  Two non-intrusive uncertainty propagation approaches are proposed for the
performance analysis of engineering systems described by expensive-to-evaluate
deterministic computer models with parameters defined as interval variables.
These approaches employ a machine learning based optimization strategy, the
so-called Bayesian optimization, for evaluating the upper and lower bounds of a
generic response variable over the set of possible responses obtained when each
interval variable varies independently over its range. The lack of knowledge
caused by not evaluating the response function for all the possible
combinations of the interval variables is accounted for by developing a
probabilistic description of the response variable itself by using a Gaussian
Process regression model. An iterative procedure is developed for selecting a
small number of simulations to be evaluated for updating this statistical model
by using well-established acquisition functions and to assess the response
bounds. In both approaches, an initial training dataset is defined. While one
approach builds iteratively two distinct training datasets for evaluating
separately the upper and lower bounds of the response variable, the other
builds iteratively a single training dataset. Consequently, the two approaches
will produce different bound estimates at each iteration. The upper and lower
bound responses are expressed as point estimates obtained from the mean
function of the posterior distribution. Moreover, a confidence interval on each
estimate is provided for effectively communicating to engineers when these
estimates are obtained for a combination of the interval variables for which no
deterministic simulation has been run. Finally, two metrics are proposed to
define conditions for assessing if the predicted bound estimates can be
considered satisfactory.
