represent, update and propagate epistemic uncertainties probabilistically. The uncertainty of physical model parameters, that are not directly observable, is represented as the prior distribution. By analyzing experimental data, that are only indirectly related to the model parameters, one can update the prior into the posterior distribution. This reduces the uncertainty of the model parameters and thus allows for more adequate model predictions. Most often the posterior distribution has to be approximated by means of sampling methods such as Markov chain Monte Carlo.
In this project we aim at developing new methods for Bayesian inference and inverse modelling in civil engineering applications. To this end one has to overcome the characteristic challenges that are typically encountered in practical problems. This includes the presence of aleatory uncertainty, i.e. parameters such as environmental conditions naturally vary, and the computational expense of the model that relates the unknown parameters to the observed data, e.g. computer models based on the finite element method. Hierarchical Bayesian models are used in order to enable inference in complex experimental situations involving both epistemic and aleatory uncertainties [1, 2]. For instance, this can facilitate the experimental analysis of the compressive strength of structural masonry [3]. In order to increase the efficiency of posterior computations, we rely on advanced stochastic sampling strategies such as Hamiltonian Monte Carlo [4]. Moreover, novel deterministic alternatives for computing the posterior density based on spectral likelihood expansions are developed [5].