Robust uncertainty quantification in structural dynamics under scarse experimental modal data: A Bayesian-interval approach

Imholz, Maurice; Faes, Matthias; Vandepitte, Dirk; Moens, David

doi:10.1016/j.jsv.2019.114983

Cited by 27 publications

(18 citation statements)

References 19 publications

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“…In case very few data-points are available, estimating the bounds of the support of the pbox might be the only option for an analyst. This estimation can for instance be based on worst-case likelihood estimation (Crespo et al, 2019), potentially in combination with Bayesian approaches (Imholz et al, 2020). Scenario optimization (Campi et al, 2018) can also be used in this context to obtain bounds with a proven degree of robustness under mild assumptions.…”

Section: Distribution Support Estimationmentioning

confidence: 99%

Engineering analysis with probability boxes: A review on computational methods

et al. 2021

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The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecise probabilities, as well as allow for an intuitive visualisation. In essence, p-boxes are defined via lower and upper bounds on the cumulative distribution function of a random variable whose exact probability distribution is unknown. However, the propagation of p-boxes on model inputs towards bounds on probabilistic measures describing the uncertainty on the model responses is numerically still very demanding, and hence is subject of intensive research. In order to provide an overview on the available methods, this paper gives a state-of-the art review for the modelling and propagation of p-boxes with a special focus on structural reliability analysis.

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Section: Distribution Support Estimationmentioning

confidence: 99%

Engineering analysis with probability boxes: A review on computational methods

et al. 2021

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“…A first, naive, approach is to take the extremes of a set of direct measurements as the bounds. These bounds can be made more 'robust' using a recently introduced Bayesian approach [22]. In case direct measurement of the uncertain quantities is not feasible, the bounds can also be estimated via an inverse approach based on comparing convex sets of model predictions and measurement data [21,23].…”

Section: Interval Field Analysismentioning

confidence: 99%

Inhomogeneous interval fields based on scaled inverse distance weighting interpolation

Mierlo

Faes

Moens

2021

Computer Methods in Applied Mechanics and Engineering

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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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Robust uncertainty quantification in structural dynamics under scarse experimental modal data: A Bayesian-interval approach

Cited by 27 publications

References 19 publications

Engineering analysis with probability boxes: A review on computational methods

Engineering analysis with probability boxes: A review on computational methods

Inhomogeneous interval fields based on scaled inverse distance weighting interpolation

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

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