Numerical simulation of structures using generalized models for data uncertainty

Abstract

The challenging task in computational engineering is to model and predict numerically the behaviour of engineering structures in a realistic manner. Beside sophisticated computational models and numerical procedures to map physical phenomena and processes onto structural responses, an adequate description of available data covering the content of provided information is of prime importance. Generally, the availability of information in engineering practice is limited due to available resources. Far beyond the capability to specify crisp values, data are imprecise, diffuse, fluctuating, incomplete, fragmentary and frequently expert specified. Beside objective characteristics like randomness, available data are influenced by subjectivity to a considerable extend. This impedes the specification of probabilistic models with crisp parameter values to describe the uncertainty. Applying imprecise probabilities objective components of the uncertainty as well as subjective components can be considered simultaneously. A sophisticated procedure to handle imprecise probabilities provide the uncertainty model fuzzy randomness. Since fuzziness, randomness, and fuzzy randomness can be processed simultaneously, it is denoted as generalized uncertainty model. The models are demonstrated by means of a numerical example to emphasize their features and to underline their applicability.

Cross-Domain Tolerance Analysis for Directional Control Valves Based on Imperfect Information

“…The associated high number of model evaluations usually leads to an impractical computational effort. Therefore, [5] proposes a sample-based determination of the cumulative distribution functions for the measures Bel Y and P l Y . In addition, to further reduce the computational effort, it's recommended to use meta-models and to progressively include only evidences for those input variables x i , against which y has the highest sensitivities.…”