Estimating uncertain regions on small multidimensional datasets using generalized PDF shapes and polynomial chaos expansion

Abstract

In uncertainty analysis, estimating the degree of uncertainty based on some physical experiments is an essential part of the process to create robust products. Both at the input and the output side of an available model, experiments may be done, which can then be (inverserely) propagated to obtain uncertain results on the other side. In probabilistic analysis, PDF shape, stochastic moments and correlation may be inferred from this data. In possibilistic analysis, these quantities are hard to interpret physically and are therefore difficult to compute. Instead, interval bounds and dependency information can be determined. This paper presents a strategy to infer both interval bounds and dependency information from a (limited) set of data points in a multidimensional space, based on Polynomial Chaos Expansion and a generalized Probability Density Distribution (PDF) shape.status: accepte