Dynamical analysis of plate models with uncertain structural properties using the interval field method

Abstract

In uncertainty quantification, interval arithmetic provides an appropriate procedure when little knowledge is available on the nature of the probability distribution of uncertain or imprecise quantities. This commonly occurs in engineering applications due to subjective knowledge or incomplete availability of test data. Intervals are by definition unable to take into account dependent input and output quantities, which forces the assumption of independency when applying them. This is a severe limitation on the accuracy of the analysis as dependency is always present to some extent. The concept of interval fields (IF) [1] provides a solution by defining non-deterministic fields using interval parameters. In its simplest form [2], the field is expressed as a weighted sum of basis functions, the weights being modelled using interval parameters. The dependency within the field is then captured by the basis functions, which describe the spatial nature of dependency, whereas the magnitude of uncertainty is captured by the weights. Field parameters are usually associated to geometric quantities (such as plate thickness), but they can be applied generally whenever multiple uncertain input or output quantities are involved. Both at the input and output side of a numerical analysis, IF can be used for a more realistic description of the estimated uncertainty. At the input side, taking into account dependency reduces overestimation on the output uncertainty bounds. At the output side, it is important that a realistic uncertain set of output quantities is represented as closely as possible without adding conservatism, as this corrupts the results of possible postprocessing or follow-up analysis. The application of IF here provides an important step towards achieving this goal. This paper aims to apply IF to analyse structural Finite Element models with uncertain structural properties. The property of interest in this paper will be the E-modulus. The concept of IF will be used to model spatial dependency within this parameter and will lead to a more accurate estimation of the output uncertainty.