A probability‐box approach on uncertain correlation lengths by stochastic finite element method

Dannert, Mona M.; Fau, Amélie; Fleury, Rodolfo M.N.; Broggi, Matteo; Nackenhorst, Udo; Beer, Michael

doi:10.1002/pamm.201800114

Cited by 16 publications

(10 citation statements)

References 4 publications

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“…Considering uncertainty on the governing parameters of a random field, the p-box concept needs to be extended. The resulting framework of imprecise random fields, introduced separately by the authors in [39] and [23], in this case proves to be a valuable tool. The approach is summarized in Section 3.2 and applied in Section 5.…”

Section: Hybrid Approaches To Model Mixed Epistemic and Aleatory Uncertaintiesmentioning

confidence: 99%

“…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: Hybrid Approaches To Model Mixed Epistemic and Aleatory Uncertaintiesmentioning

confidence: 99%

Section: Imprecise Random Fieldsmentioning

confidence: 99%

Imprecise random field analysis for non-linear concrete damage analysis

Dannert

Faes

Fleury

et al. 2021

Mechanical Systems and Signal Processing

Self Cite

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“…In engineering practice, unavoidable uncertainties are of uttermost importance for system reliability assessment. The combination of both aleatory (stochastic) uncertainty and epistemic (lack of knowledge) uncertainty leads to the framework called "mixed uncertainty" or "hybrid uncertainty", and it is ubiquitous in engineering systems [4]. Uncertainties mainly arise from the following aspects: observational uncertainty, model uncertainty and parametric uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Importance measure of probabilistic common cause failures under system hybrid uncertainty based on bayesian network

Beer

et al. 2020

Eksploatacja i Niezawodność – Maintenance and Reliability

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Importance measure of probabIlIstIc common cause faIlures under system hybrId uncertaInty based on bayesIan network oparta na sIecI bayesowskIej mIara ważnoścI probabIlIstycznych uszkodzeń spowodowanych wspólną przyczyną w warunkach nIepewnoścI hybrydowej systemuWhen dealing with modern complex systems, the relationship existing between components can lead to the appearance of various dependencies between component failures, where multiple items of the system fail simultaneously in unpredictable fashions. These probabilistic common cause failures affect greatly the performance of these critical systems. In this paper a novel methodology is developed to quantify the importance of common cause failures when hybrid uncertainties are presented in systems. First, the probabilistic common cause failures are modeled with Bayesian networks and are incorporated into the system exploiting the α factor model. Then, probability-boxes (bound analysis method) are introduced to model the hybrid uncertainties and quantify the effect of uncertainties on system reliability. Furthermore, an extended Birnbaum importance measure is defined to identify the critical common cause failure events and coupling impact factors when uncertainties are expressed by probability-boxes. Finally, the effectiveness of the method is demonstrated through a numerical example.

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“…In the context of imprecise random field analysis, Verhaeghe et al [31] where the first to study the effect of computing with interval-valued correlation lengths in a random field with exponential covariance kernel. Similarly, Dannert et al [32] recently introduced a p-box framework for the propagation of imprecise random fields with interval-valued correlation length where they select samples from the correlation length interval a priori. Gao et al [33] also recently proposed an efficient sampling approach to cope with impreciseness in random field analysis to determine bounds on the relia-bility of structural components under mixtures of stochastic and non-stochastic system inputs.…”

Section: Introductionmentioning

confidence: 99%

Imprecise random field analysis with parametrized kernel functions

Faes

Moens

2019

Mechanical Systems and Signal Processing

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The application of isotropic random fields in engineering analysis requires the definition of their first two central moments, as well as their covariance function.In general, insufficient data are available to make a fully objective crisp estimate on these quantities, and hence, subjectivity enters implicitly into the analysis.The framework of imprecise probabilities is gaining popularity in this context, as it allows to explicitly separate the epistemic uncertainty, present due to data insufficiency, from the aleatory nature of the random parameters. However, an approach that is capable of handling imprecision in the complete definition of the imprecise random field is lacking to date. This paper proposes a framework for imprecise random field analysis with parametrized covariance functions. As such, the functional form of the covariance function is assumed to be known deterministically, whereas the governing parameters are subjected to imprecision.First, a comprehensive analysis of the effect of imprecise random fields, given imprecision on both the mean and auto-covariance structure, is presented. It is shown that the discretization of an imprecise random field, given interval-valued correlation lengths cannot be performed using interval arithmetical procedures as the resulting basis functions are in that case no longer a complete basis on L 2 . Therefore, an iterative procedure is proposed where the bounds on the imprecise random field basis are determined via an optimization procedure. This

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A probability‐box approach on uncertain correlation lengths by stochastic finite element method

Abstract: In order to regard mixed aleatory and epistemically uncertain random fields within stochastic finite element method, a probability box approach using stochastic collocation method is introduced. The influence of an interval-valued correlation length on the output is investigated.

Cited by 16 publications

References 4 publications

Imprecise random field analysis for non-linear concrete damage analysis

Imprecise random field analysis for non-linear concrete damage analysis

Importance measure of probabilistic common cause failures under system hybrid uncertainty based on bayesian network

Imprecise random field analysis with parametrized kernel functions

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