Probabilistic bounding analysis in the Quantification of Margins and Uncertainties

Sentz, Kari; Ferson, Scott

doi:10.1016/j.ress.2011.02.014

Cited by 32 publications

(18 citation statements)

References 46 publications

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“…In addition to the traditional probabilistic description of uncertainties, other approaches, such as interval analysis [30] and probability bounds analysis [16,42], have also been used to describe imprecise knowledge associated with uncertainties. These alternative approaches for defining and combining uncertainties are conservative [20].…”

Section: Elements Of Error-domain Model Falsification Is Presented Inmentioning

confidence: 99%

“…This new uncertainty distribution is a hybrid approach combining traditional probabilistic representation of uncertainties with other approaches such as interval analysis [30] and probability bounds analysis [16,42]. It overcomes the limitations of traditional probabilistic representations that may be too deterministic and other representations that may be over-conservative for the purpose of structural identification.…”

Section: Extended Uniform Distributionmentioning

confidence: 99%

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Hybrid probabilities and error-domain structural identification using ambient vibration monitoring

Goulet

Michel²,

Smith

2013

Mechanical Systems and Signal Processing

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For the assessment of structural behavior, many approaches are available to compare model predictions with measurements. However, few approaches include uncertainties along with dependencies associated with models and observations. In this paper, an error-domain structural identification approach is proposed using ambient vibration monitoring (AVM) as the input. This approach is based on the principle that in science, data cannot truly validate an hypothesis, it can only be used to falsity it. Error-domain model falsification generates a space of possible model instances (combination of parameters), obtains predictions for each of them and then, rejects instances that have unlikely differences (residuals) between predictions and measurements. Models are filtered in a two step process. Firstly a comparison of mode shapes based on MAC criterion ensures that the same modes are compared. Secondly, the frequencies from each model instance are compared with the measurements. The instances for which the difference between the predicted and measured value lie outside threshold bounds are discarded. In order to include "uncertainty of uncertainty" in the identification process, a hybrid probability scheme is also presented. The approach is used for the identification of the Langensand Bridge in Switzerland. It is used to falsify the hypothesis that the bridge was behaving as designed when subjected to ambient vibration inputs, before opening to the traffic. Such small amplitudes may be affected by lowlevel bearing-device friction. This inadvertently increased the apparent stiffness of the structure by 17%. This observation supports the premiss that ambient vibration surveys

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Section: Elements Of Error-domain Model Falsification Is Presented Inmentioning

confidence: 99%

Section: Extended Uniform Distributionmentioning

confidence: 99%

Hybrid probabilities and error-domain structural identification using ambient vibration monitoring

Goulet

Michel²,

Smith

2013

Mechanical Systems and Signal Processing

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“…In [103] and [104] probability bounds analysis is applied to reliability assessment for a dike revetment and a nite-element structural analysis respectively, and the results are compared to traditional probabilistic methods with Monte Carlo simulation. In these examples, the risks can be underestimated with traditional methods whereas probability bounding is able to cover the actual risk range comprehensively, and often with less overall computational eort than Monte Carlo methods.…”

Section: Engineering Application Eldsmentioning

confidence: 99%

“…Probability bounds analysis has been used in uncertainty computations in many contexts including series system failure analysis and system reliability [140], quantication of margins of uncertainty [103], nite-element structural [172,112,173,104], dierential equations of chemical reactions [174], engineering design [123,175], validation [176,113], pharmacokinetics [177], human health and ecological risk assessments at Superfund sites [178,179,180], and even global circulation models [181]. The Wikipedia page for probability bounds analysis lists over two dozen applications of the method to various engineering problems.…”

Section: Probability Bounds Analysis With P-boxesmentioning

confidence: 99%

Imprecise probabilities in engineering analyses

Beer

Ferson

Kreinovich

2013

Mechanical Systems and Signal Processing

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384

193

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Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantication to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantication is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sucient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical dierences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved.This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another.

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“…Due to the necessity and importance of treating the aleatory and epistemic uncertainties properly with corresponding mathematical methods rather than simply using the traditional probabilistic methods to treat all the uncertainties as random ones under strong assumptions (Der Kiureghian and Ditlevsen 2009), there emerges increasing literature in recent years to address the reliability analysis problems under both aleatory and epistemic uncertainties, e.g. Fuzzy set theory (Zhang and Huang 2010;Li et al 2014;He et al 2015), random set theory (Oberguggenberger 2015) and probabilistic bounding analysis (Sentz and Ferson 2011), combined probabilistic and interval analysis method (Jiang et al 2013), combined probabilistic and evidence theory method (Du 2008;Eldred et al 2011;Yao et al 2013b), and other numerical approaches such as doubleloop Monte-Carlo Simulation (MCS) (Du et al 2009), perturbation based method (Gao et al 2010(Gao et al , 2011, encapsulation based method (Jakeman et al 2010;Chen et al 2013), families of Johnson distributions based probabilistic method (Urbina et al 2011;Zaman et al 2011), etc. Among these researches, one of the widely used methods is to model the epistemic uncertainties with intervals and generally the interval bounds are fixed.…”

Section: Introductionmentioning

confidence: 99%

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

Chen

Yao

Zhao

et al. 2016

Struct Multidisc Optim

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The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing welldeveloped and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.

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Probabilistic bounding analysis in the Quantification of Margins and Uncertainties

Cited by 32 publications

References 46 publications

Hybrid probabilities and error-domain structural identification using ambient vibration monitoring

Hybrid probabilities and error-domain structural identification using ambient vibration monitoring

Imprecise probabilities in engineering analyses

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

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