A Non-Intrusive Polynomial Chaos Method For Uncertainty Propagation in CFD Simulations

Hosder, Serhat; Pérez, Rafael; Walters, Robert W.

doi:10.2514/6.2006-891

Cited by 250 publications

(187 citation statements)

References 12 publications

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“…To overcome such difficulties, non-intrusive polynomial chaos (NIPC) approaches have been developed for efficient uncertainty quantification. There are two major methodologies in NIPC, sampling-based approaches [13][14][15] and quadrature-based approaches. 13,16) In both methodologies, the expanded polynomial coefficients are determined through sampling or numerical integration without any change in the deterministic high-fidelity CFD simulation code.…”

Section: Introductionmentioning

confidence: 99%

“…This approach is often referred to as an inexpensive Monte-Carlo simulation (IMCS). [7][8][9][10] The polynomial chaos (PC) method [11][12][13][14][15][16] is another positive approach to model and propagate uncertainty in computational simulations. In the PC method, uncertain parameters or variables are expanded to include random variables by utilizing orthogonal polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…Uncertainty quantification is being watched with keen interest these days [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] since high-fidelity computational fluid dynamics (CFD) simulations typically assume perfect knowledge of all parameters. In reality, however, there is much uncertainty due to manufacturing tolerances, in-service wear-and-tear, approximate modeling parameters and so on.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Drag Analysis via Polynomial Chaos Uncertainty Quantification

Yamazaki

2015

Trans. Japan Soc. Aero. S Sci.

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In this paper, uncertainty quantification approaches are applied to an aerodynamic uncertainty quantification problem with a far-field drag breakdown approach. Two uncertainty quantification approaches, a non-intrusive polynomial chaos approach and an inexpensive Monte-Carlo simulation approach on a response surface model are compared and investigated for more advanced aerodynamic uncertainty quantification. Using the drag breakdown approach, total drag of a body can be decomposed into three physical and one unphysical drag components: wave, viscous, induced and spurious drag components. The drag source distribution can also be visualized on the flowfield using this approach. An uncertainty quantification problem of two-dimensional airfoil with four uncertain input variables is analyzed with the drag breakdown approach to extract more aerodynamic design information about its uncertainty propagation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Drag Analysis via Polynomial Chaos Uncertainty Quantification

Yamazaki

2015

Trans. Japan Soc. Aero. S Sci.

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“…Related techniques are boundary perturbation [26], Lagrangian approach [1] and isoparametric mapping [5]. Other techniques dealing with geometric uncertainty include polynomial chaos with remeshing of geometry [8,9] as well as chaos collocation methods with fictious domains [3,17].…”

Section: Introductionmentioning

confidence: 99%

The effect of uncertain geometries on advection–diffusion of scalar quantities

Wahlsten

Nordström

2017

Bit Numer Math

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The two dimensional advection-diffusion equation in a stochastically varying geometry is considered. The varying domain is transformed into a fixed one and the numerical solution is computed using a high-order finite difference formulation on summation-by-parts form with weakly imposed boundary conditions. Statistics of the solution are computed non-intrusively using quadrature rules given by the probability density function of the random variable. As a quality control, we prove that the continuous problem is strongly well-posed, that the semi-discrete problem is strongly stable and verify the accuracy of the scheme. The technique is applied to a heat transfer problem in incompressible flow. Statistical properties such as confidence intervals and variance of the solution in terms of two functionals are computed and discussed. We show that there is a decreasing sensitivity to geometric uncertainty as we gradually lower the frequency and amplitude of the randomness. The results are less sensitive to variations in the correlation length of the geometry.

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“…Puvkov et al [6] proposed that if the Wiener-Askey polynomial chaos expansion is chosen according to the probability distribution of the random input, then it can be used to construct simple algorithms for the statistical analysis of dynamic systems. Several PC expansion-based methods have been proposed including nonintrusive polynomial chaos expansions [7], the stochastic response surface method [8], and the deterministic equivalent modeling method (DEMM) [6,9,10], also known as the probabilistic collocation method (PCM). Controllers for processes with stochastic uncertainties can be designed based on the statistical characteristics of the response.…”

Section: Introductionmentioning

confidence: 99%

Robust PID controller design for processes with stochastic parametric uncertainties

Duong

Lee

2012

Journal of Process Control

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a b s t r a c tThe stability and performance of a system can be inferred from the evolution of statistical characteristics of the system's states. Wiener's polynomial chaos can provide an efficient framework for the statistical analysis of dynamical systems, computationally far superior to Monte Carlo simulations. This work proposes a new method of robust PID controller design based on polynomial chaos for processes with stochastic parametric uncertainties. The proposed method can greatly reduce computation time and can also efficiently handle both nominal and robust performance against stochastic uncertainties by solving a simple optimization problem. Simulation comparison with other methods demonstrated the effectiveness of the proposed design method.

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A Non-Intrusive Polynomial Chaos Method For Uncertainty Propagation in CFD Simulations

Cited by 250 publications

References 12 publications

Stochastic Drag Analysis via Polynomial Chaos Uncertainty Quantification

Stochastic Drag Analysis via Polynomial Chaos Uncertainty Quantification

The effect of uncertain geometries on advection–diffusion of scalar quantities

Robust PID controller design for processes with stochastic parametric uncertainties

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