Finite Element Structural Analysis using Imprecise Probabilities Based on P-Box Representation

Imprecise probability identifies a number of various mathematical frameworks for making decisions when precise probabilities (or PDF) are not known. Imprecise probabilities are normally associated with epistemic sources of uncertainty where the available knowledge is insufficient to construct precise probabilities. While there is no “unified theory of imprecise probabilities”, most frameworks describe the uncertainty in terms of bounded possibilities or unknown probabilities between a specified lower and upper bounds. In this paper, the authors’ previous developed interval finite element methods are extended to compute pbox structures of a finite element solution where loading parameters are described by p-box structures. Both discrete p-box structures and interval p-box Monte Carlo algorithms are presented along with example problems that illustrate the capabilities of the new methods. The computational efficiency of the p-box finite element methods is also presented.