Stochastic Simulation Methods for Structural Reliability under Mixed Uncertainties (2020)

Supervisors: Prof. Dr. Michael Beer (Leibniz Universität Hannover, Germany)

Keywords: Uncertainty quantification; Imprecise probabilities; Line sampling; Active Learning; Gaussian process regression; Bayes rule; Dimension reduction

Uncertainty quantification (UQ) has been widely recognized as an important and challenging task in structural engineering. This thesis contributes three developments concerning efficient numerical propagation of mixed uncertainties, including aleatory and epistemic uncertainties. First, a generalized Non-intrusive Imprecise Stochastic Simulation (NISS) method is proposed to successfully solve the NASA Langley UQ challenge. Second, the classical line sampling is injected into the NISS framework to substantially improve the efficiency of rare event analysis. Third, an active learning strategy is embedded into line sampling procedure to tackle highly nonlinear problems. The effectiveness of those developments is clearly interpreted with real-world test examples.