A Bayesian approach for quantification of model uncertainty

Park, Inseok; Amarchinta, Hemanth K.; Grandhi, Ramana V.

doi:10.1016/j.ress.2010.02.015

Cited by 116 publications

(53 citation statements)

References 20 publications

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“…Assuming there are N theoretical models M k ; k ¼ 1; Á Á Á N, the post-conditional probability of Model M k with experimental data y ¼ ½y 1 ; Á Á Á ; y L can be expressed as 10)…”

Section: Bayesian Posteriori Estimation Theorymentioning

confidence: 99%

“…Hence, its mean value and variance can be calculated based on the posterior probability of each theoretical model uncertainty. The expression is written as follows 10)…”

Section: Bayesian Posteriori Estimation Theorymentioning

confidence: 99%

“…Until now, the major available method for model uncertainty quantification is based on Bayesian Posteriori Estimation. 10,11) It is a good tool to quantify the probability distribution of model uncertainty in a model set, based on known experimental results. It can tackle with several theoretical models simultaneously while the mentioned MC and other methods cannot.…”

Section: Introductionmentioning

confidence: 99%

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Aeroservoelastic Model Modification and Uncertainty Quantification with Bayesian Posteriori Estimation

Dai

Yang

2015

Trans. Japan Soc. Aero. S Sci.

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A half model of a scaled aircraft is designed and tested in a wind tunnel. Based on the step-sinusoidal swept frequency test, the aeroservoelastic frequency response function is measured and compared with the predictions of a theoretical model. According to the discrepancies, the key uncertainty factors such as actuator model uncertainty, aileron aerodynamic uncertainty and structural damping uncertainty are investigated. Therefore, the original theoretical model is modified and updated with these model uncertainties considered, respectively. Motivated by the still existing discrepancies of experimental data and comprehensive updated theoretical outcomes, we take the above aeroservoelastic model uncertainty as an aleatory probabilistic one. Hence, the probability of each model uncertainty is quantified by Bayesian Posteriori Estimation theory. In addition, the uncertainty probabilities of aeroservoelastic response and aeroservoelastic stability boundary are predicted. The aeroservoelastic uncertainty quantification methodology with model uncertainty is validated by comparing the probabilistic predictions of the theoretical model set with experimental data. Taking model uncertainty into consideration, the present method is able to predict the probabilistic aeroservoelastic stability bounds and response as well. Results indicate that the updated comprehensive model is the best theoretical model with the highest posterior probability. In addition, the unsteady aerodynamics due to aileron deflection has the most significant effect on aeroservoelastic response.

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“…Assuming there are N theoretical models M k ; k ¼ 1; Á Á Á N, the post-conditional probability of Model M k with experimental data y ¼ ½y 1 ; Á Á Á ; y L can be expressed as 10)…”

Section: Bayesian Posteriori Estimation Theorymentioning

confidence: 99%

“…Hence, its mean value and variance can be calculated based on the posterior probability of each theoretical model uncertainty. The expression is written as follows 10)…”

Section: Bayesian Posteriori Estimation Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Aeroservoelastic Model Modification and Uncertainty Quantification with Bayesian Posteriori Estimation

Dai

Yang

2015

Trans. Japan Soc. Aero. S Sci.

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show abstract

“…In this approach only uncertainties due to the model choice are considered. The expected value and the variance of the prediction are given in [2] as…”

Section: Estimation Of Model Framework Uncertaintymentioning

confidence: 99%

“…In the recent years some more or less empirical estimates of model uncertainty have been proposed [3,4,2], which were motivated to find the best model out of a given set of plausible models, which is more appropriate for the prediction of an unknown response. For model selection based on a known response in terms of measurements, Bayesian methods have become very popular in the recent years [5,6].…”

Section: Introductionmentioning

confidence: 99%

Assessment of structural simulation models by estimating uncertainties due to model selection and model simplification

Most

2011

Computers & Structures

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Application of uncertainty quantification techniques in the framework of process safety studies: Advanced dispersion simulations

Bellegoni,

Marroni,

Mariotti

et al. 2024

Can J Chem Eng

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In the framework of process safety studies, consequence assessment of accidental scenarios is a crucial step affecting the eventual risk profile associated with the facilities under analysis. Conventional models used for consequence assessment are based on integral models, and may not be adequate to cope with the dynamic evolution of accidental scenarios and their three‐dimensional features. On the other hand, consequence assessment models based on computational fluid dynamics (CFD) approaches are promising to cope with complex scenarios and environments, but setting the simulation introduces relevant uncertainties associated with both the input data, assumptions, and with the modelling of physical effects involved. In the present study, uncertainty quantification (UQ) techniques are applied to support advanced safety studies based on CFD simulations of hazardous gas dispersion. Firstly, the accidental scenarios are characterized by defining release scenarios and conditions and quantifying source terms using integral models. At the same time, input meteorological data are gathered. This enables the development of high‐fidelity CFD simulations of gas dispersion based on different input sets and eventually the implementation of UQ techniques. The generalized polynomial chaos (gPC) expansion is employed to obtain hazardous gas concentration based on the variation of wind direction and speed. The present method is applied for the analysis of a real plant featuring a complex layout. The results show the advantages of the present approach by quantifying the influence of meteorological conditions and providing indications for supporting the development of protection systems and emergency measures.

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A Bayesian approach for quantification of model uncertainty

Cited by 116 publications

References 20 publications

Aeroservoelastic Model Modification and Uncertainty Quantification with Bayesian Posteriori Estimation

Aeroservoelastic Model Modification and Uncertainty Quantification with Bayesian Posteriori Estimation

Assessment of structural simulation models by estimating uncertainties due to model selection and model simplification

Application of uncertainty quantification techniques in the framework of process safety studies: Advanced dispersion simulations

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