ABSTRACT
The realistic quantification of uncertainties and their numerically efficient processing in complex analyses are the two key challenges in this context. This chapter presents emerging concepts and approaches which address these challenges in three directions. Due to the inherent uncertainties, a deterministic description of the problem cannot reflect its nature and physics appropriately and needs to be very conservative approximation in order to not compromise the safety requirements. On the economic side, the effects of uncertainties, which have not been accounted for in a realistic manner materialise in unexpected maintenance costs, which sometimes even exceed the cost of a new structure. The explicit quantification of the effects of uncertainties increases these computational costs by order of magnitude. Aleatory uncertainties refer to variability, which can be captured with probabilistic concepts, and epistemic uncertainty is commonly associated with subjectivity. Aleatory uncertainty and subjective probabilistic information are captured in probabilistic models, and imprecision in the probabilistic model specification is described with fuzzy sets.
