A Stochastic Projection Method for Fluid Flow

Maîetre, Olivier P. Le; Reagan, Matthew T.; Najm, Habib N.; Ghanem, Roger; Knio, Omar M.

doi:10.1006/jcph.2002.7104

Cited by 471 publications

(250 citation statements)

References 34 publications

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“…We develop methods to substantially reduce the cost of evaluating the posterior density, based on a stochastic spectral reformulation of the forward problem. These methods have their roots in uncertainty quantification (UQ) using polynomial chaos (PC) expansions [40,59,21].…”

Section: Xxxxmentioning

confidence: 99%

“…These stochastic finite element approaches have found numerous modeling applications, including transport in porous media [36], and solid [37,38] or structural [39] mechanics. Le Maître et al [59,61] extended these techniques to thermo-fluid systems. Xiu et al [104] used generalized polynomial chaos [103] for uncertainty quantification in fluidstructure interactions and in diffusion problems [102], while Debusschere et al [20] used polynomial chaos to characterize uncertainty in electrochemical microfluid systems.…”

Section: Xxxxmentioning

confidence: 99%

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Computationally efficient Bayesian inference for inverse problems.

Marzouk¹,

Najm²,

Rahn³

2007

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Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problemsrepresenting indirect estimation of model parameters, inputs, or structural componentscan be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field.We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties.We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.3 xxxx Acknowledgements

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Section: Xxxxmentioning

confidence: 99%

Section: Xxxxmentioning

confidence: 99%

Computationally efficient Bayesian inference for inverse problems.

Marzouk¹,

Najm²,

Rahn³

2007

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“…For this purpose, polynomial chaos expansion (PCE) has received much attention over the last two decades (e.g., [2,3,4,5,6,7,8,9]). In computer models in engineering, PCE has been proven useful for the analyses of uncertainty, sensitivity and risk of failure.…”

Section: Introductionmentioning

confidence: 99%

Bayesian sparse polynomial chaos expansion for global sensitivity analysis

Shao

Younès

Fahs

et al. 2017

Computer Methods in Applied Mechanics and Engineering

106

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Polynomial chaos expansions are frequently used by engineers and modellers for uncertainty and sensitivity analyses of computer models. They allow representing the input/output relations of computer models. Usually only a few terms are really relevant in such a representation. It is a challenge to infer the best sparse polynomial chaos expansion of a given model input/output data set. In the present article, sparse polynomial chaos expansions are investigated for global sensitivity analysis of computer model responses. A new Bayesian approach is proposed to perform this task, based on the Kashyap information criterion for model selection. The efficiency of the proposed algorithm is assessed on several benchmarks before applying the algorithm to identify the most relevant inputs of a double-diffusive convection model.

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“…Research areas for the stochastic modeling are: linear elasticity of solids and mechanics [4], plasticity of solids and mechanics [6,7], large deformations [8,9], fluid flow [10,11,12], flow-structure interactions [13,14] and linear convection problems [15]. An open task is the application of the modeling of rubber-like materials, such as natural rubber, which is constitutively represented by an Ogden model and is therefore the focus of this paper.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Stochastic Material Modeling at Large Deformations Considering Parameter Correlations

Penner¹,

Caylak²,

Mahnken³

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. In many engineering applications the material behavior, e.g. hyper-elasticity and plasticity, is described by appropriate mathematical models. However, these become uncertain due to different types of uncertainty such as variation in the manufacturing process, measurement errors and missing or incomplete information on material properties. This contribution presents a framework for nonlinear elastic stochastic material model at large deformations. As a key idea uncertainty of the material is described by parameters, which are modeled as stochastic variables.To this end, 150 specimens for three different rubber materials are experimentally investigated in tensile tests. Based on experimental results 1000 artificial data are generated by aid of an ARMA process [1]. The artificial data are used for parameter identification of an Ogden material model for rubber materials . Furthermore, statistical analysis of material parameters including their correlations is studied. The number of material parameters define the dimension of the stochastic space. Usually, the stochastic material parameters are considered as stochastically independent. However, in our work we consider the dependency including the correlation obtained from experimental data.The hyperelastic stochastic material parameters are expanded with the multivariate PCE. In this context, the stresses depend on stochastic variables. To determine the corresponding PC coefficients for non-independent stochastic material parameters we use a Cholesky decomposition. As a numerical example we consider the static problem for uniaxial tension of the rectangular plate. This structure is investigated in order to represent the experimental setup conditions.

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A Stochastic Projection Method for Fluid Flow

Cited by 471 publications

References 34 publications

Computationally efficient Bayesian inference for inverse problems.

Computationally efficient Bayesian inference for inverse problems.

Bayesian sparse polynomial chaos expansion for global sensitivity analysis

Multidimensional Stochastic Material Modeling at Large Deformations Considering Parameter Correlations

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