Representation and Propagation of both Probabilistic and Interval Uncertainty

This paper develops and illustrates a probabilistic approach for uncertainty representation and propagation in system analysis, when the information on the uncertain input variables and/or their distribution parameters may be available as either probability distributions or simply intervals (single or multiple). The uncertainty described by interval data is represented through a flexible family of probability distributions. Conversion of interval data to a probabilistic format enables the use of computationally efficient methods for probabilistic uncertainty propagation. Two methods are explored for the implementation of the proposed approach, based on: (1) sampling and (2) optimization. The sampling based strategy is more expensive and tends to underestimate the output bounds. The optimization based methodology improves both aspects.