Development of fuzzy probability based random fields for the numerical structural design

Schietzold, F. Niklas; Schmidt, Albrecht; Dannert, Mona M.; Fau, Amélie; Fleury, R.M.N.; Graf, Wolfgang; Kaliske, Michael; Könke, Carsten; Lahmer, Tom; Nackenhorst, Udo

doi:10.1002/gamm.201900004

Cited by 18 publications

(21 citation statements)

References 19 publications

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“…However, in a general engineering context, describing the quantities that are required to represent a random field crisply is often non-trivial or even impossible, given the omnipresent constraints on data availability. This observation led to the so-called concept of imprecise random fields (see e.g., [40,39,20,23]), which form a generalization of p-boxes towards tempospatially uncertain quantities [4].…”

Section: Imprecise Random Fieldsmentioning

confidence: 99%

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Imprecise random field analysis for non-linear concrete damage analysis

Dannert

Faes

Fleury

et al. 2021

Mechanical Systems and Signal Processing

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Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding random field is discretized by Karhunen-Loève expansion. In a first study, the effect of the series truncation is discussed as well as the resulting variance error on the probability box (p-box) that represents uncertainty on the damage in a concrete beam as a result of the imprecise random field. It is shown that a certain awareness for the influence of the truncation order on the local field variance is needed when the series is truncated according to a fixed mean variance error.In the following case study, the main investigation is on the propagation of imprecise random fields in the context of non-linear finite element problems, i.e. quasi-brittle damage of a four-point bended concrete beam. The global and local damage as the quantities of interest are described by a p-box. The influence of several imprecise random field input parameters to the resulting p-boxes is studied. Furthermore, it is examined whether correlation length values located within the interval, so-called intermediate values, affect the p-box bounds. It is shown that, from the engineering point of view, a pure vertex analysis of the correlation length intervals is sufficient to determine the p-box in this context.

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Section: Imprecise Random Fieldsmentioning

confidence: 99%

“…This special mixed uncertain properties are then called imprecise random fields and have been investigated in several settings. In terms of material parameters, the mean value and standard deviation are considered interval valued in [19], while interval and fuzzy valued correlation lengths are explored by [20].…”

Section: Introductionmentioning

confidence: 99%

Imprecise random field analysis for non-linear concrete damage analysis

Dannert

Faes

Fleury

et al. 2021

Mechanical Systems and Signal Processing

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“…If one or several parameters cannot be determined precisely, the classically aleatory random field includes also epistemic uncertainties, e.g. by interval or fuzzy valued parameters [10]. To avoid further assumptions on the fuzziness, this work considers epistemic parameters to be interval valued.…”

Section: Probability Box Approachmentioning

confidence: 99%

“…The random field parameters that cannot be determined precisely, e.g. the correlation length, can be described as interval [3] or fuzzy valued [10]. Propagating such imprecise random fields through an FE model, the quantity of interest is described by a p-box, meaning a lower and upper bound instead of a crisp distribution.…”

Section: Introductionmentioning

confidence: 99%

Limit Representations of Imprecise Random Fields

Dannert¹,

Häufler²,

Nackenhorst³

2021

4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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In order to describe spatially uncertain parameters by random fields, the underlying autocorrelation structure in engineering structures is usually not known.. The idea of imprecise random fields is to acknowledge this lack of knowledge by adding epistemic uncertainties. Within this contribution the influence of the correlation length is studied. In particular, it is shown that there exist bounds that limit the case of having no idea at all. This "absolutely no idea p-box" is defined by white noise and the random variable corresponding to the mean value and standard deviation of the imprecise random field. By this, the limits of having "absolutely no idea" can be described without the need of Karhunen-Loève expansion and random field propagation. Then, at least for linear problems, every response in between can be estimated by linear interpolation without any need for sampling.

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“…Interval probability-based random fields are introduced exemplary for polymorphic uncertainty models. Further models (like fuzzy probability-based random variables) can be found in [6].…”

Section: Polymorphic Uncertainty Modelsmentioning

confidence: 99%

Efficient domain decomposition based reliability analysis for polymorphic uncertain material parameters

Schmidt

Lahmer

2021

Proc Appl Math & Mech

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Realistic uncertainty description incorporating aleatoric and epistemic uncertainties can be described within the framework of polymorphic uncertainty, which is computationally demanding. Utilizing a domain decomposition approach for random field based uncertainty models the proposed level‐based sampling method can reduce these computational costs significantly and shows good agreement with a standard sampling technique. While 2‐level configurations tend to get unstable with decreasing sampling density 3‐level setups show encouraging results for the investigated reliability analysis of a structural unit square.

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Development of fuzzy probability based random fields for the numerical structural design

Cited by 18 publications

References 19 publications

Imprecise random field analysis for non-linear concrete damage analysis

Imprecise random field analysis for non-linear concrete damage analysis

Limit Representations of Imprecise Random Fields

Efficient domain decomposition based reliability analysis for polymorphic uncertain material parameters

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