Development of fuzzy probability based random fields for the numerical structural design

In structural analysis with multivariate random fields, the underlying distribution functions, the autocorrelations, and the crosscorrelations require an extensive quantification. While those parameters are difficult to measure in experiments, a lack of knowledge is included. Therefore, polymorphic uncertainty models are attained by involving uncertainty models with epistemic characteristic for the quantification of the stochastic models in this contribution. Three extensions for random fields with polymorphic uncertainty modeling are introduced. Interval probability based random fields, fuzzy probability based random fields, and structural dependent autocorrelations for random fields are shown. Applications for engineering problems are shown for each extension, where uncertainty analysis of structures with different materials is performed. In this contribution, a damage simulation of a concrete beam with interval valued parametrization of stochastic models, an application for porous media in a multiphysical structural analysis with fuzzy valued parametrization and an uncertainty analysis with structural dependent autocorrelations for timber structures are presented.