Machine learning based optimization for interval uncertainty propagation

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 employ a machine learning based optimization strategy, so-called Bayesian optimization, evaluating upper and lower bounds generic response variable over set possible responses obtained when each varies independently its range. The lack knowledge caused not function all combinations variables is accounted developing probabilistic description itself using Gaussian Process regression model. An iterative procedure developed selecting small number simulations to be evaluated updating this statistical model well-established acquisition functions assess bounds. In both approaches, an initial training dataset defined. While one approach builds iteratively two distinct datasets separately variable, other single dataset. Consequently, will produce different bound estimates at iteration. expressed point from mean posterior distribution. Moreover, confidence on estimate provided effectively communicating engineers these combination which no simulation has been run. Finally, metrics define conditions assessing if predicted can considered satisfactory. applicability illustrated numerical applications, focusing vibration vibro-acoustics.