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This contribution extends the known optimal uncertainty quantification (OUQ) framework to the capability of polymorphic uncertainty quantification by presenting two approaches to incorporate aleatory uncertainties, in addition to the epistemic uncertainties in the original framework. This enables the calculation of the sharpest bounds on the probability of failure of engineering structures given uncertain input quantities which may or may not follow specified stochastic distribution functions. This will be of practical relevance for most engineering problems since typically a lot of data are only available for some uncertain quantities allowing for the approximation through stochastic distribution functions, whereas for some quantities only quite limited data are available which prohibits the use of stochastic distributions for those quantities. To this end, two different approaches are proposed mainly differing in accuracy and computational effort. In addition to that, the alpha-level discretization known from fuzzy analysis is incorporated in order to allow a suitable analysis of varied sets of considered input data on the uncertain quantities. In order to achieve an overall speedup of the numerical procedure, the Dirac parameterization as part of the OUQ is transformed to the space of canonical moments. The presented method is demonstrated by means of two basic mechanical problems to show the capabilities and performance.
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