Derivation of an Input Interval Field Decomposition Based on Expert Knowledge Using Locally Defined Basis Functions

Imholz, Maurice; Vandepitte, Dirk; Moens, David

doi:10.7712/120215.4290.583

Cited by 16 publications

(21 citation statements)

References 19 publications

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“…Note that any other data‐enclosing convex approximation (using for instance set‐theoretical concepts), will always include more conservatism in the analysis. This can for instance be warranted to account for data scarcity as presented in …”

Section: Computing With Dependent Intervalsmentioning

confidence: 99%

On auto‐ and cross‐interdependence in interval field finite element analysis

Faes

Moens

2020

Numerical Meth Engineering

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Summary This paper discusses the concepts of auto‐ and cross‐interdependence in interval field finite element analysis. In classic interval analysis, independent intervals are used to construct hyper‐rectangular input spaces that correspond to the bounded uncertainty that is present on some model parameters. This is a direct result from the inability of modeling interdependence. Such assumption of complete independence might prove in some cases to be highly over‐conservative. A first example is the modeling of spatial uncertainty, where the interdependence is governed by allowable spatial gradients of field realizations. Secondly, interdependence can also occur in case uncertainty in several structural quantities has the same root cause (eg, the manufacturing process). Recent work by the authors introduced concepts for modeling dependence between intervals in a spatial and multivariate context. However, it is unclear how an analyst has to deal with multiple quantities that have a spatial uncertainty component and are furthermore interdependent. This paper presents an approach to link multiple interval fields using recently introduced convex hull pair constructions and inverse distance weighting interpolation. Two case studies to illustrate the new methodology are included, proving the flexibility of the methodology in the modeling of auto‐ and cross‐interdependence between multiple interval scalars and/or interval fields.

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Section: Computing With Dependent Intervalsmentioning

confidence: 99%

On auto‐ and cross‐interdependence in interval field finite element analysis

Faes

Moens

2020

Numerical Meth Engineering

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“…It should be noted that other distance-based interpolation functions, such as radial base functions are equivalently applicable as base vectors, as long as they maintain the decoupling of the interval scalars. Also other principles for interval field decomposition can be equally applied in the framework of the identification method presented in this work, such as the Local Interval Field Decomposition technique as developed by Imholz et al [39], as the presented procedure is independent of the parameters of ψ i (r).…”

Section: Example 2: Cantilever Beam Casementioning

confidence: 99%

Identification and quantification of multivariate interval uncertainty in finite element models

Faes

Cerneels

Vandepitte

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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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

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“…For the modelling of the uncertainty on the density, we use an interval representation introduced by the authors in [20], which includes the spatial dependency of the density by setting bounds on the maximal gradient of the density. The general definition is given in eq.…”

Section: Spatial Variabilitymentioning

confidence: 99%

Modelling of Material Parameter Uncertainty of Resonance Wood Used in Violins Using the Interval Field

Imholz¹,

Vandepitte²,

Moens³

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. The interval field method can be used to model spatial uncertainty in finite element models. When analysing spatial uncertainty, dependency is an important quantity to consider, as it is physically implausible to assume a quantity is independent in locations that are close to each other. The interval field method was introduced to join this concept of dependency with classical interval analysis, omitting the need to define probability distributions. This paper will apply the theory of interval field (IF) to the dynamical properties of a violin top plate, with uncertain stiffness and density.

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Derivation of an Input Interval Field Decomposition Based on Expert Knowledge Using Locally Defined Basis Functions

Cited by 16 publications

References 19 publications

On auto‐ and cross‐interdependence in interval field finite element analysis

On auto‐ and cross‐interdependence in interval field finite element analysis

Identification and quantification of multivariate interval uncertainty in finite element models

Modelling of Material Parameter Uncertainty of Resonance Wood Used in Violins Using the Interval Field

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