Analysis of polymorphic data uncertainties in engineering applications

Abstract

In this contribution, several case studies with data uncertainties are presented which have been performed in individual projects as part of the DFG (German Research Foundation) Priority Programme SPP 1886 “Polymorphic uncertainty modelling for the numerical design of structures.” In all case studies numerical models with uncertainties are derived from engineering problems describing concepts for handling and incorporating measurement data, either of model input parameters or of the system response. The first case study deals with polymorphic uncertain data based on computer tomographic scans with respect to air voids which are acquired, simplified and integrated in numerical models of adhesive bonds. In the second case study, the variation sensitivity analysis is presented to provide suitable prior knowledge for numerical soil analyses, for example, in order to reduce required input data. The uncertainty in friction processes is treated in case study 3 whereby measurement data are used in data driven methods to improve the numerical predictions. In case study 4, the failure behavior of die‐cast window hinges, which is affected by an uncertain initial pore distribution, is investigated by means of a Markov chain approach. In the last two case studies, mathematical methods of statistical inference and updating algorithms for uncertainty models are shown. Due to the heterogeneous spectrum of problems, a generalized strategy for data modeling, acquisition, and assimilation is developed and applied on each case study.

Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains

“…Fig. 1 Computed tomography scan of a Henkel beam taken from [24]. Material imperfections are noticeable but the present resolution does not reveal the exact shapes of the imperfections…”

“…1 shows a computed tomography scan of an imperfect adhesive bond within a Henkel beam, cf. [24]. Apparently, the image is noisy, blurred, pixelated and exhibits artefacts.…”

Polymorphic Uncertainty Quantification of Computational Soil and Earth Structure Simulations via the Variational Sensitivity Analysis

“…To overcome this drawback, a new strategy based on the Variational Sensitivity Analysis (VSA) is presented. The Global Impact Analysis (GIA) [8] quantifies how sensitive the solution state is to a global change of a material input parameter m. The Local Impact Analysis (LIA) [9] quantifies how much a change of material input parameter m in an arbitrary sub-domain affects the output quantities and thus the spatial dependence. The underlying physical model for the coupled multi-phase description is the Theory of Porous Media (TPM) [5,6], which provides a thermodynamically consistent theory within the Finite Element Method (FEM).…”

“…This requirement is used for the development of the material sensitivities and results in the linear approximation of the current equilibrium state. The Global Impact Analysis (GIA) [8] quantifies how sensitive the solution state is to a global change of a material input parameter m. The Local Impact Analysis (LIA) [9] quantifies how much a change of material input parameter m in an arbitrary sub-domain affects the output quantities and thus the spatial dependence. Herewith, two essential questions can be answered in advance: 'Which parameters should be investigated (GIA)?'…”

Towards an interactive crash simulation

“…2.1 with the help of a probability density functions based on the experts/designer knowledge. Note that one could have also used intervals instead [35,129,130]. As the finite element model G is deterministic, its inputs are only samples of the parameter set, meaning that each change in the input would lead to a corresponding new expensive simulation.…”