Technical Report: UTEP-CS-12-44a

To appear in Mechanical Systems and Signal Processing.


Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another.