Modeling and Analysis with Epistemic Uncertainties

Epistemic uncertainties appear across all engineering fields to quite some significant extent. Although they can often be described phenomenologically and qualitatively, they counteract a rigorous quantitative description, which is needed as a basis for a realistic risk assessment. In the presence of epistemic uncertainties the specification of a probabilistic model and the associated risk analysis lead to hypothetical results presuming some intuitive guess to capture the influence of the epistemic uncertainty. That is, we quantify risk based on conditions that represent assumptions rather than facts. Such results can be significantly misleading. It is thus of paramount importance to quantify epistemic uncertainties most realistically. This quantification should neither introduce unwarranted information nor should it neglect information. On this basis there is a clear consensus that epistemic uncertainties need to be taken into account for a realistic assessment of risk and reliability. However, there is no clearly defined procedure to master this challenge. There are rather a variety of concepts and approaches available to deal with epistemic uncertainties, from which the engineer can chose. This choice is made difficult by the perception that the available concepts are competing and opposed to one another rather than being complementary and compatible. Clearly, the first consideration should be devoted to a probabilistic modelling, naturally through subjective probabilities, which express a belief of the expert and can be integrated into a fully probabilistic framework in a coherent manner via a Bayesian approach. While this pathway is widely accepted and recognized as being very powerful, the potential of set-theoretical approaches and imprecise probabilities has only been utilized to some minor extent. Those approaches, however, attract increasing attention in cases when available information is not rich enough to meaningfully specify subjective probability distributions. The presentation will feature models for epistemic uncertainties, and it will highlight their capabilities and added value when used for engineering analysis and design. Illustrative examples are used to explain the respective features. The discussion on the models is complemented by presenting a powerful numerical technology for processing epistemic uncertainties even in very complex and nonlinear engineering analyses. This technology can be used not only for reliability analysis, but also for sensitivity analysis, design, model updating and more.