Imprecise stochastic dynamics via operator norm theory

This contribution presents a highly efficient and effective approach to bound the reliability of linear structures subjected to combinations of epistemic and aleatory uncertainty. These combinations can take the form of imprecise probabilities or hybrid uncertainties. Typically, the computation of the bounds on the reliability involves solving a nested double loop problem, which is intractable without resorting to surrogate modeling schemes. In this paper, a method is presented to break this double loop by virtue of the operator norm theorem. Indeed, in case linear models are considered, the paper shows that the computational efficiency of propagating these uncertainties can be reduced to solving two optimization problems and two calculations of the structural reliability. A case study involving a finite element model of a six-story building is included to illustrate the application, efficiency and effectivity of the developed technique.