Efficient Utilization of Surrogate Models for Uncertainty Quantification

Abstract

AbstractNumerical simulations for the analysis and the design of structures or systems are often based on deterministic characteristics, whereas the reality is determined by data and information which are characterized by various types of uncertainty (variability, imprecision, inaccuracy, incompleteness). Besides traditional probabilistic approaches, possibilistic uncertainty models are most recently in the focal point of research. Combining the characteristics of aleatoric and epistemic uncertainties, polymorphic uncertainty yields various uncertainty approaches related to the application field of imprecise probability models. Uncertainty analysis schemes, based on pointwise evaluation of a fundamental solution (structural analysis), usually lead to high computational costs, due to repetitive evaluations. Especially for complex uncertainty models, each uncertainty characteristic demands a separate quantification. Hence, surrogate models are indispensable in uncertainty quantification.Considering complex, high dimensional structural models, even single model evaluations are defined by significant computational cost. Therefore, the transition from traditional space‐filling sampling schemes towards adaptive sampling schemes allows for an overall decrease of computational cost while maintaining a necessary accuracy of the prediction. A variance based adaptive sampling strategy is proposed, constituted by the combination of exploration and exploitation of a given input space. The predictions' variances of multiple surrogate models are hereby utilized to detect regions of interest and define sampling points accordingly.The contribution briefly introduces the fundamentals of fuzzy‐set theory and interval based uncertainty analysis as well as a polymorphic uncertainty model. A generalized computational framework for uncertainty analysis is presented with special respect to corresponding computational effort. Subsequently, a concept for an variance based sampling scheme is explained and further utilized in an uncertainty analysis of a multi story structural example with uncertain material properties.