Using random set theory to propagate epistemic uncertainty through a mechanical system

The Epistemic Uncertainty Project of Sandia National Laboratories (NM, USA) proposed two challenge problems intended to assess the applicability and the relevant merits of modern mathematical theories of uncertainty in reliability engineering and risk analysis. This paper proposes a solution to Problem B: the response of a mechanical system with uncertain parameters. Random Set Theory is used to cope with both imprecision and dissonance affecting the available information. Imprecision results in an envelope of CDFs of the system response bounded by an upper CDF and a lower CDF. Different types of parameter discretizations are introduced. It is shown that: (i) when the system response presents extrema in the range of parameters considered, it is better to increase the fineness of the discretization than to invoke a global optimization tool; (ii) the response expectation differed by less than 0.5% when the number of function calls was increased 15.7 times; (iii) larger differences (4–5%) were obtained for the lower tails of the CDFs of the response. Further research is necessary to investigate (i) parameter discretizations aimed at increasing the accuracy of the CDFs (lower) tails; (ii) the role of correlation in combining information.