Identification and quantification of multivariate interval uncertainty in finite element models

Abstract

The objective of this work is to develop and validate a methodology for the identification and quantification of multivariate interval uncertainty in finite element models. The principal idea is to find a solution to an inverse problem, where the variability on the output side of the model is known from measurement data, but the multivariate uncertainty on the input parameters is unknown. For this purpose, the uncertain simulation results set created by propagating interval uncertainty through the model is represented by its convex hull. The same concept is used to model the uncertainty in the measurements. A metric to describe the discrepancy between these convex hulls is defined based on the difference between their volumes and their mutual intersection. By minimisation of this metric, the interval uncertainty on the input side of the model is identified. It is further shown how the procedure can be optimized with respect to output quantity selection. Validation of the methodology is done using simulated measurement data in two case studies. Numerically exact identification of multiple, coupled parameters having interval uncertainty is possible following the proposed methodology. Furthermore, the robustness of the method with respect to the analysts initial estimate of the input uncertainty is illustrated. The method presented in this work in se is generic, but for the examples in this paper, it is specifically applied to dynamic models, using eigenfrequencies as output quantities, as

Identification and Quantification of Multivariate Possibilistic Manufacturing Uncertainty in Dynamic Numerical Models

“…However, in order to apply these powerfull techniques, a realistic assessment of the uncertainty has to be made, based on measurement data. In this context, the authors presented a novel methodology for the identification and quantification of multivariate interval uncertainty in FE Models [3,2]. However, the application of this novel methodology to high-dimensional datasets still presents a challenge.…”

“…This basis is then used to reduce the dimensionality of both the measurement data as the result of the interval FE model. The quantification of the multivariate interval uncertainty, as presented by the authors in [3,2], is then performed using projections of the datasets on subspaces of this orthogonal basis in order to reduce the computational burden of the analysis. The method was illustrated on the AIRMOD test structure, which proved to be a highly challenging example due to the high dimensionality at the input side of the model.…”

“…This section explains the novel methodology for the identification and quantification of multivariate interval uncertainty, as presented by the authors in [2,3] and V s , are hereto computed. All convex hull computations are performed using the QHULL library, which makes use of the Quickhull algorithm [1].…”

“…This high dimensional data set is subsequently reduced by projecting it on a lower-dimensional basis. The identification of the interval uncertainty, based on the method presented in [3,2], is then performed using well-defined projections of the measurement data set in this lower-dimensional basis. The DLR AIRMOD structure is a scaled replica of the GARTEUR SM-AG19 benchmark.…”

“…The authors proposed in this context a generic methodology for the identification of multivariate interval uncertainty [3,2], based on the computation of the convex hulls over the computed realisations of the input non-determinism and the set of repeated measurement data. However the promising results obtained on simple academic cases, no validation of the method was performed on a model having a realistic amount of degrees of freedom.…”